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Author Topic: [Discussion] DominionStrategy Qualifier for 2012 US National Championships  (Read 24486 times)

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theory

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Please leave feedback for the tournament here.
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antony

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+2

Does "American" mean American nationality or just living in the US?
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theory

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+2

I believe it is people who live in the US, but I will clarify.
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popsofctown

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Whats the date? I still can't find it :/
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nightdance

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I signed up without looking at the time and I actually cannot make it tomorrow. Can you remove me from the list for tomorrow? Thanks.
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theory

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Whats the date? I still can't find it :/
The date for the US Nationals?  July 14.
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ednever

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Theory: are you still running a round of the tournament tomorrow? I can't find anything in the forum. Did I miss something?

Ed
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zxcvbn2

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Ed:
Look at the front page. Here: dominionstrategy.com
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popsofctown

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I suffered from my habit of ignoring the front page as well.
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HiWay2Hello

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Question:

If only three people in a qualifying pod show up, how is seating order determined for the fourth game?
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theory

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That is an excellent question to which I do not have a good answer.  I would suggest the standard Dominion rule, which is the person to the left of the last person that won goes first, and rotate around from there.
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HiWay2Hello

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Ok, seems reasonable enough!
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zxcvbn2

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Re: DominionStrategy Qualifying Day Results
« Reply #12 on: June 24, 2012, 05:34:32 pm »
+2

I'm really, really sorry for beating this dead horse but there really needs to be a point system here. It is not really close to fair, with some people playing four 3p games (more wins available per player each match) and some shared wins resulting in more wins per player per match. I know it's really too late to change anything, and now that we've started I definitely wouldn't advocate changing anything now that we've started, but this is not close to fair.

/endswhining
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Stringer Bell

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #13 on: June 24, 2012, 05:38:18 pm »
0

I'm really, really sorry for beating this dead horse but there really needs to be a point system here. It is not really close to fair, with some people playing four 3p games (more wins available per player each match) and some shared wins resulting in more wins per player per match. I know it's really too late to change anything, and now that we've started I definitely wouldn't advocate changing anything now that we've started, but this is not close to fair.

/endswhining

It is a very strange system, it would have been much easier to assign points based on finish in each game, like so many other tournaments do. Give 4 points to the winner, 3 points to second, and so on. In the case of a tie, like we had in the pod I was in, the two tied for first place would each get 3.5 points, and the two tied for third would each get 1.5 points. If you want to put more weight on winning the match, give 5 points to the winner, and 3, 2, and 1 to the rest.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #14 on: June 24, 2012, 05:57:11 pm »
0

I'm really, really sorry for beating this dead horse but there really needs to be a point system here. It is not really close to fair, with some people playing four 3p games (more wins available per player each match) and some shared wins resulting in more wins per player per match. I know it's really too late to change anything, and now that we've started I definitely wouldn't advocate changing anything now that we've started, but this is not close to fair.

/endswhining
How would it have changed the results so far?  I don't think it's too late to change.

I think it's going to be fundamentally unfair no matter what, when you have both 4p and 3p games.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #15 on: June 24, 2012, 06:04:11 pm »
0

I'm really, really sorry for beating this dead horse but there really needs to be a point system here. It is not really close to fair, with some people playing four 3p games (more wins available per player each match) and some shared wins resulting in more wins per player per match. I know it's really too late to change anything, and now that we've started I definitely wouldn't advocate changing anything now that we've started, but this is not close to fair.

/endswhining
How would it have changed the results so far?  I don't think it's too late to change.

I think it's going to be fundamentally unfair no matter what, when you have both 4p and 3p games.
It IS too late to change. I definitely would have played differently in my third game if the tournament were structured differently, and my best guess would be that I get 2nd there rather than 4th. I probably don't qualify anyway, but the point is you play differently. There's one of the other games where I would have ended it whilst in second, and I end up getting second anyway, but again, the point is that you play differently.

Of course, I agree that having 3s mixed with 4s is going to make intrinsically unfair, and moreso than this effect.

theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #16 on: June 24, 2012, 06:06:56 pm »
+1

No, what I mean is, if the current system is unfair, we can change it for the next days.  Obviously I will not change retroactively.

That having been said, yeah, the go-for-the-win or settle-for-second is a deep philosophical problem, and we have to pick a side.  I think a points system would misleadingly suggest that settling for seconds can actually have you advance: even under most point systems, you'll need to win in order to advance.  (E.g., with 5-3-2-1 I believe the results would be identical to today's, as 4 wins > 3 wins > 2 wins no matter what.)
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #17 on: June 24, 2012, 06:07:31 pm »
0

I'm really, really sorry for beating this dead horse but there really needs to be a point system here. It is not really close to fair, with some people playing four 3p games (more wins available per player each match) and some shared wins resulting in more wins per player per match. I know it's really too late to change anything, and now that we've started I definitely wouldn't advocate changing anything now that we've started, but this is not close to fair.

/endswhining

How would it have changed the results so far?


First of all, that's not what prompted my feelings on this.

Second of all, the it depends on how you score it. If 3-player wins are equal to 4-player wins, than virtually nothing changes. If they are worth different amounts (which I think they should be) than the qualifiers wouldn't have changed, but knaacka probably would have taken third or fourth, maybe even lower for having no second place finishes (third place = 0 points).

And the fact that it doesn't change the results in this case is not a good argument for. It could have affected the results.

I'm going to actually calculate and edit.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #18 on: June 24, 2012, 06:16:04 pm »
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No, what I mean is, if the current system is unfair, we can change it for the next days.  Obviously I will not change retroactively.

That having been said, yeah, the go-for-the-win or settle-for-second is a deep philosophical problem, and we have to pick a side.  I think a points system would misleadingly suggest that settling for seconds can actually have you advance: even under most point systems, you'll need to win in order to advance.  (E.g., with 5-3-2-1 I believe the results would be identical to today's, as 4 wins > 3 wins > 2 wins no matter what.)
Generally. But 1st x3, 4th == 1stx2, 2nd x3; 1st, 2nd x3 beats some 2 win things, etc. Which will probably not come into play much, but it depends on how many people you get - and I would guess you'd get less, not more, in subsequent qualifiers.
Further, I very much like consistency, and though I prefer point systems, I wouldn't change at this point. Not to mention that actual nationals are Winner-Take-All

Kirian

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #19 on: June 24, 2012, 06:16:22 pm »
+1

Well what about HiWay2Hello in our pod? He had a 2nd, t-1st, 3rd, and 1st. Does the t-1st count as a win? That would put him on the same level as Personman...would they have to have a playoff in order to figure out who moved on?
Even if it counted as a win, people defeated is the first tiebreak, yes? And HiWay2Hello would have one fewer person defeated, because he certainly didn't beat the guy he tied with.

Neither did Personman.  They each defeated 8 and tied 1 by my count.
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Kirian

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #20 on: June 24, 2012, 06:26:29 pm »
+1

I'm going to go out on a limb here and suggest again that multiplayer winner-take-all is the most arbitrary system that could have been used, that still involved actual gameplay.  And I'm actually not convinced that using a poll would have been more arbitrary, especially given the total of only four games used, all with the same four people.  Not a single qualifier demonstrated superiority of play over more than three people here.

The seat rotation method used was poor too, since we're bringing up flaws.  With two excellent players and two people who bought cards at random in a pod, it was possible for one of the excellent players to go before the other one three times.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #21 on: June 24, 2012, 06:38:19 pm »
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By weighting 4-player matches as 4 points a win and 3 player matches as 3 points a win, which I think is pretty fair, knaacku ends in a tie for 7th.

I use two different methods. One was 4-2-1-0 for 4 player games and 3-1-0 for 3 player games. The other was 8-3-1-0 for 4p and 6-2-0 for 3 player. Points were shared in ties. For instance, a two-player tie for first in a four player game was 3 points each in the first method, 5.5 in the second. In both scenarios, the order was:
1. pirate ship economist
2. Cielo Azor
3. Personman
4. Mic Qsenoch

If you don't think that's fair, to weight four-player games more than 3-player games, then I guess that's a different argument.

Edit: Here's a spreadsheet with everyone's score by either method. I didn't include the 3p that didn't play all their games. https://docs.google.com/spreadsheet/ccc?key=0Ah6dTyQTfYBBdFUtS2VRVlVWUmpjdElqMVhPcENkbnc

Edit 2: I just looked at it again. In the first method, Mic Qsenoch and HiWay2Hello would have needed to play a playoff match to decide the winner.
« Last Edit: June 24, 2012, 06:50:39 pm by zxcvbn2 »
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Mic Qsenoch

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #22 on: June 24, 2012, 06:38:38 pm »
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The tiebreak rules definitely need clarification, especially the "number of opponents defeated". I thought this was just a way to distinguish between the four and three player pods, but others in this thread have taken it differently (and their interpretation is perfectly reasonable). The other thing which is unclear to me is how ties within a game are counted. Is a 3-4 tie counted as a third place finish for both players or something between third and fourth?
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knaacku

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #23 on: June 24, 2012, 07:07:32 pm »
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I think ideally you take x-number of signups.  Everyone else in a waiting list, so they can fill the slots of the no shows.  This way you can everyone have 4-p games.  I like the scoring now, as long as there is the same number of players in each game.
« Last Edit: June 24, 2012, 07:32:54 pm by knaacku »
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Mic Qsenoch

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #24 on: June 24, 2012, 07:48:03 pm »
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zxcvbn's proposal is still unbalanced, it just gives the three player pods the shaft now. Winning three of 4 games should be enough for the three player pod winners to advance. I think the point values need adjustment, but its hard to find the right spot where all the outcomes seem reasonable.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #25 on: June 24, 2012, 07:51:00 pm »
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Yeah -- winning three player pods is obviously easier than winning four player pods, but it is unfair to those randomly drawn into a three-player pod if it is impossible for them to score as high as someone drawn in a four player pod.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #26 on: June 24, 2012, 07:51:23 pm »
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zxcvbn's proposal is still unbalanced, it just gives the three player pods the shaft now. Winning three of 4 games should be enough for the three player pod winners to advance. I think the point values need adjustment, but its hard to find the right spot where all the outcomes seem reasonable.

You have a 1 in 3 shot at winning a 3 player game. you have a 1 in 4 shot of winning a 4 player game. I fail to see how it's unfair to award 3 points for winning a 3 player game, and 4 for winning a 4 player game.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #27 on: June 24, 2012, 07:53:01 pm »
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Yeah -- winning three player pods is obviously easier than winning four player pods, but it is unfair to those randomly drawn into a three-player pod if it is impossible for them to score as high as someone drawn in a four player pod.

But it's that much more difficult to score that much higher in a 4 player game. You have that much tougher of a time winning 3 games in a four player match than in a 3 player match. You're so much more likely to win 3 games in a 3 player match than in a 4 player match.

Obviously, this isn't my call, and I understand your perspective. There is just SO much difference between 3 and 4 players.
« Last Edit: June 24, 2012, 07:55:39 pm by zxcvbn2 »
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #28 on: June 24, 2012, 07:57:39 pm »
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I think we have two separate debates going on here, so let's clarify.

4p vs 3p

Obviously we'd love to minimize 3p games.  But we'll have them, and either you get screwed if you are in a 3p game or you get a benefit.  I think the current system offers a small benefit, with the caveat that you basically lose all ties with anyone who got the same number of wins in 4p games.

In other words, if I had to choose between a 3p player who went 1-1-2 and a 4p player who went 1-2-2-2, I will go with the 3p player, and if the 4p player went 1-1-2-4, I'll go with the 4p player.

Points vs wins

I really don't think this makes any difference at all.  Most point scoring systems are functionally equivalent to wins-matter-most, with second places only being a tiebreaker.  If you can point out an example of a situation where a fair points system would differ from a wins system and lead to a clear inequity, then I may change my mind.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #29 on: June 24, 2012, 08:09:35 pm »
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The nice thing about winner take all is that all opps have same objective.  If one player is playing for 2nd or 3rd, they can dramatically change the pace.  It introduces more tournament meta gaming. 

Having walk on alts to fill up 3p games might be nice though.
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Mic Qsenoch

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #30 on: June 24, 2012, 08:10:06 pm »
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You have a 1 in 3 shot at winning a 3 player game. you have a 1 in 4 shot of winning a 4 player game. I fail to see how it's unfair to award 3 points for winning a 3 player game, and 4 for winning a 4 player game.
Those aren't the only points awarded in your system though. A second place (4 player) finish is worth twice as many points as a second place (3p) finish in one of your schemes. I'm not sure there's a way to balance the points between the two types of pods.

Also theory, I was hoping you could clarify how ties within a game are being accounted for. Are ties for first worth as much as a standalone win, and do ties at say 3-4 count as 3rd place finishes or something in between 3rd and 4th? Mostly I'm wondering how this is considered for final tiebreak situations.
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Kirian

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #31 on: June 24, 2012, 08:11:38 pm »
+1

Points vs wins

I really don't think this makes any difference at all.  Most point scoring systems are functionally equivalent to wins-matter-most, with second places only being a tiebreaker.  If you can point out an example of a situation where a fair points system would differ from a wins system and lead to a clear inequity, then I may change my mind.

Player 1:  Takes 1st twice and 4th twice.  5 + 5 + 1 + 1 = 12.
Player 2:  Takes 1st once and 2nd thrice:  5 + 3 + 3 + 3 = 14.
Player 3:  Takes 1st once, 2nd twice, and 3rd once:  5 + 3 + 3 + 2 = 13

Obviously player 2 is better than player 3 by any measure.  Tougher to say if player 1 is truly better than the other, though.  And that's ignoring seating troubles.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #32 on: June 24, 2012, 08:12:29 pm »
+2

The nice thing about winner take all is that all opps have same objective.  If one player is playing for 2nd or 3rd, they can dramatically change the pace.  It introduces more tournament meta gaming. 

Having walk on alts to fill up 3p games might be nice though.
Of course, I disagree with this assessment entirely, and think that there's more problems of this ilk with a winner-take-all system. But we've been through this multiple multiple times now.

rrenaud

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #33 on: June 24, 2012, 08:14:50 pm »
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This is a different claim.  It's not about settling for 2nd in a particular game.

It's about gunning for 2nd in the 3rd or 4th game of the tournament from the start of the game. 
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #34 on: June 24, 2012, 08:19:07 pm »
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I don't see any meaningful way to AIM for 2nd from the beginning of a game, rather than playing what you think to be the best strategy anyway.
Edit: Moreover, I don't see the problem with that.
« Last Edit: June 24, 2012, 08:24:44 pm by WanderingWinder »
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #35 on: June 24, 2012, 08:33:43 pm »
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In a 3 player game you are twice as likely to win at least 3 games as in a 4 player game. (1/9 as opposed to 13/256) Maybe it's just me, but I see this as more than a small benefit. Yes, winning 4 games has is worth 4/3 as much in my setup, but it's also also over 3 times more likely. (Obviously, these are all assuming equal ability.)

Perhaps my scoring method could have been tweaked to award 2nd player in 3p games more points (indeed this was my intention with the second method). I still think it was fairer than what we have, though I really don't want to continue arguing after this post, because I do believe we should keep the format we started with for the sake of continuity.
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popsofctown

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #36 on: June 24, 2012, 08:38:13 pm »
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I don't see any meaningful way to AIM for 2nd from the beginning of a game, rather than playing what you think to be the best strategy anyway.
Edit: Moreover, I don't see the problem with that.
If you're aiming for second you're less likely to go for "lottery ticket" strategies like turn 2 and 3 Treasure Maps.  You can just play a stable game and take second.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #37 on: June 24, 2012, 08:50:03 pm »
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Is there any seeding for how to separate players into pods? If it is random it sounds like a larger problem for me. That is, if someone wins 4 out of 4, I imagine it tells more that his opponents are weak rather than he is super strong. This is the strongest problem I see for a winner-take-all format. Basically 2 equally strong players will destroy each other with similar luck.

I therefore think a point system is better. Like match points. Convert how many opponents you have beaten into percentages. So 4p: 100% 67% 33% 0%, 3p:100% 50% 0%. I have to say I feel this points reflects skill better than the sole winner.
« Last Edit: June 24, 2012, 09:13:24 pm by timchen »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #38 on: June 24, 2012, 08:53:15 pm »
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We seeded by iso rank, so the top N/4 players didn't have any other the other top N/4 in their pods.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #39 on: June 24, 2012, 09:12:32 pm »
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but judging from the results, the (mainly) 2p ranking is probably not a good way to seed...
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #40 on: June 24, 2012, 09:13:16 pm »
0

but judging from the results, the (mainly) 2p ranking is probably not a good way to seed...

This was a very small sample size.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #41 on: June 24, 2012, 09:20:58 pm »
0

Also, I'm just talking and don't want anything changed, but have just ONE more thing. I think, if we would have rotated opponents, the advantage of those playing 3p matches would have been spread out and we wouldn't have that much of a problem.

.

.


.

Okay, now I'm done talking about it. No, really.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #42 on: June 24, 2012, 09:21:53 pm »
0

theory: All I remember before this, in terms of what could be construed as a "decree," was this:

Quote from: theory
This is completely overblown, this points-vs-winners thing.

Let's be realistic.  With any of the points systems we're considering, (5-3-2-1), those with 4 wins will always beat those with 3 wins will always beat those with 2 wins.  So this is a completely unnecessary distinction at this point.

Although a lot of players today probably just played as best as they could, some might not have. Many of us agree that whatever system is used encourages playing towards that system, and not necessarily Dominion in general. Because there wasn't anything set in stone beforehand, you should award spots based on most wins, with collective non-win placements as tiebreaks.

Re: Seeding @ timchen:

If you were to seed based on 4p rankings, you're going to have a lot of participants just flat-out unseeded (and those might be the best players of all). Since 2p is the primary way we play, 2p is the only logical & available way to separate players.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #43 on: June 24, 2012, 09:22:28 pm »
0

Also, I'm just talking and don't want anything changed, but have just ONE more thing. I think, if we would have rotated opponents, the advantage of those playing 3p matches would have been spread out and we wouldn't have that much of a problem.

.

.


.

Okay, now I'm done talking about it. No, really.
I think you get to try again on Tuesday if you failed to qualify today. Is that correct? Is that also enough rotation for you?
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #44 on: June 24, 2012, 09:25:07 pm »
0

Quote
If you were to seed based on 4p rankings, you're going to have a lot of participants just flat-out unseeded (and those might be the best players of all). Since 2p is the primary way we play, 2p is the only logical & available way to separate players.

I know. I am just saying, a match point system can alleviate this problem. :3 Also it is fairer w.r.t 3p and 4p games.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #45 on: June 24, 2012, 09:25:29 pm »
0

Also, I'm just talking and don't want anything changed, but have just ONE more thing. I think, if we would have rotated opponents, the advantage of those playing 3p matches would have been spread out and we wouldn't have that much of a problem.

.

.


.

Okay, now I'm done talking about it. No, really.
I think you get to try again on Tuesday if you failed to qualify today. Is that correct? Is that also enough rotation for you?

You misunderstand me. I don't think there was a problem with playing the same opponent four times. I think many people playing 3 4p games and 1 3p game is more fair than a few playing 4 3p games.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #46 on: June 24, 2012, 09:35:36 pm »
+1

I'm going to go out on a limb here and suggest again that multiplayer winner-take-all is the most arbitrary system that could have been used, that still involved actual gameplay.  And I'm actually not convinced that using a poll would have been more arbitrary, especially given the total of only four games used, all with the same four people.  Not a single qualifier demonstrated superiority of play over more than three people here.

The seat rotation method used was poor too, since we're bringing up flaws.  With two excellent players and two people who bought cards at random in a pod, it was possible for one of the excellent players to go before the other one three times.
Are you sure you're using "arbitrary" correctly?

I agree about the seat rotation being pretty harsh - there's 24 different seating orders that could be used, though, it's not like it's easy to figure out what's going to be fair. Here's what I'd suggest:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B

Everyone gets every seat, and you're only sitting before/after the same person in games 1 and 4.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #47 on: June 24, 2012, 09:37:03 pm »
0

Also, I'm just talking and don't want anything changed, but have just ONE more thing. I think, if we would have rotated opponents, the advantage of those playing 3p matches would have been spread out and we wouldn't have that much of a problem (This isn't a very serious proposal, btw).

.

.


.

Okay, now I'm done talking about it. No, really.
I think you get to try again on Tuesday if you failed to qualify today. Is that correct? Is that also enough rotation for you?

You misunderstand me. I don't think there was a problem with playing the same opponent four times. I think many people playing 3 4p games and 1 3p game is more fair than a few playing 4 3p games.
Oh, yes. I'm actually not delving into the 3p vs. 4p debate quite yet because I don't have a great solution for that. My recommendation would definitely be to have backup players.

Honestly, there's not a good objective way to do the 3p pods. I think the 3p results need to just count 2/3 as much, which means that they have to pull 3 wins to have a shot. Again...it's not ideal or fair, but it's not fair for someone any way it is right now.
« Last Edit: June 24, 2012, 09:48:47 pm by metzgerism »
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Kirian

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #48 on: June 24, 2012, 10:10:25 pm »
+1

I'm going to go out on a limb here and suggest again that multiplayer winner-take-all is the most arbitrary system that could have been used, that still involved actual gameplay.  And I'm actually not convinced that using a poll would have been more arbitrary, especially given the total of only four games used, all with the same four people.  Not a single qualifier demonstrated superiority of play over more than three people here.

The seat rotation method used was poor too, since we're bringing up flaws.  With two excellent players and two people who bought cards at random in a pod, it was possible for one of the excellent players to go before the other one three times.
Are you sure you're using "arbitrary" correctly?

See definition 4.

Quote
Here's what I'd suggest:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B

Everyone gets every seat, and you're only sitting before/after the same person in games 1 and 4.

And since the person you're directly before or after doesn't make much difference, that last part isn't an issue.  What you've posted is perfect, as every player goes before every other player twice.  Thanks for taking the time to actually do that.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #49 on: June 24, 2012, 10:25:20 pm »
0

I'm going to go out on a limb here and suggest again that multiplayer winner-take-all is the most arbitrary system that could have been used, that still involved actual gameplay.  And I'm actually not convinced that using a poll would have been more arbitrary, especially given the total of only four games used, all with the same four people.  Not a single qualifier demonstrated superiority of play over more than three people here.

The seat rotation method used was poor too, since we're bringing up flaws.  With two excellent players and two people who bought cards at random in a pod, it was possible for one of the excellent players to go before the other one three times.
Are you sure you're using "arbitrary" correctly?

See definition 4.

Quote
Here's what I'd suggest:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B

Everyone gets every seat, and you're only sitting before/after the same person in games 1 and 4.

And since the person you're directly before or after doesn't make much difference, that last part isn't an issue.  What you've posted is perfect, as every player goes before every other player twice.  Thanks for taking the time to actually do that.
You're welcome! Made sense to me :) Although I disagree about the "who you're sitting before and after" part - Possession, Masquerade, and final turn dynamics care about those things.

---

I disagree strongly to your assessment that winner-take-all is arbitrary based on that definition of the term, and now I have an ace-in-the-hole reason:

From the Dominion rulebook, page 8: "Game End"
Quote
The player with the most victory points wins.
If the highest scores are tied at the end of the game, the tied player who has
had the fewest turns wins the game.
If the tied players have had the same number of turns, they rejoice in their shared victory.

Nowhere in the rulebook does it state anything about players who did not finish with the most points, only that they were not victorious. There's no talk about second-place points, third-place, etc. None.

The only distinction made is between players who won, and players who did not win. According to the actual Dominion rules, there's only one prize handed out: victory (shared or outright). Therefore, winner-take-all seems like the LEAST arbitrary system to employ, in my observation and opinion.

EDIT: I don't really want to open this can of worms again, but the use of "arbitrary" really bristled me, and I just remembered to use the rules as evidence. So I have.
« Last Edit: June 24, 2012, 10:28:06 pm by metzgerism »
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #50 on: June 24, 2012, 10:31:56 pm »
0

What I've learned from the ongoing, cyclical debate between those debating points vs. wins.

Multi-player Tournaments: Never again.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #51 on: June 24, 2012, 10:40:18 pm »
0

What I've learned from the ongoing, cyclical debate between those debating points vs. wins.

Multi-player Tournaments: Never again.
As long as people want to hold them, they will continue to exist. Which basically means, as long as there will be over-the-table tournaments, this will continue to be a thorn in the side of some people. Most notably, myself.

---

I understand there's a decent amount of derailment going on here, but since zxcvbn and kirian are watching (and I'm sure WW is too):

For those of you that want to see a point system: what's the reason?
(I can sum up the points given, but I'm already biased and don't trust myself to be objective about what I don't agree with - so please, someone answer it for me, then ask the same question about winner-take-all)
« Last Edit: June 24, 2012, 10:44:39 pm by metzgerism »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #52 on: June 24, 2012, 11:01:30 pm »
+1

Hey, so here is a suggestion about how to balance points in 3p vs 4p. First off, let's make each game zero sum in points. In other words, the point distribution is:

4p game: 3, -1, -1, -1
3p game: 2, -1, -1

The motivation behind this is so that it doesn't matter too much how many games you play, because the average points among all participants remains zero. OK, now, for 4p, the maximum points you can achieve in 4 games is 12. To make it fair for 3p, the maximum points achievable in the games you play should also be 12, so 3p players should play 6 games, ideally.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #53 on: June 24, 2012, 11:39:37 pm »
+2

Why Point system:

My main reason is that the result reflects more skill than luck. Multiplayer Dominion is a very swingy and luck-dependent game. You can just lose to a newbie with bad draws. 4p game is the most severe, as engines are more unlikely to be built. My experience in multiplayer game is that I am more often powerless to win, but I do have more control not to be last, say in a 3p game. Note that if only 4 wins and 3 wins can proceed this reason is probably not relevant.

A slightly less important reason is that point system has less king-making. Basically in winner-take-all, you cannot predict what opponents will do once they find themselves highly unlikely to win. In addition, since in the current format one only faces the same set of opponents, it is unlikely for anyone to have a chance to play suboptimally in order to make his main competitor even less likely to win.

A even less important reason is that a point based system has no problem dealing with 3 or 4 players or ties.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #54 on: June 24, 2012, 11:42:32 pm »
0

Hey, so here is a suggestion about how to balance points in 3p vs 4p. First off, let's make each game zero sum in points. In other words, the point distribution is:

4p game: 3, -1, -1, -1
3p game: 2, -1, -1

The motivation behind this is so that it doesn't matter too much how many games you play, because the average points among all participants remains zero. OK, now, for 4p, the maximum points you can achieve in 4 games is 12. To make it fair for 3p, the maximum points achievable in the games you play should also be 12, so 3p players should play 6 games, ideally.
I think this is fine as long as 3p pods play 6 games. Not really a point system, and the negative range for 3p is larger than 4p.  There's still a level of inequity involved in how match-ups pan out, but there's only so much you can mitigate. This does the job well by making 3p games accountable within a similar framework as 2p games.

How do you score ties, though?
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #55 on: June 25, 2012, 12:02:19 am »
0

[snip for brevity]
The only distinction made is between players who won, and players who did not win. According to the actual Dominion rules, there's only one prize handed out: victory (shared or outright). Therefore, winner-take-all seems like the LEAST arbitrary system to employ, in my observation and opinion.

Perhaps, but of course those rules only apply to a single game of Dominion.  By the same rules (including Intrigue rules), a single game of (regulation) Dominion cannot determine the winner of a group of larger than 6 players.  Therefore, the victory rules in the rulebook cannot apply to a tournament situation.  QED.

I should be clear that I don't think it was the non-points system that is arbitrary nearly as much as the only four games and the all of those games with the same players problems, not to mention the seating problem.  I actually think all of those trump the winner-take-all problem.  But I should have been more clear on that, I think, since I harped on the 4P WTA initially and mainly.

For those of you that want to see a point system: what's the reason?
(I can sum up the points given, but I'm already biased and don't trust myself to be objective about what I don't agree with - so please, someone answer it for me, then ask the same question about winner-take-all)

In my opinion, a multi-game winner-take-all scenario encourages poor play, especially from the fourth seat.  There have been discussions about the inherent necessity of taking extra risks from the P2 position in 2P games.  That necessity scales with the number of players.  In a 4P game, P4 must be willing to take risks that are poor play but might still win the game.  Buying two unsupported Maps is, I'm sorry, bad play--but it's good enough, on average, to overcome that huge fourth seat deficit.

It also compounds luck.  Consider a series of four games.  A player who wins one (say, the one where he started) and takes second in three is, in my opinion, likely to be a better player than someone who wins two games--the one he started, and the one where he lucked into T5 Maps as P4--and came in fourth in the other two.  It's reasonable to guess that this player would not have won that game without such great luck.  However, that single lucky win bumps him into serious contention.

Both of these can probably be mitigated by more games.

And I see timchen has already noted these, along with the kingmaker argument.
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rrenaud

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #56 on: June 25, 2012, 12:17:03 am »
0

Did the fixed pods bother other players?  It seemed like a nice win.  You know what's better than waiting in a Dominion lobby?  Playing dominion.  Maybe 4 games of fixed player pods games happens as fast as 2 or 3 variable player pod games.

The big problem with it is that you can get really screwed if you are in a strong pod because the players don't rotate. 
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #57 on: June 25, 2012, 12:29:54 am »
0

If abandoning the fixed pods is an option then we can try Swiss! after every round (say, have a time limit of 30 minutes), everyone takes seat according to their current score. The score is the matchpoints I talked about, with the sum of seating as tie breaker. The first player sits at 4th seat on table one, second player sits at 3rd seat on the same table, etc. Can play 4-5 rounds.*

*not really suggesting it, probably induces more luck.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #58 on: June 25, 2012, 01:01:47 am »
0

Why winner-take-all:

1) It is the only result prescribed in the rules. There is no mention of credit for 2nd or 3rd place in the rulebook for Dominion, just winners (tied or outright). This means that there is no official precedent for having any credit given to players who do not win a game.

2) It is what matters in the latter stages of most tournaments and championships. With a few exceptions, Dominion tournaments are won in a matter of a single game, or a best-of series. To crown a champion, neither of these methods take into account any losers, except for some tiebreakers.

3) It discourages players from colluding with certain opponents to gain a beneficial result for both of them. If you've ever watched a major international soccer tournament, you know that the last two games of the pool rounds are played concurrently. This is meant to mitigate a "common-enough-to-make-a-rule-about-it" situation where the participants of one game will both advance to the next round, regardless of the result of the other game, if they play for a known and exact result. It happened in 1982 and the rule was instituted, although the phenomenon is not preventable in soccer's current regular tournament format (Euro 2012's Group C had this problem scenario). With a winner-take-all system & a first-to-X-wins format, this problem ceases to exist. Without a first-to-X-wins format, winner-take-all still helps prevent this collusion between, for example, a first and second place player.

If I am playing a tournament or league of anything, I want to be playing the actual game prescribed (Reason 1), not a modified or watered-down version of it. I also want to be playing under as-close-to-the-same rules as possible from start to finish (Reason 2), because with different incentives come different styles of play. Finally, I will be playing to win; if there is some loophole in the format that will guarantee my progression in the tournament, I will take it, spirit-of-the-game be damned (Reason 3). I've done it before, and I'd do it again, because it's the organizer's job to make the rules, not mine. My goal is to win.

As an organizer, these are the primary concerns I have, which is why a winner-take-all system (ideally with a first-to-X-wins series) is the only proper way to organize a Dominion tournament, in my opinion.

Now, to respond (please feel free to respond to mine - I'm trying to be formal and equal, so please do the same for me):

Why Point system:

My main reason is that the result reflects more skill than luck. Multiplayer Dominion is a very swingy and luck-dependent game. You can just lose to a newbie with bad draws. 4p game is the most severe, as engines are more unlikely to be built. My experience in multiplayer game is that I am more often powerless to win, but I do have more control not to be last, say in a 3p game. Note that if only 4 wins and 3 wins can proceed this reason is probably not relevant.
I agree that Dominion can be a very swingy and luck-dependent game, and it scales upwards in player count poorly. However, long ago we started having best-of and multi-game series for Dominion, and that's basically become the norm in tournament play. This provides a simple solution for this problem, and retains the game in it's complete form - Dominion is swingy, why prevent that through metagaming? It's just a part of the game, and it still takes a decent amount of skill to see which combo is going to provide your best path to victory.

A slightly less important reason is that point system has less king-making. Basically in winner-take-all, you cannot predict what opponents will do once they find themselves highly unlikely to win. In addition, since in the current format one only faces the same set of opponents, it is unlikely for anyone to have a chance to play suboptimally in order to make his main competitor even less likely to win.
Aside from speaking about the current format, I disagree completely, as the kingmaking is worse with a point system. Assuming everyone plays as optimally as possible, and does not "fall on their sword" so to speak, a winner-take-all system would have everyone not in the lead positioning themselves for the best possible path to victory. This gives the player with the lead the unenviable task of trying to end the game without any help from someone playing poorly.

Having a point system changes this completely. Instead of everyone fighting in their own self-interests, someone with the opportunity to end the game in 2nd place might do so, simply to screw over the two people they are leading. The 1st place player gets a lot more points simply because one of their opponents decided that kingmaking them was preferable to trying to win themselves, and in reality could lead to players without a decent endgame strategy gaining a lot of points simply because their opponents thought it preferable to place 2nd next to them.

This opens up the table for late-round collusion, sub-optimal play, and metagaming. If two players can be guaranteed advancement via an alliance, you have now added politics to the game that DXV tried so hard to make non-political.

A even less important reason is that a point based system has no problem dealing with 3 or 4 players or ties.
I recommended a system almost identical to the old one-off BGGDL system. This would be strictly "winner-take-all," cares about the players that you beat (you winning, them not winning), including shared victory. It scales perfectly and ignores ties.

[snip for brevity]
The only distinction made is between players who won, and players who did not win. According to the actual Dominion rules, there's only one prize handed out: victory (shared or outright). Therefore, winner-take-all seems like the LEAST arbitrary system to employ, in my observation and opinion.

Perhaps, but of course those rules only apply to a single game of Dominion.  By the same rules (including Intrigue rules), a single game of (regulation) Dominion cannot determine the winner of a group of larger than 6 players.  Therefore, the victory rules in the rulebook cannot apply to a tournament situation.  QED.
Agreed, a single game of Dominion cannot determine a winner in a larger group. Furthermore, we generally have no framework for a tournament with >3 players/teams per game. But that doesn't mean that the rulebook is unimportant or should be discarded in a larger tournament setting - we should use it as a framework for organizing. As I state above, once you modify the terms of victory, you might not be playing Dominion anymore.

I should be clear that I don't think it was the non-points system that is arbitrary nearly as much as the only four games and the all of those games with the same players problems, not to mention the seating problem.  I actually think all of those trump the winner-take-all problem.  But I should have been more clear on that, I think, since I harped on the 4P WTA initially and mainly.

For those of you that want to see a point system: what's the reason?
(I can sum up the points given, but I'm already biased and don't trust myself to be objective about what I don't agree with - so please, someone answer it for me, then ask the same question about winner-take-all)

In my opinion, a multi-game winner-take-all scenario encourages poor play, especially from the fourth seat.  There have been discussions about the inherent necessity of taking extra risks from the P2 position in 2P games.  That necessity scales with the number of players.  In a 4P game, P4 must be willing to take risks that are poor play but might still win the game.  Buying two unsupported Maps is, I'm sorry, bad play--but it's good enough, on average, to overcome that huge fourth seat deficit.

It also compounds luck.  Consider a series of four games.  A player who wins one (say, the one where he started) and takes second in three is, in my opinion, likely to be a better player than someone who wins two games--the one he started, and the one where he lucked into T5 Maps as P4--and came in fourth in the other two.  It's reasonable to guess that this player would not have won that game without such great luck.  However, that single lucky win bumps him into serious contention.

Both of these can probably be mitigated by more games.
As I stated above, "more games" is generally the norm. However, I disagree with you completely about a 1-3 player with three 2nd places being better than a 2-2 player without - because the objective of the game is to finish with the most VP, and the 2-2 player did that more often than the 1-3 player, that 2-2 player is clearly better at fulfilling the winning objective of the game. Subjectively believing that the consistent 1-3 player is a better player is just that: subjective. The 2-2 player did what was asked - win - more often, and is therefore more likely to win a game.

Expand this to a 400 game series. Is the 100-300 player any better than the 200-200 player?

Also, is there a better argument against winner-take-all in Dominion, specifically, than "2 Treasure Maps?" I'm not a big fan of the card, but everyone still has the same access to the kingdom, right? No matter what you do, you're going to have to choose a strategy that may not pan out. I see Treasure Maps as an indictment against having one-offs, and not against winner-take-all. In fact, Treasure Maps ARE a part of the game, and if you're just implementing a metagaming system to prevent against the 1/12 chance there's a Treasure Map in the kingdom, you might as well just have a rule saying "No Treasure Maps" instead. Seems a little simpler, but still isn't Dominion.

And I see timchen has already noted these, along with the kingmaker argument.
Which I addressed above. I know for a fact that kingmaker would be worse (I'd exploit it, for one) with a point system that gives primary competition credit for non-winning performances. I think, in regards to the kingmaker issue, you're considering the presence of sub-optimal players in a tournament setting. I'm not.

Sub-optimal players exist in the early rounds, but they get eliminated quickly UNLESS you have a system that encourages them to continue playing sub-optimally. That's fine if the format continues in that way, although I'd say you're not playing Dominion anymore, and instead something quite watered down.

Most of the time, halfway through the tournament, you adopt a bracket system and the point system goes completely out the window. You're playing real Dominion again! But you don't necessarily have the best Dominion players in your bracket. And these sub-optimal players could compound the problem by denying a truly strong player advancement through their poor play. It's a slippery slope that leads to either not playing a Dominion tournament as written in the rules, or not having the best players play each other when the games count the most.

Kirian: I agree about the 4p pods being arbitrary. There's nothing about them that doesn't seem that way. I just wish I hadn't misunderstood your comment!
« Last Edit: June 25, 2012, 01:18:11 am by metzgerism »
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #59 on: June 25, 2012, 01:47:35 am »
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Aside from speaking about the current format, I disagree completely, as the kingmaking is worse with a point system. Assuming everyone plays as optimally as possible, and does not "fall on their sword" so to speak, a winner-take-all system would have everyone not in the lead positioning themselves for the best possible path to victory. This gives the player with the lead the unenviable task of trying to end the game without any help from someone playing poorly.

Having a point system changes this completely. Instead of everyone fighting in their own self-interests, someone with the opportunity to end the game in 2nd place might do so, simply to screw over the two people they are leading. The 1st place player gets a lot more points simply because one of their opponents decided that kingmaking them was preferable to trying to win themselves, and in reality could lead to players without a decent endgame strategy gaining a lot of points simply because their opponents thought it preferable to place 2nd next to them.

This opens up the table for late-round collusion, sub-optimal play, and metagaming. If two players can be guaranteed advancement via an alliance, you have now added politics to the game that DXV tried so hard to make non-political.
I think what you say here is an overall impression, but does not apply here. The key difference is that you are playing the same opponents in 4 rounds. Given the advancing threshold, it's quite likely only one out of the four players can advance, if it's close, even none. It is thus in your best interest to play as optimal as possible. In your example, imagine how it can happen. If it's the first match, are you willing to take 2nd? Certainly not as long as you still have a shot to win. If you have already won one? I think it is similar. If you've already won two? Maybe. But given you have won the first two it probably does not matter for the rest of the players anyway. If you have already won three than it definitely does not matter.

One can play with numbers, but the conceptual point here is that here a player pretty much has to best all other three players in order to advance. Therefore, getting some credit for being 2nd or not does not matter that much when comparing among players in the same pod. However, those points can be very important in order to compare players from different pods.

Now, I've already said elsewhere, but asking players to play for the win under all circumstances is just unrealistic. For example, if I am behind by more than a Province from the leading player and everyone seems possible to get that last Province. If I can, should I get it? According to your thoughts I should not as I will not win. But this is debatable. The current winning player may have something to say if I didn't take it, as if I am really behind it just looks as if I am keeping that province for the next player. Why should I?  Instead, if we play points by positions, I can comfortably take it as it improves my position.

Yeah, I now see your comment "aside from speaking about the current format", so my point is moot. I agree (especially in Swiss tournaments) it is highly possible. But are we trying to change the pods? I thought the waiting and arranging is just too cumbersome.

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I agree that Dominion can be a very swingy and luck-dependent game, and it scales upwards in player count poorly. However, long ago we started having best-of and multi-game series for Dominion, and that's basically become the norm in tournament play. This provides a simple solution for this problem, and retains the game in it's complete form - Dominion is swingy, why prevent that through metagaming? It's just a part of the game, and it still takes a decent amount of skill to see which combo is going to provide your best path to victory.
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2) It is what matters in the latter stages of most tournaments and championships. With a few exceptions, Dominion tournaments are won in a matter of a single game, or a best-of series. To crown a champion, neither of these methods take into account any losers, except for some tiebreakers.
I imagine Dominion is designed mainly as a casual game. So casually speaking I have no objections here. But if we are talking about a qualification to a tournament, I think the purpose of the qualification is to try to find the best candidate to represent our community, and to have the best chance to win the tournament. Since luck is not something a player can control, we should try to find the players that can win not only based on his luck. (This is in response to quote part 2) If the required skill set is the same for the different format of the qualification tournament (which I do think so, while strategy can be a bit different), we should choose the one which measures least luck, instead of the one used by the higher level/official tournaments.

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1) It is the only result prescribed in the rules. There is no mention of credit for 2nd or 3rd place in the rulebook for Dominion, just winners (tied or outright). This means that there is no official precedent for having any credit given to players who do not win a game.
You should probably ask theory to remove the rule that the point counter should be used first. It's not in the rules. And seriously. I don't think you are  allowed to use one IRL.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #60 on: June 25, 2012, 02:10:38 am »
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@Tim

Well, unless there's any other points you want to make I think the derailment is over. I'm speaking generally and you're speaking conditionally, and in these conditions that all makes a bit more sense to me.

I still believe that we must rank players by wins first, and (especially with 4 games played) in no scenario will several 2nd place finishes out-do a single 1st place, but I don't really think you're arguing that. Tiebreakers will matter significantly in this format, anyways.
« Last Edit: June 25, 2012, 02:13:11 am by metzgerism »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #61 on: June 25, 2012, 02:15:50 am »
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As I stated above, "more games" is generally the norm. However, I disagree with you completely about a 1-3 player with three 2nd places being better than a 2-2 player without - because the objective of the game is to finish with the most VP, and the 2-2 player did that more often than the 1-3 player, that 2-2 player is clearly better at fulfilling the winning objective of the game. Subjectively believing that the consistent 1-3 player is a better player is just that: subjective. The 2-2 player did what was asked - win - more often, and is therefore more likely to win a game.

Expand this to a 400 game series. Is the 100-300 player any better than the 200-200 player?

Ah, now that is actually an interesting question!  A 400 game series has essentially obliterated the ultra-luck factor, as that ultra-luck is likely to be spread around the table, as opposed to one person getting ultra-lucky in one game.  And this ultra-luck extends to a lot of things:

Being the only 5/2 on a good 5/2 board (of which there are a multitude, pick one).
Being the only 5/2 on a board with no 2s or 5s (ultra-luck hits both ways, of course).
Drawing CEEE with Chapel on T3, and other players get CCCE on T4/5.
Winning the first Prize early (where no other cursers or attacks are available).
And many many others.

I think a 400 game series is plenty to spread that around.  The question is one of "how many games is enough?"  I'll posit that if you can meaningfully segregate good players from poor players in N 2P games, it will require at least 2N games to do the same in 4P.  I don't think anyone would buy an argument that even best-of-three is enough to do this in 2P; best-of-five is probably the minimum.  In 4P, a 10 game series is probably OK, though I'm making a guess here.  Alas, my last Stats course was in... 1999.  So yeah.

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I see Treasure Maps as an indictment against having one-offs, and not against winner-take-all.

Sure.  But I see them as an indictment against even best-of-5 in multiplayer.  Let me further posit:  The more games played in a series, the less meaningful a points system is, and the better winner-take-all becomes.

Kirian: I agree about the 4p pods being arbitrary. There's nothing about them that doesn't seem that way. I just wish I hadn't misunderstood your comment!

No problem, I think I was really unclear.  I think it's really the combination that bothers me:  players each playing against only the same people, only four games, and winner-take-all.  Increase the number of games and shuffle the people around and my argument for a points system really starts to fall apart.  This is where a Swiss-like system starts to make more sense, actually, though I still think you're talking about 10+ games to meaningfully segregate the players.

Alas, we probably could spend an entire other thread discussing this; and I'm only spectating, as I can't go to Nationals or Gencon.  And I'm tired, so I'm off to bed. :)  We'll talk more tomorrow evening I'm sure.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #62 on: June 25, 2012, 02:22:32 am »
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I still believe that we must rank players by wins first, and (especially with 4 games played) in no scenario will several 2nd place finishes out-do a single 1st place, but I don't really think you're arguing that. Tiebreakers will matter significantly in this format, anyways.
I don't quite understand where this conclusion is from. Isn't the whole discussion about whether we should progress a player have something like 1-2-2-2 rather than 1-1-4-4?
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #63 on: June 25, 2012, 02:40:59 am »
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@Kirian

And I think whatever discussion we had is done here too (it's working OMG :D)

Yes, I'd prefer to have players in a LOT of games, as you and tim probably remember from the BGGDL. While that blew up out of control because I didn't control the format properly (and the ranking system came into play, effectively replacing the primary goal of league), if I ever run one again, it'd have a similar nature: encourage playing games, discourage metagame elements, and don't require the administrator to be omni-present. In a tournament format like this things would be a little different.

Ironically, at each player count it might be safe to say "first to 3 wins" for a truly interesting and seemingly fair format, but that honestly has more to do with the succession of each win itself: 1 lucky win, 1 good win, and 1 clincher.

Something like that.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #64 on: June 25, 2012, 03:52:31 am »
+1

So I noticed that at least in games 1 and 2 of the CieloAzor, michaeljb, farik, pkbrooklyn pod, the "same starting hands" option was not used, despite being called for in the rules. I guess we probably don't care at this point, but since not everyone in my pod was aware of it either, perhaps it should be called out more forcefully for future days?
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #65 on: June 25, 2012, 09:12:13 am »
+1

I'm glad no one here was at the qualifier event in Chicago, it would have never gotten finished.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #66 on: June 25, 2012, 09:24:44 am »
+1

Did the fixed pods bother other players?  It seemed like a nice win.  You know what's better than waiting in a Dominion lobby?  Playing dominion.  Maybe 4 games of fixed player pods games happens as fast as 2 or 3 variable player pod games.

The big problem with it is that you can get really screwed if you are in a strong pod because the players don't rotate. 
They bug me, yes. i guess to elaborate on the last point, if you have a strong pod, they're ALL screwed, more or less (I mean, I guess not entirely]/i]; I feel like I had a strong pod yesterday, and someone still managed to take three). If you get a really weak pod, then even a moderately good player can crush them terribly.
Strength of schedule is really important, which makes me feel it's comparing apples and oranges.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #67 on: June 25, 2012, 09:39:39 am »
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Fixed pods

After watching what happened yesterday, it's absolutely out of the question to do anything but fixed pods.  It would have tripled the amount of time required.

More to the point, only one person can advance, period.  So if you can't beat your pod on any day out of 4 days, you aren't going to be in contention in the end anyway.

This is a more general point that applies to the below: it is unfortunate, but this tournament isn't really designed to find out who is second-best or third-best.  As long as it results in the correct #1 choice, then it's good enough. 

EDIT: I guess this is not actually entirely true, because if #1 - #4 are all equal in strength and drawn together every single day then perhaps none of them advance.  I think that is unlikely, and seeding is the best we can do about that, assuming that 2p dominion skill is even vaguely a 4p skill proxy.

points vs wins

Here's the best example I can see for a points system: 1-1-4-4 vs 1-2-2-2.  Maybe you think the second player here should advance: but note that under pretty much any system other than 4-3-2-1, the first player is going to advance no matter what.  Does everyone really think 1-2-2-2 is clearly superior to 1-1-4-4? 

I worry that if I implement that, the Day 2 results topic will be "omg kingmaking!".  Yeah, you play screwy when you're P4 and go for TMap x2, but you also play screwy when you realize the other person is gunning for second and will happily end it in a losing position.

Note also that neither player could have possibly qualified yesterday.

3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing. 
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #68 on: June 25, 2012, 09:44:40 am »
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Re: 3p v 4p

While not a perfect solution, if you could get someone to fill in for a missing player (drafted out of the Great Hall lounge, if necessary) so that people don't play 3 player games...it'd be at least better than the current situation.

Anyway, I appreciate the effort that went into this tournament and regret that I will be mostly unable to participate in the other qualifiers.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #69 on: June 25, 2012, 09:49:48 am »
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Preliminary results suggest that based on the rules as written, the advancers are:


knaacku - 3x 1st, 1x 3rd
pirate ship economist - 3x 1st, 1x 3rd
Cielo Azor - 3x 1st, 1x 3rd
Personman - 2x 1st, 1x 2nd, 1x 3rd (8 players defeated)
HiWay2Hello - 2x 1st, 1x 2nd, 1x 3rd (8 players defeated)

The rules call for a playoff between Pman and HW2H ... so you two should play each other (you two can decide how many games, I'd recommend at least a best of 3) and report back.  Feel free to both sign up for Day 2.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #70 on: June 25, 2012, 09:56:50 am »
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Why winner-take-all:

1) It is the only result prescribed in the rules. There is no mention of credit for 2nd or 3rd place in the rulebook for Dominion, just winners (tied or outright). This means that there is no official precedent for having any credit given to players who do not win a game.
I don't find this relevant, as the rules are not geared toward a competitive setting, and say nothing of series or tournament play. Obviously, if you're only talking about one game at a time, winning is restricted to one place. If you take tournaments to be knockout, everyone is going to agree winner-take-all?

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2) It is what matters in the latter stages of most tournaments and championships. With a few exceptions, Dominion tournaments are won in a matter of a single game, or a best-of series. To crown a champion, neither of these methods take into account any losers, except for some tiebreakers.
Best-of-series by no means have to include only winning. That is precisely what I'm debating. A single game is a lousy format, so I find holding that up as 'precedent' to be... unconvincing. Actually, I find most precedent arguments unconvincing.

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3) It discourages players from colluding with certain opponents to gain a beneficial result for both of them. If you've ever watched a major international soccer tournament, you know that the last two games of the pool rounds are played concurrently. This is meant to mitigate a "common-enough-to-make-a-rule-about-it" situation where the participants of one game will both advance to the next round, regardless of the result of the other game, if they play for a known and exact result. It happened in 1982 and the rule was instituted, although the phenomenon is not preventable in soccer's current regular tournament format (Euro 2012's Group C had this problem scenario). With a winner-take-all system & a first-to-X-wins format, this problem ceases to exist. Without a first-to-X-wins format, winner-take-all still helps prevent this collusion between, for example, a first and second place player.
I have explained many times why this is backwards, but because you seem to keep throwing it out, I'll explain it again. But it gets its own post.

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If I am playing a tournament or league of anything, I want to be playing the actual game prescribed (Reason 1), not a modified or watered-down version of it.
So you have huge problems playing with identical starting hands, using the point tracker, having random kingdoms rather than letting the players agree on a method, using a 25-card black market deck, etc.? However, mostly I want to go with my response to your point 1 here as well.
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I also want to be playing under as-close-to-the-same rules as possible from start to finish (Reason 2), because with different incentives come different styles of play. Finally, I will be playing to win;
You keep saying this, and it's not a relevant factor - we're all playing to win, too! The point is, we have different notions of what winning is.
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if there is some loophole in the format that will guarantee my progression in the tournament, I will take it, spirit-of-the-game be damned (Reason 3). I've done it before, and I'd do it again, because it's the organizer's job to make the rules, not mine. My goal is to win.

As an organizer, these are the primary concerns I have, which is why a winner-take-all system (ideally with a first-to-X-wins series) is the only proper way to organize a Dominion tournament, in my opinion.


Having a point system changes this completely. Instead of everyone fighting in their own self-interests, someone with the opportunity to end the game in 2nd place might do so, simply to screw over the two people they are leading.
This IS their own self-interest ::)
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The 1st place player gets a lot more points simply because one of their opponents decided that kingmaking them was preferable to trying to win themselves, and in reality could lead to players without a decent endgame strategy gaining a lot of points simply because their opponents thought it preferable to place 2nd next to them.

This opens up the table for late-round collusion, sub-optimal play, and metagaming. If two players can be guaranteed advancement via an alliance, you have now added politics to the game that DXV tried so hard to make non-political.
Guess this goes into my next separate post on the topic anyway.
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I recommended a system almost identical to the old one-off BGGDL system. This would be strictly "winner-take-all," cares about the players that you beat (you winning, them not winning), including shared victory. It scales perfectly and ignores ties.
Bolding mine, and bolded because it's a ridiculous claim.
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Agreed, a single game of Dominion cannot determine a winner in a larger group. Furthermore, we generally have no framework for a tournament with >3 players/teams per game. But that doesn't mean that the rulebook is unimportant or should be discarded in a larger tournament setting - we should use it as a framework for organizing. As I state above, once you modify the terms of victory, you might not be playing Dominion anymore.
This ignores the argument though. Basically, this might not be wrong, but if you want to define this as "it's not dominion", then you can't effectively play tournament dominion. I guess you can have knockouts that everyone hates.

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As I stated above, "more games" is generally the norm. However, I disagree with you completely about a 1-3 player with three 2nd places being better than a 2-2 player without - because the objective of the game is to finish with the most VP,
Again, the whole debate is what we're interpreting the objective of the game to be, so you can't just make this claim. Being first falls under the category of having the most VP, but playing to 'maximize the number of players you have more VP than' also fits the bill. I guess my big problem with your arguments can thusly be summed up: you assume that you're correct, which makes your arguments totally ineffectual to people who disagree with you. And there's little point in arguing with people you already agree with.
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and the 2-2 player did that more often than the 1-3 player, that 2-2 player is clearly better at fulfilling the winning objective of the game. Subjectively believing that the consistent 1-3 player is a better player is just that: subjective. The 2-2 player did what was asked - win - more often, and is therefore more likely to win a game.
Your interpretation is subjective as well. Indeed, if you look at sports analytics at all, you'll know that previous win/loss record, analogous to the 'winner-take-all' thing here, is not the most predictive indicator of future success, and some form of score differential (analogous to the placement here), wipes the floor with it basically every time.

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Expand this to a 400 game series. Is the 100-300 player any better than the 200-200 player?
Depends on what the 300 and 200 are. Is a player who gets 1st 19999 times and second 20001 times REALLY worse than the player who gets 1st 20000 times and 4th 20000 times? Because that is what you are saying.

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Also, is there a better argument against winner-take-all in Dominion, specifically, than "2 Treasure Maps?"
Yes. In fact, you quoted some of them here.
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I'm not a big fan of the card, but everyone still has the same access to the kingdom, right? No matter what you do, you're going to have to choose a strategy that may not pan out. I see Treasure Maps as an indictment against having one-offs, and not against winner-take-all. In fact, Treasure Maps ARE a part of the game, and if you're just implementing a metagaming system to prevent against the 1/12 chance there's a Treasure Map in the kingdom, you might as well just have a rule saying "No Treasure Maps" instead. Seems a little simpler, but still isn't Dominion.
The point isn't treasure map. Treasure map isn't even the swingiest card. But it's an exemplar of a card that, straight-up, without help, leads to a strategy requiring little to no skill being able to WIN most often, without actually being able to do well very consistently at all. It's a card that, without support (as an aside, with support, it's a totally fine card - takes a lot of skill to use well), you can have a situation where the game is very directly decided by your Random Number Generator. People don't like that. Now, it's always true to some extent, but TM gives you very little control. But the problem isn't "Treasure Map" per se; TM just represents mindless, luck strategies, where taking risks that on average leave you behind are rewarded.
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Sub-optimal players exist in the early rounds, but they get eliminated quickly UNLESS you have a system that encourages them to continue playing sub-optimally.
Like a winner-take-all format!
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Most of the time, halfway through the tournament, you adopt a bracket system and the point system goes completely out the window. You're playing real Dominion again!
Okay, you advocate brackets. Nobody wants to play that, so while this is logically consistent, it's not something that should be pursued. It's a game, yes? So we should do what people like, what people want to do. You know, you want it one way, and that's valid. But the point is that if everyone else wants to play Dominion+, then they should play Dominion+, you know?
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But you don't necessarily have the best Dominion players in your bracket. And these sub-optimal players could compound the problem by denying a truly strong player advancement through their poor play.
Like in a winner-take-all format!

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #71 on: June 25, 2012, 09:58:27 am »
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I'm glad no one here was at the qualifier event in Chicago, it would have never gotten finished.
The actual playing went quite quickly. The whole thing was done in about an hour. And the people posting here are largely the same ones who played.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #72 on: June 25, 2012, 10:00:27 am »
+1

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I worry that if I implement that, the Day 2 results topic will be "omg kingmaking!".

To be fair, this happened yesterday already in our group. pops had no chance of winning game one (or even taking anything but 4th) and bought the last province before me and methods had a chance at it. We were both down by less than a province, I think I was down one and methods was down three. He bought it because he felt he had the better shot at advancing if the lowest ranked player won. [Log: http://councilroom.com/game?game_id=game-20120624-113610-823a76de.html]

My only point to this is that you can't eliminate kingmaking in any format. This shouldn't really be a reason for choosing one.

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but you also play screwy when you realize the other person is gunning for second and will happily end it in a losing position.

Can someone explain to me how you can gun for second before the endgame in Dominion? This might be relevant in other games, but I don't see how this can happen in Dominion.

.

With all that said, I honestly would prefer we keep the same tournament format throughout. A question about the top 16 however. Will that be single elimination? All it says on the front page is that they will "duke it out." Does this mean 4p single elimination?
« Last Edit: June 25, 2012, 11:07:49 am by zxcvbn2 »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #73 on: June 25, 2012, 10:08:20 am »
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Fixed pods

After watching what happened yesterday, it's absolutely out of the question to do anything but fixed pods.  It would have tripled the amount of time required.
I don't see evidence for this, and I suspect it's a big exaggeration, but whatever. It will take longer of course, and I understand that given our constraints, logistical concerns must trump other concerns.

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More to the point, only one person can advance, period.  So if you can't beat your pod on any day out of 4 days, you aren't going to be in contention in the end anyway.
Are you trying to impose this as an additional constraint? Because it seems EMINENTLY plausible to me that a pod has two people who go 1-1-2-2 or maybe a 1-1-2-3 or something, and that gets them both through some day, if 1-per-pod is not an actual rule.

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This is a more general point that applies to the below: it is unfortunate, but this tournament isn't really designed to find out who is second-best or third-best.  As long as it results in the correct #1 choice, then it's good enough. 

EDIT: I guess this is not actually entirely true, because if #1 - #4 are all equal in strength and drawn together every single day then perhaps none of them advance.  I think that is unlikely, and seeding is the best we can do about that, assuming that 2p dominion skill is even vaguely a 4p skill proxy.

points vs wins

Here's the best example I can see for a points system: 1-1-4-4 vs 1-2-2-2.  Maybe you think the second player here should advance: but note that under pretty much any system other than 4-3-2-1, the first player is going to advance no matter what.  Does everyone really think 1-2-2-2 is clearly superior to 1-1-4-4? 
Except that in almost EVERY point system, 1-2-2-2 advances over 1-1-4-4. 4-3-2-1, 5-3-2-1, 6-3-1-0, 4-2-1-0, 8-3-1-0... in short, every system that's been discussed sees 1-2-2-2 being better. So... I'm calling that out - you have that backwards, and apparently haven't done the calculation there? Or one of us is calculating wrong. But I'm fairly sure I've got the calculations down here.
I don't think 1-2-2-2 is clearly superior to 1-1-4-4, but that's just because nothing is clear after 4 games :P. In general though, I do think that set 1 of the results does indicate superior performance, yes.

Quote
I worry that if I implement that, the Day 2 results topic will be "omg kingmaking!".  Yeah, you play screwy when you're P4 and go for TMap x2, but you also play screwy when you realize the other person is gunning for second and will happily end it in a losing position.
This will be addressed in a soon-to-come-post.

Quote
Note also that neither player could have possibly qualified yesterday.

3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing. 
I like this, if you can figure out the 'somehow'.

theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #74 on: June 25, 2012, 10:11:01 am »
+1

Apologies on the points system.  I was thinking of another example.

I'm happy to try out points for tomorrow, and see how that affects things.

Quote
Are you trying to impose this as an additional constraint? Because it seems EMINENTLY plausible to me that a pod has two people who go 1-1-2-2 or maybe a 1-1-2-3 or something, and that gets them both through some day, if 1-per-pod is not an actual rule.
I meant, only one person will ever advance from this tournament.  Obviously more than 1 can advance from the same pod.
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #75 on: June 25, 2012, 10:11:18 am »
0

Quote
points vs wins

Here's the best example I can see for a points system: 1-1-4-4 vs 1-2-2-2.  Maybe you think the second player here should advance: but note that under pretty much any system other than 4-3-2-1, the first player is going to advance no matter what.  Does everyone really think 1-2-2-2 is clearly superior to 1-1-4-4? 

I worry that if I implement that, the Day 2 results topic will be "omg kingmaking!".  Yeah, you play screwy when you're P4 and go for TMap x2, but you also play screwy when you realize the other person is gunning for second and will happily end it in a losing position.

Note also that neither player could have possibly qualified yesterday.
With all due respect, I still don't see why you think someone gunning for second (if they can!) is more likely being affected. Who can screw them up anyway? If you are playing for the first place? If so you have every right to screw everyone. If you are gunning for 2nd place yourself? Dunno why you want to do that, but if you do, I find it justified as well. If you are 3rd or 4th and just want to screw people? This problem is there already, and even more severe with winner-take-all.

Quote
3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing.
I don't like the comment you say it is unfair no matter what. Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard. Sure you are more likely to get first place in a 3 player game; but you are also more likely to get last place, which is as damaging in this scoring system.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #76 on: June 25, 2012, 10:15:01 am »
0

Quote
Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard.

I like this a lot.  Let's go with the following system for Day 2, and give it a shot:

4p:

3 points for win
2 points for second
1 points for third
0 points for fourth

3p:

3 points for win
1.5 points for second
0 points for third
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #77 on: June 25, 2012, 10:15:58 am »
0

Quote
Quote
3p v 4p

Maybe the best way to do this is to make sure 3p games don't happen, somehow.  It is unfair no matter what.  Either you basically can never advance out of a 3p pod, or you get a great chance of advancing.
I don't like the comment you say it is unfair no matter what. Specifically if you use 1 2/3 1/3 0 for 4 players and 1 1/2 0 for 3 players and 4 games for 4 players and 3 games for 3 players, the average score per game sounds like a fair standard. Sure you are more likely to get first place in a 3 player game; but you are also more likely to get last place, which is as damaging in this scoring system.

That's unfair because, as I keep trying to point out, a 3p win =/= 4p win.

I actually agree with theory. No one point system will be completely fair, because we all value different things and 3p and 4p are almost as different as 2p and 3p.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #78 on: June 25, 2012, 10:17:25 am »
0

The difference being, under this system, your expected value is the same regardless of which group you enter.  In other words, a priori, you would not choose to enter a 4p group or a 3p group.
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #79 on: June 25, 2012, 10:24:19 am »
0

The odds of getting at least 20 points (an arbitrary number in the ballpark of what you should need to advance) in 3p is about 6.1%, while in 4p it's about 3.5%. So still, you're almost twice as likely to advance if you're in a 3p pod as opposed to a 4p pod if you assume equal ability. (Those numbers are 5 in 81 and 9 in 256 if anyone wants to check my math.)
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #80 on: June 25, 2012, 10:25:52 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #81 on: June 25, 2012, 10:30:49 am »
+2

Additional question: was the seat rotation that bothersome?  I.e., was it so terrible that the relative order remained fixed, such that we should try to explain and enforce:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #82 on: June 25, 2012, 10:33:23 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.

This is incorrect. Each game, assuming equal ability, you have an equal chance of 6, 4, and 2 points in 4p and 6, 3, and 0 points in 3p. If you do all the permutations of those, you end up with 256(4 to the 4th) possible results in 4p and 81 (3 to the 4th). So first, you have a 1 in 256 chance in getting 24 points in 4p, and a 1 in 81 in 3p. You have a 4 in 256 chance of getting 22 points in 4p. You have a 4 in 81 chance of getting 21 points.You have a 4 in 81 chance of getting 20 points in 4p.

I can post all the permutations if you like, but it would be quite long. The point is that no, it's not quite that simple.

Just FYI, I'm currently in my final year as a math major and have taken two stats courses. I'm absolutely positive these are correct.

EDIT: This is actually incorrect. The actual difference is only .3 percentage points, as is noticed later on. I made an error in my haste. Sorry, and thanks timchen!
« Last Edit: June 25, 2012, 10:52:53 am by zxcvbn2 »
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nopawnsintended

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #83 on: June 25, 2012, 10:36:26 am »
0

Interesting discussion.

My view is that the 3p versus 4p is a bigger difference than whether winner take all or points is adopted. 

I don't have much to add to the discussion except that I think it would be fun if two of the qualifying days were points and two were winner take all.  On a practical level, everyone could participate in their favorite qualifying format before the semis.  As an added benefit, you could use the semifinals as a "test" for whether winner take all or points selects better (making sure that two wta players get matched with two points players in each pod).  Of course, the format of the semifinals would matter a lot for the outcome of the test.  To increase the power of the test, I'd be up for a longer series in the semifinals.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #84 on: June 25, 2012, 10:38:06 am »
+2

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
« Last Edit: June 25, 2012, 10:42:54 am by timchen »
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nopawnsintended

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #85 on: June 25, 2012, 10:39:08 am »
0

Additional question: was the seat rotation that bothersome?  I.e., was it so terrible that the relative order remained fixed, such that we should try to explain and enforce:

A-B-C-D
D-C-B-A
B-A-D-C
C-D-A-B

I noticed the "fixed" seating order in our pod (may have made a difference in the last game).  I thought that the suggestion to mix up the seats was one of the better ones in the thread.
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theory

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #86 on: June 25, 2012, 10:39:53 am »
0

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
Just FYI, I'm currently in my final year as a math major and have taken two stats courses. I'm absolutely positive these are correct.
I don't doubt you at all!  There is a reason why rrenaud does all the math stuff and I do all the writing stuff :)
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #87 on: June 25, 2012, 10:40:45 am »
+1

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Crap, got me. Maybe absolute positive was the wrong phrase XP. Those are within .3 percentage points. I suppose that's acceptable. Thanks.
« Last Edit: June 25, 2012, 10:48:02 am by zxcvbn2 »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #88 on: June 25, 2012, 10:44:08 am »
+1

Quote
Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable. 

You're right. I'm sorry, that was low.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #89 on: June 25, 2012, 10:58:22 am »
0

First off, I want to say that when I advocate below for point-systems, it's a general advocacy, and not meant for this tournament. I believe that this tournament should be winner-take all, because Nats are WTA, and more importantly because that's how the rules were laid out from the beginning.
Furthermore, I don't discuss how things ARE set up, because this is a discussion (at least the one I want to have) of how they SHOULD be set up, and the way things are has extremely little to no relevance on that.

Having said that:
The first big difference I see in points vs WTA is in what kind of play they promote. WTA encourages you to take risks, because all that matters is getting first place or not. Points encourages you to play some system which is less risky and more consistent. Note that you probably still ought to take SOME risks, as is inherent in all forms of dominion, and the direct amount of risks you take is dependent on which point system you select. On the surface, these are just two different things, with neither being straight better than the other. It's a preference thing. However, I have a strong preference for points, and let me explain why.
So there's the cliched treasure map example, which has so much baggage that I'm going to step away from it. Here's another example. Opening something like fortune teller/potion when the cheapest potion-cost card on the board is golem. Now, assuming the other player doesn't attack you or mess with you or anything (which may not be the best assumption given that there's an attack, but this is a concept that makes sense anyway), your probability of spiking a golem on your first reshuffle is a hair's breath over 1/3. This probably makes it totally worth it under a WTA format, assuming it's a deck where golem can help you out a lot. But on average, this is a play that actually HURTS your deck quality, hurts your position. I don't particularly like encouraging this, first of all, but let's dig a little deeper. If this really is worth it, then everyone does it, yes? I mean, if they're playing well, making the 'right' decisions, they're all going to do this, yeah? But the point is, you now all have marginal chances of making that hit. Most probably, one of you gets this advantage, and the other three are way behind, and there's a HUGE spin toward that one guy - not that the game is totally over, but he has a MUCH larger chance of winning - based solely on how the shuffle fell, right off the bat. Basically what I'm saying is that WTA promotes strategies where, on a larger number of boards, a small amount of luck makes a large amount of difference. And especially for competitive environments, I don't like that.

Second, there's the issue of the number of games you have to play to get clear results. This is the direct result of having more information carry over from the point system than WTA. If you play 8 4-player games, you don't have a great idea as to who the best players are by your WTA metric. Probably nobody has more than 4 wins, and because of the high variance from a single game, we don't have that great an idea that mr. 4-win or mr. 5-win is really the best guy. However, if you play points matches, you have a much better idea, because you have more data. Now, of course, if you think winning is the only thing that matters, you reject this assessment, because you don't think the points metrics are meaningful; and this is mostly a logistical issue, really. But my point is that if you accept metric A, WTA, you need more games for results to have the same stability you get in fewer games from metric B, a points-based system. Because A has a higher inherent coefficient of variation than B does.

Finally, there's the kingmaking stuff. Which gets its own post.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #90 on: June 25, 2012, 11:03:53 am »
+1

[Logs aren't updated from yesterday's matches on council room yet, I'll post it when they are.]
I don't know what went wrong, but I think the updates are progressing now.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #91 on: June 25, 2012, 11:09:37 am »
+1

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
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zxcvbn2

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #92 on: June 25, 2012, 11:13:00 am »
0

Quote
Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

That's true, but there's already so much variance in 3 and 4 player games. By the time you put together values for skill, turn order, shuffle luck, etc., in four games it's practically a roll of the dice anyway, at least in such a small sample size (which I realize we don't have time for a larger one).
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #93 on: June 25, 2012, 11:26:08 am »
+2

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?

As one of the first round qualifiers, I'm happy to fill in if there are not enough alternates to fill a full set of 4p games.  Not sure how people feel about the strategic aspect of previously qualified players, but I still think my incentive is to play as well as I can.
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #94 on: June 25, 2012, 11:27:15 am »
+1

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
I think it is a least requirement for a fair method to pass the test of a simple model. Beyond that it's harder to say. For a good player for example (suppose that means he always get to ranked #1 or #2), seems a 3p game will benefit him. But in that case the difference is not as large as to average players if we try to tilt the rules to compensate this. And anyway I have the belief we don't really have an idea who are the better players at 4p.

I don't like substitutes. By definition they can't win; do I still expect they are playing to win? Using qualified players may solve this problem, but then the field is probably stronger than it should be. 

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Polk5440

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #95 on: June 25, 2012, 11:32:31 am »
0

The tournament was organized so quickly at the last minute, people are bound to disagree with how it is set up. I am just happy that there was a tournament. It's been fun so far.  It would have been better to have these discussions about structure before the tournament since there seems to be a tradeoff between fairness and fun. The way it's set up now with four players, everyone gets to play, everyone has a chance to win, and there is no down time. It's fun! I think it would be a big mistake to change the rules of the tournament while it's in progress unless there is an obvious, glaring, easily-fixable issue --which there isn't.

However, for the future, it would be worth thinking about what the ideal tournament would look like. To me, something like the on-line Starcraft tournaments would be a good fit for Dominion.  For example, see: <http://www.ign.com/ipl/starcraft-2/ipl4/tournament>. Starcraft is a real time strategy game of 2 or more players, but is at its most fair/strategic with two players. In particular:
     1. Tournaments have a large selection of approved maps (picked for symmetry/fairness) among which the ones played are randomly selected.  Likewise in Dominion there would be "tournament approved cards/kingdoms."
     2. There are pods in which a round robin tournament is played. Usually there are 4 pods and members determined by seed to have equal strength across pods. Everyone plays 1 on 1, best of three for the "point." Two player games avoid the hassle of trying to decide how to interpret 2nd-, third-, fourth-, ... place finishes.
     3. Winners of each pod compete in a elimination-style bracket tournament to determine the winner. (Ties within pod are broken by most games won, then sudden-death playoff.)

Really it's like having a mini football season with conference play then a post-season playoff all in one tournament. The downside of this would be significant set-up costs for administrators and more downtime for participants. But it is on-line, so times for each set of 3 games in the round robin can be organized ahead of time.

Even with two players there are concerns about fairness in Dominion that are not present in Starcraft -- namely first player advantage. Here we could take a cue from tennis. The reason you must win by two in tennis is that the server has a distinct advantage and to win and prove you are the better player, you must "break" your opponent's serves. This is also why each tennis match is so long and has so many parts (points, games, sets) even though it is a bracket-based tournament. To adapt this to Dominion and the structure outlined above: make it "first to 4, win by 2, alternating who goes first" instead of "best of 3."

The downside here is that it adds significantly to the number of games played.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #96 on: June 25, 2012, 11:35:54 am »
0

So, kingmaking stuff.
I think there are two problems here. One is the actual kingmaking, a la collusion. This can happen in any format, and you can't truly stop it in one as opposed to another. You can, of course, incentivize or disincentivize it, to an extent. So what the WTA people are worried about here is that I will 'prematurely' end the game because player B is ahead overall, and I need him to do poorly. Now, this is somewhat of a valid point, I will grant you. But typically, you're more interested in your own advancement, because you're playing against 4 other people, not just one. Furthermore, WTA doesn't really fix this. If wins are all that matter, and I'm in first, I'm liable to end the game WHENEVER my closest challenger isn't winning, regardless of how I'm doing. I mean, I can seriously just build a big engine that has really no way of getting victory points, but can pile things out relatively at will. This is a huge distortion of the game, of course. And you don't get it in points-based systems as much, because getting last, as you probably will doing this, hurts you more than just getting not-1st.
But I think the thing is with multiplayer games, you have to play not only the board, but also the other players. And that means that you have to react to what they're doing, to adjust the tempo vs staying power of your deck, to be able to deal with the different situations they present you with. Right? That's a huge multiplayer skill, and a big reason that multiplayer is a higher-variance game is that the more opponents you have, the less you can perfectly adjust to them.
How this deals with this, is the second post. The real important thing is to be able to have some ability to predict what your opponents will do. The best way to have this, is to have people to have dogs in the fight, i.e. they need to have something to play for. And in the WTA scenario, people who are way behind have to play only for other people's orderings. In the points-based scenario, they have their own ranking to play for. So people are much more predictable in the points-based scenario, because they have much more to play for. And that's what you really want. What you don't want is seemingly random 'it-doesn't-really-matter-what-I-do-at-this-point-for-myself' things that you get more often in WTA, because there's no way to improve your outcome more often in WTA.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #97 on: June 25, 2012, 11:38:52 am »
+1

I'm confused.  Is this some probability thing I'm not getting?  Seems like you are expected to get exactly 1.5 points per game, and so you are therefore expected to get 1.5X points.
But as rrenaud says, expected value isn't important. Getting in the middle, or somewhat above average, doesn't matter. What matters is whether or not you get at or near the top. And as it's a LOT easier to win a 3-player than a 4-player, you have a significantly better chance of being able to qualify from the 3-player. I would a priori take the 3-player every time.
The other issue is that they're just such different games, 3p and 4p, that it's somewhat inherently unfair to try to compare them.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #98 on: June 25, 2012, 11:41:23 am »
0

potential tourney format

The problem we have isn't that we have a lack of tournament experience. We know how to set up two-player tournaments (or at least have a general idea about what's fair and what's not). We've already set up several tournaments with the DS finals earlier this year, several IsoDoms, and a couple of one day tournaments.

The trouble is that we're dealing with a type of tournament that we've largely avoided. We were forced to play 3-4 player matches, as to maintain a similar format to nationals/ world championships. This is something that we're pretty unfamiliar with, and we had a very short time to put it together. I think theory did a tremendous job in setting this up when we had so little time to discuss the semantics in a tournament that most here (including me) are a lot more unfamiliar with. I'm sure if we do a similar (multiplayer) tournament in the future, most players will be much happier with the format, because we'll have experience and more time to set it up.
« Last Edit: June 25, 2012, 11:43:46 am by zxcvbn2 »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #99 on: June 25, 2012, 11:42:16 am »
0

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
Yeah, but this is still a problematic way of looking at it. There are this many ways of getting qualified, of course, but it is simply easier to get these cases form the 3p.
Importantly, it's not about getting to a point threshhold, it's about beating the other guys. The 3p are much more likely to produce a point total that is in the top X, as opposed to the 4p.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #100 on: June 25, 2012, 11:44:07 am »
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Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
I don't like substitutes. By definition they can't win; do I still expect they are playing to win? Using qualified players may solve this problem, but then the field is probably stronger than it should be. 
Wait, why can't substitutes win?

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #101 on: June 25, 2012, 11:45:36 am »
0

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
I don't like substitutes. By definition they can't win; do I still expect they are playing to win? Using qualified players may solve this problem, but then the field is probably stronger than it should be. 
Wait, why can't substitutes win?

You can't qualify for the semis twice. You're just in or out.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #102 on: June 25, 2012, 11:46:03 am »
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Quote
Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

That's true, but there's already so much variance in 3 and 4 player games. By the time you put together values for skill, turn order, shuffle luck, etc., in four games it's practically a roll of the dice anyway, at least in such a small sample size (which I realize we don't have time for a larger one).
But I don't think the answer to large variance is to throw our hands up and say 'ah, it's a crapshoot anyway, screw it'. I think we should try to do the best we can, given the limitations we're given. And there's much MORE variance in 4p than 3p. But I mean, if you think that it's such a roll of the dice anyway, then why have a tournament at all? Now, obviously there's a lot of luck, but I still think there's SOME appreciable amount of skill....

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #103 on: June 25, 2012, 11:46:43 am »
0

Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

Of course, still the best answer is don't have 3p games.  Can we come up with a system using alternates or previously qualified players filling up the brackets?
I don't like substitutes. By definition they can't win; do I still expect they are playing to win? Using qualified players may solve this problem, but then the field is probably stronger than it should be. 
Wait, why can't substitutes win?

You can't qualify for the semis twice. You're just in or out.
Right, but then he says that using pre-qualified players SOLVES this problem, so I assumed he DIDN'T mean those when he was talking about substitutes.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #104 on: June 25, 2012, 11:57:35 am »
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One thing about hard pods that we can do is try to keep them as balanced as possible using the iso level.

The first round algo was rank by iso level, assuming that we have a perfectly sized player pool, split into N/4 groups where N = num entrants.  Each of the N/4 groups gets exactly one top rated player, and the other 3 players are random.

I could make those other 3 player pools have as close to the average rating as possible.

That's right guys, I'll be solving (or approximating) NP-complete problems for you.  http://en.wikipedia.org/wiki/Partition_problem

Of course, this assumes iso level is the right way to balance groups, which is just the first kind of reasonable thing I could think of.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #105 on: June 25, 2012, 11:59:01 am »
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Quote
Right, but then he says that using pre-qualified players SOLVES this problem, so I assumed he DIDN'T mean those when he was talking about substitutes.
Two problems here. Either the substitute player may not play to win (if we just find some random player) or the player is too strong (if we use the qualified players).
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #106 on: June 25, 2012, 11:59:33 am »
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Quote
Advancing in the tournament is not about expected value, it's about the chance of being near the max, and the chance that players win is not 1/N.  I am not sure if simple models will really help you or mislead you.

That's true, but there's already so much variance in 3 and 4 player games. By the time you put together values for skill, turn order, shuffle luck, etc., in four games it's practically a roll of the dice anyway, at least in such a small sample size (which I realize we don't have time for a larger one).
But I don't think the answer to large variance is to throw our hands up and say 'ah, it's a crapshoot anyway, screw it'. I think we should try to do the best we can, given the limitations we're given. And there's much MORE variance in 4p than 3p. But I mean, if you think that it's such a roll of the dice anyway, then why have a tournament at all? Now, obviously there's a lot of luck, but I still think there's SOME appreciable amount of skill....

I agree with you. I don't think that there's any system that will give us meaningful results in four games' time. I think a Swiss would probably come closest. I totally agree with you. There's so much more variance in 4p than 3p. But the alternative is either turning people away, having players play who have no chance of winning, or... ?

Obviously I like my system more, that rewards 4p more than theory's. I get the feeling nobody else here does, though because it has a lower ceiling for 3p games. I also really like rotating opponents. Theory's basically said that's off the table. Basically I've come to that point of saying, "Screw it, it's a crapshoot, anyway."

I'm sure if we do a multi-player tourney again, we'll be able to do some major rehauling of the format. For now, I just think we have to deal with the unbalanced nature of 3 player games vs. 4 player games.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #107 on: June 25, 2012, 12:18:06 pm »
0

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
Yeah, but this is still a problematic way of looking at it. There are this many ways of getting qualified, of course, but it is simply easier to get these cases form the 3p.
Importantly, it's not about getting to a point threshhold, it's about beating the other guys. The 3p are much more likely to produce a point total that is in the top X, as opposed to the 4p.
No it is not simpler for 3p, as the simple calculation shows. If you think otherwise, it's better to show via at least some qualitative arguments instead of just saying it...

As I said, using the points, getting 4th place/3rd place in a 4/3p game is as serious as getting 1st. So if the players are roughly equally skilled the above calculation is valid. You can generalize the calculation for a good player (say I just randomly choose that he can get #1 50% and #2 50% in a 4p game; in a 3p game to have the same expectation value of points he then should get #1 2/3 of the time and #2 1/3 of the time. Putting the numbers in then (suppose the threshold is 20 points again)

4p: 1/16+1/16*4+1/16*6=11/16
3p: 16/81+32/81=16/27.

Actually in this case 4p is better!

To qualitatively understand this, note that #2 in 3p game is worth a bit less than #2 in a 4p game. To get above the same threshold you thus need to push harder for #1 in a 3p game which may or may not be easier than trying to score #2 in a 4p game. The situation can change if you play with the percentages and the threshold, but I think the difference of the chances are too small to matter. To put this way. In the tournament using this scoring system, I am perfectly willing to concede my chance of playing in a 3p game.
« Last Edit: June 25, 2012, 12:27:51 pm by timchen »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #108 on: June 25, 2012, 12:22:57 pm »
0

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
Yeah, but this is still a problematic way of looking at it. There are this many ways of getting qualified, of course, but it is simply easier to get these cases form the 3p.
Importantly, it's not about getting to a point threshhold, it's about beating the other guys. The 3p are much more likely to produce a point total that is in the top X, as opposed to the 4p.
No it is not simpler for 3p, as the simple calculation shows. If you think otherwise, it's better to show via at least some qualitative arguments instead of just saying it...

As I said, using the points, getting 4th place/3rd place in a 4/3p game is as serious as getting 1st. So if the players are roughly equally skilled the above calculation is valid. You can generalize the calculation for a good player (say I just randomly choose that he can get #1 50% and #2 50% in a 4p game; in a 3p game to have the same expectation value of points he then should get #1 2/3 of the time and #2 1/3 of the time. Putting the numbers in then (suppose the threshold is 20 points again)

4p: 1/16+1/16*4+1/16*6=11/16
3p: 16/81+32/81=16/27.

Actually in this case 4p is better!

I *believe* in this case he's referring to something that is more difficult to describe analytically, which is that a better player is more likely to win a 3p game than a 4p game because the game itself is more swingy. In other words, suppose each was a weighted die, one with three sides and the other with four, but the 3-sided die  was more unevenly weighted than the 4-sided.

Councilroom may or may not have statistics to support this. I doubt it, because there are so few games among high-level players played with 3 or 4 players. I will say, it seems correct. This doesn't mean it is.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #109 on: June 25, 2012, 12:30:00 pm »
0

I think you miscalculated. with 20 points (6-4-2-0) as a threshold, there are actually 15 cases (6 of them being 2 first places and 2 second places) so the chance for 4p is 15/256. 15/256 and 5/81 are close enough to me.

This difference is caused by the quantization of the points. it does not give definite advantage to 3p or 4p however (depending on the threshold.)

Just to respond to someone says he's absolutely correct: in 4p the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 22 pts
1-1-1-3 (4) 20 pts
1-1-2-2 (6) 20 pts

so this is 15/256.

in 3p
the cases are
1-1-1-1 (1) 24 pts
1-1-1-2 (4) 21 pts

this is 5/81.

Sorry if this sounds a bit harsh, but I usually find claim of correctness based on who you are kinda laughable.  ;)
Yeah, but this is still a problematic way of looking at it. There are this many ways of getting qualified, of course, but it is simply easier to get these cases form the 3p.
Importantly, it's not about getting to a point threshhold, it's about beating the other guys. The 3p are much more likely to produce a point total that is in the top X, as opposed to the 4p.
No it is not simpler for 3p, as the simple calculation shows. If you think otherwise, it's better to show via at least some qualitative arguments instead of just saying it...

As I said, using the points, getting 4th place/3rd place in a 4/3p game is as serious as getting 1st. So if the players are roughly equally skilled the above calculation is valid. You can generalize the calculation for a good player (say I just randomly choose that he can get #1 50% and #2 50% in a 4p game; in a 3p game to have the same expectation value of points he then should get #1 2/3 of the time and #2 1/3 of the time. Putting the numbers in then (suppose the threshold is 20 points again)

4p: 1/16+1/16*4+1/16*6=11/16
3p: 16/81+32/81=16/27.

Actually in this case 4p is better!
I do give a qualitative reason. I mean, it's actually a numbers reason that I didn't provide numbers for.  The thing is that you need to score in the top 4 out of all the players. It's not about reaching any particular threshhold. If it were 'everyone who scores at least X points advances' then, if X were 20, your calculations would be valid. But there is no fixed value for X. My argument is that it is more likely for things to work out so that the qualifying value, whatever that turns out to be, will be met by a 3p than a 4p. But these things are not independent. How well 3p guys score, how well 4p guys score, has a direct impact on how many you NEED to score to get through. Of course it's also dependent on how many sign up, which makes it too much math to do, I think. If you can somehow explain to me that 20 points is the absolute threshold where below it, you can't qual, and above it, you can, then I will accept your calculations. But that's not what's happening. My entire point is that the threshold is NOT valid.

But ok, here's another reason. There's the inherent difference between 3p and 4p games. Of course, this means that some players may be better suited to one or the other, which is a big real issue, but let's even ignore that for the moment. Let's even use your example - 2/3 win, 1/3 2nd in 3p should be much easier to achieve than 50% win and 50% 2nd in 4-player. Just much much easier. This is down to the nature of the very games themselves - there's more randomness inherent to the 4p. This is the hugest source of inequity.

Of course, I don't have particular evidence to support this, and I don't think the data really exists either way. But I'm quite confident in my assessment of that, and I think most people will agree.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #110 on: June 25, 2012, 12:50:53 pm »
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Do you mean that in terms of points, a good player will have a higher expectation value of score in a 3p game than in a 4p game using this point system? If that is the case then sure, playing in a 3p game is better. I have no reason to believe this is the case however.

If the expected score is the same but the variance is different, you can play with the numbers. But it seems to me the variance tends to be larger in a 4p game for a good player, simply because he has more places to be. If this is so then indeed 3p games are better for good players, as if his expected score is higher than the threshold he would like the variance to be as small as possible. But as I showed in a typical case above, at least we can say the difference is not that significant.

@WW:
for the threshold, I have no particular reason to choose 20 points, except it seems to get a similar outcome to our first day qualifiers. Now you can actually calculate for every possible threshold (say, from 15 to 24), and you will see that the advantage oscillates between 3p and 4p. I don't see how a fixed number entrant criteria can fix the threshold to be favorable to 3p in this case.

Quote
But ok, here's another reason. There's the inherent difference between 3p and 4p games. Of course, this means that some players may be better suited to one or the other, which is a big real issue, but let's even ignore that for the moment. Let's even use your example - 2/3 win, 1/3 2nd in 3p should be much easier to achieve than 50% win and 50% 2nd in 4-player. Just much much easier. This is down to the nature of the very games themselves - there's more randomness inherent to the 4p. This is the hugest source of inequity.
Yeah, by this you just mean the expected score will be higher for the same player in 3p. I dunno. I don't think so, but maybe you are right.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #111 on: June 25, 2012, 12:55:00 pm »
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In the current format surely game 4 of each match only usually matters to 1 possibly 2 of the players playing it?
This opens up a huge potential for collusion.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #112 on: June 25, 2012, 01:01:20 pm »
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Do you mean that in terms of points, a good player will have a higher expectation value of score in a 3p game than in a 4p game using this point system? If that is the case then sure, playing in a 3p game is better. I have no reason to believe this is the case however.

If the expected score is the same but the variance is different, you can play with the numbers. But it seems to me the variance tends to be larger in a 4p game for a good player, simply because he has more places to be. If this is so then indeed 3p games are better for good players, as if his expected score is higher than the threshold he would like the variance to be as small as possible. But as I showed in a typical case above, at least we can say the difference is not that significant.

@WW:
for the threshold, I have no particular reason to choose 20 points, except it seems to get a similar outcome to our first day qualifiers. Now you can actually calculate for every possible threshold (say, from 15 to 24), and you will see that the advantage oscillates between 3p and 4p. I don't see how a fixed number entrant criteria can fix the threshold to be favorable to 3p in this case.
Sure, you can do it for every possible threshhold, but that still misses my point. My point is that the threshold is correlated to the other things, i.e. I think it's more likely for the threshold to be in a place that favours a 3p  than a 4p pod. The main point I'm trying to make in this section is that you aren't taking into account that the threshold is moving based on how people do, which is an important factor.
I missed where we were discussing a fixed number of participants.
I do actually think that the rotating number of participants is going to be a big thing too, and I seriously doubt that 20 points is going to be a very stable point for qualification. But this has more to do with how many people I expect to sign up, and a little with the inherent randomness of the game, than anything else.

Quote
Quote
But ok, here's another reason. There's the inherent difference between 3p and 4p games. Of course, this means that some players may be better suited to one or the other, which is a big real issue, but let's even ignore that for the moment. Let's even use your example - 2/3 win, 1/3 2nd in 3p should be much easier to achieve than 50% win and 50% 2nd in 4-player. Just much much easier. This is down to the nature of the very games themselves - there's more randomness inherent to the 4p. This is the hugest source of inequity.
Yeah, by this you just mean the expected score will be higher for the same player in 3p. I dunno. I don't think so, but maybe you are right.
Okay, I guess we just disagree here.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #113 on: June 25, 2012, 01:38:20 pm »
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Quote
Sure, you can do it for every possible threshhold, but that still misses my point. My point is that the threshold is correlated to the other things, i.e. I think it's more likely for the threshold to be in a place that favours a 3p  than a 4p pod. The main point I'm trying to make in this section is that you aren't taking into account that the threshold is moving based on how people do, which is an important factor.
My argument is that in any case, the threshold should change in a continuous manner. That is, if the competition is fierce, the threshold moves down, if there are clearly better players, the threshold moves up. And since I think the threshold favors either 3p or 4p in a oscillatory manner (the difference being small anyway), I don't see how the dependency on various things can somehow always fix the threshold at some places that favors 3p. Like say, at 22 it favors 3p (just say that randomly, not that it is correct), now the threshold can change depend on a few things as said, it can move to 21 or 23 lets say. But at 21 and 23 it may very well favor 4p. and at 20 or 24 it can again favor 3p. You know what I mean.
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #114 on: June 25, 2012, 02:04:44 pm »
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Quote
Sure, you can do it for every possible threshhold, but that still misses my point. My point is that the threshold is correlated to the other things, i.e. I think it's more likely for the threshold to be in a place that favours a 3p  than a 4p pod. The main point I'm trying to make in this section is that you aren't taking into account that the threshold is moving based on how people do, which is an important factor.
My argument is that in any case, the threshold should change in a continuous manner. That is, if the competition is fierce, the threshold moves down, if there are clearly better players, the threshold moves up. And since I think the threshold favors either 3p or 4p in a oscillatory manner (the difference being small anyway), I don't see how the dependency on various things can somehow always fix the threshold at some places that favors 3p. Like say, at 22 it favors 3p (just say that randomly, not that it is correct), now the threshold can change depend on a few things as said, it can move to 21 or 23 lets say. But at 21 and 23 it may very well favor 4p. and at 20 or 24 it can again favor 3p. You know what I mean.
Right. But I don't think that it's oscillatory, and I'm not at all convinced that the difference is small. At any rate, I don't feel like taking the time to calculate all that stuff out right now.

metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #115 on: June 25, 2012, 02:17:05 pm »
+1

In the current format surely game 4 of each match only usually matters to 1 possibly 2 of the players playing it?
This opens up a huge potential for collusion.
I agree with this, with the current format, and I believe it's a bigger problem than points vs. wins and actually spins my opinions in the reverse a bit.

Let's say one player has won games 1-3.
Is there any reason to play game 4? Probably not.

Let's say one player has 2 wins, and another has 1.
Is there any reason for the other two players to play game 4? Probably not.

Let's say the first 3 games have been split, one apiece to three players.
Is there any reason for the 0-3 player to play game 4? Probably not.

We've already got the evidence that this is likely the case - you need at least 2 wins to advance, and even then it's probably a play-in of some sort. I prefer WTA obviously, and since that's likely what the brackets and championships will use, you've got to have it. Regardless, a point system will mitigate this, but absolutely cannot eliminate it. I mentioned my preference for a best-of-X/first-to-3-wins series - a first-to-2-wins may actually be the best option, with additional games played in 3p to find 2nd place in a pod.

That said, it's a little too late - we're just going to have to run with it as-is.
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #116 on: June 25, 2012, 02:18:26 pm »
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Since we're changing it up for each qualifying round, maybe we can do the next round as a "first-to-2" or "first-to-3" wins scenario? The kingmaking problems become a little more clear that way, however.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #117 on: June 25, 2012, 02:21:30 pm »
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Since we're changing it up for each qualifying round, maybe we can do the next round as a "first-to-2" or "first-to-3" wins scenario? The kingmaking problems become a little more clear that way, however.
But you can't do that, because you have more pods than qualifiers.

knaacku

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #118 on: June 25, 2012, 03:18:29 pm »
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Here is the game 2 log for Fading, TheBlueFool, and knaacku that was missing prior.  We did have the order of 2nd and 3rd wrong, but I do not think that changes anything. (1st knaacku, 2nd TheBlueFool, 3rd Fading)

http://councilroom.com/game?game_id=game-20120624-120138-896ed538.html
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metzgerism

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #119 on: June 25, 2012, 04:39:58 pm »
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Since we're changing it up for each qualifying round, maybe we can do the next round as a "first-to-2" or "first-to-3" wins scenario? The kingmaking problems become a little more clear that way, however.
But you can't do that, because you have more pods than qualifiers.
Right, and I gave it a little thought and decided it's probably not worth it.

In a 3p "best 2/4," you're going to have an obvious problem: game 2 will, with ideal political play, never be won by the winner of game 1. Neither of the other players can allow it and survive. Game 3 returns back to a veritable free-for-all, with the exception that both previous winners would rather hand game 3 to the trailing player and finish it in game 4. Effectively, a best-of-4 makes for marginalized, politicized games 2 and 3. In 4p "best 2/5," the same issues arise in the same way for games 2, 3, and 4 (game 3 being a little odd this way). Even in best 3/9, the same problems exist, only with more chances to use and/or ignore them.

I do believe that the issue is with which format best represents a multiplayer game. One method, probably the cleanest, is to have single or double (or triple) elimination in one-off games - unfortunately, we've long established that one-offs are not even closely representative of Dominion skill, and having a loser's bracket as the mitigating factor doesn't really solve that. Another possibility is swiss, which is good because all players have similar stakes in all games - the main downside being that the length of the tournament needs to be long enough to be anything more than single-elimination in practice.

I'm not beyond saying that multiplayer Dominion just makes for bad tournaments...upon serious analysis, it all feels like a crapshoot.
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Polk5440

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #120 on: June 25, 2012, 04:41:56 pm »
+1

The problem we have isn't that we have a lack of tournament experience. We know how to set up two-player tournaments (or at least have a general idea about what's fair and what's not)....The trouble is that we're dealing with a type of tournament that we've largely avoided. We were forced to play 3-4 player matches, as to maintain a similar format to nationals/ world championships. This is something that we're pretty unfamiliar with, and we had a very short time to put it together.

That's a good point.

However, the two main problems, comparing across pods and how to deal with seating advantage, are present no matter the number of players, so it still may be helpful to think about how to structure tournaments from scratch with only two players even if you are interested in 4 player versions. For instance, what I proposed deals with these two problems for 2 players. The problems are just compounded with 4 players.

For three/four players, in order to eliminate comparing across pods one could either
1) Add an extra round to have playoffs among winners of pods (so we don't need to determine whether a winner of a three player game is the same as a four player game).
or
2) Have only four pods and more people and 4-player only matches within each pod round robin style. The problem with more than 2 players per game is how to pick a winner out of a pod.
     a) One way this can be done is to play a "reasonable" number of matches and choose the Condorcet winner, if present, and sudden-death playoff among Condorcet ties otherwise.
     b) Another way to do this is to play a "reasonable" number of matches (of 4 players per match) allocate a "point" to each winner in the match-up. To earn the point for the match, play first to three wins to earn the point (rotating seating appropriately). This preserves the inventive to win a little better than allocated points per place and playing a fixed number of games.

Really, it seems like most of the problems boil down to: In order to have better tournaments, more games need to be played. This is especially true with 4 players.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #121 on: June 25, 2012, 05:35:22 pm »
0

Since we're changing it up for each qualifying round, maybe we can do the next round as a "first-to-2" or "first-to-3" wins scenario? The kingmaking problems become a little more clear that way, however.
But you can't do that, because you have more pods than qualifiers.
Right, and I gave it a little thought and decided it's probably not worth it.

In a 3p "best 2/4," you're going to have an obvious problem: game 2 will, with ideal political play, never be won by the winner of game 1. Neither of the other players can allow it and survive. Game 3 returns back to a veritable free-for-all, with the exception that both previous winners would rather hand game 3 to the trailing player and finish it in game 4. Effectively, a best-of-4 makes for marginalized, politicized games 2 and 3. In 4p "best 2/5," the same issues arise in the same way for games 2, 3, and 4 (game 3 being a little odd this way). Even in best 3/9, the same problems exist, only with more chances to use and/or ignore them.

I do believe that the issue is with which format best represents a multiplayer game. One method, probably the cleanest, is to have single or double (or triple) elimination in one-off games - unfortunately, we've long established that one-offs are not even closely representative of Dominion skill, and having a loser's bracket as the mitigating factor doesn't really solve that. Another possibility is swiss, which is good because all players have similar stakes in all games - the main downside being that the length of the tournament needs to be long enough to be anything more than single-elimination in practice.

I'm not beyond saying that multiplayer Dominion just makes for bad tournaments...upon serious analysis, it all feels like a crapshoot.

I think you're over-estimating the effect of politicization. I mean, the semi-targeted attacks (does different things depending on player - spy, to some extent thief, and especially swindler), are the biggest thing here, I think, but even there, by helping opponent A to hurt opponent B, you're hurting yourself pretty badly.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #122 on: June 25, 2012, 05:50:10 pm »
+1

Ok. I've woken up more now, and I have a way of phrasing my nebulous-sounding concerns better (I hope!), and I've got some math. What timchen is looking at is exactly what to do to figure out the probability of any one player reaching a certain threshold of points. Incidentally, here's the breakout of that, from 15 points up:
4p chance              Points      3p chance
1/256  ~= 00.39%   23-24      1/81  ~= 01.23%
5/256  ~= 01.95%   22              1/81  ~= 01.23%
5/256  ~= 01.95%   21              5/81  ~= 06.17%
15/256 ~= 05.86%   19-20      5/81  ~= 06.17%
35/256 ~= 13.67%   17-18      15/81 ~= 18.52%
66/256 ~= 25.78%   16              15/81 ~= 18.52%
66/256 ~= 25.78%   15               31/81 ~= 38.27%

As we can see, 19-20 is by far the closest, and the rest have pretty substantial gaps.

However, the important thing comes here: what will the threshold actually be? To figure out what you'd expect this to be, you'd need to know what the maximum score from any given pod will be, and then how many pods there are. And it's going to be different for 3p pods and 4p pods, so you actually need to know how many of each type you have.
Now, if we make a few assumptions, we can actually break this down. For now, let's assume that every game is independent of every other (bad because of player skill and seating order), and that every person is equally likely to get every place in every game.
Note that we can't just use what timchen started and I expanded on above, because the different players in a pod are NOT independant of each other. i.e., if one guy gets 1st 4 times, we know that nobody else got first, so those possibilities get sliced out, if somebody gets 1st twice, nobody else can get 1st more than twice, if two guys get first twice, nobody else can get first, etc.
Anyway, in a 3p pod, there are 6 distinct orderings that any game can finish in. 4 games makes 1296 orderings, but we get one factor of 6 back because at the end, if we switch all the As for Bs, or all the Bs for Cs, etc., this doesn't make a substantive difference (i.e. ABC ABC ABC ABC == BCA BCA BCA BCA == BAC BAC BAC BAC == CAB CAB CAB CAB, etc.).
So we have 216 possibilities. Now, I'm not going to sit and count them all out right now, because I don't have time. But just take the top case, 24 points. To get 24 points, someone had to score perfect. The other guys could have (B gets 2nd 4 times, C gets 3rd 4 times; B gets 2nd thrice; B gets 2nd twice, etc.).

...aaaaand I realize my counting brain has gone offline here. Someone else who is skilled in the mathematical arts want to progress this?

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #123 on: June 25, 2012, 07:33:20 pm »
0

... lol. Was looking forward to the following.

Also the delta between 4p and 3p advancing chances is indeed oscillatory as a function of threshold.

Coincidentally, this suggest that setting a fixed cut at 19-20 is probably a good idea (instead of fixing only 4 people can proceed.)
« Last Edit: June 25, 2012, 07:37:23 pm by timchen »
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Re: Re: DominionStrategy Qualifying Day Results
« Reply #124 on: June 25, 2012, 10:34:24 pm »
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Okay. Think I'm counting right again now? 3p pod means 216 order-invariant possible result lines, with 8 of these giving perfect scores, for a ~3.7% chance. 4p pod means 13824 lines with 216 of them giving perfect scores, for a rate of only 1.5625%. As the number of possibilities grows, though, it becomes increasingly difficult to count them, because there's LOTS of different cases, especially for the middle ones like 18 points. But the point is, a 3p pod is more likely to produce players at these higher point threshholds, even if any particular player may not be so much favoured. Which is important insofar as the 3p pods increase the threshold more quickly than 4p pods do.
Of course, this is just intuitive also. If I add an extra player to the pod, it is more likely that the top player in that pod will score worse, even with the added points injected. Certainly you see this at the top end, which is what is really important.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #125 on: June 26, 2012, 01:34:09 am »
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Quote
Okay. Think I'm counting right again now? 3p pod means 216 order-invariant possible result lines, with 8 of these giving perfect scores, for a ~3.7% chance. 4p pod means 13824 lines with 216 of them giving perfect scores, for a rate of only 1.5625%. As the number of possibilities grows, though, it becomes increasingly difficult to count them, because there's LOTS of different cases, especially for the middle ones like 18 points.
So first you are trying to calculate the chance for a pod to have at least one player qualify, given some threshold.
Note that
8/216=1/27=1/81*3 (3 players each have 1/81 chance to win 4 straight games)
216/13824=1/64=1/256*4
is identical the first table you have given. Yes, if you go down further it will start to be different for obvious reasons (that is, the probability can not be larger than one so obviously you cannot just multiply that number by 3 or 4), but it is more due to the fact that when there are more than one player qualifying then a naive multiplication counts those instances multiple times. It is not due to the fact that sometimes one sequence can prevent another (for example, when one player scores 1111 the others can't.) Actually when there are mutual exclusiveness the probability will be that number multiply by the number of players.

A better question to ask perhaps is given a threshold what is the expected number of players per pod to qualify. This question can also be answered more easily. And more importantly, the answer to this question is the same as if we treat the record of each player as independent.

The reason is as follows: let us denote the record for a player (ex. something like 1-4-3-2) R. R1 denotes the record of the first player, etc. Now in a 4p game, R1, R2, R3, R4 are four correlated random variables; say if R1=1111 then R2 cannot be 1234. Notice there are conditional probability as well; ex. given R1=1221 the chance for R2 to be 2134 will be different from not knowing R1=1221.

We can encode all this information in the joint probability density function P(R1,R2,R3,R4): P(1111,1234,R3,R4)=0, etc.
Let us also define the threshold function Q(R), basically when a record qualifies it returns 1. So for example if threshold=22, (with 6-4-2-0 scoring) then Q(1111)=Q(1112)=Q(1121)=Q(1211)=Q(2111)=1 and the rest is zero.

The expected number of qualified players is then <Q(R1)+Q(R2)+Q(R3)+Q(R4)>.

Now here is an important observation. When we know nothing about other players, the probability of say P1 to have a certain record is the same as our previous calculation, which let us call it p(R) (That is, assuming equally skilled players, the chance to score 1111 is 1/256, 1112 and the like 4/256, etc, etc.) In equations it reads

sum_(R2,R3,R4)P(R1,R2,R3,R4)=p(R1).

So, even though they are not independent (ie, P(R1,R2,R3,R4)!=p(R1)p(R2)p(R3)p(R4)), the marginal probability is the same. Intuitively, since you know nothing about others, correlations don't matter.

The expected number of player to qualify, then can be calculated as

<Q(R1)+Q(R2)+Q(R3)+Q(R4)>=<Q(R1)>+<Q(R2)>+<Q(R3)>+<Q(R4)>=4 <Q(R)>.

That is, the expected number of qualified player per pod is just the chances you tabulated times the number of players.

Now as we see the difference of the chance between 3p and 4p is oscillating, which means that it does not favor 3p pods in particular. (I do agree if you look in detail at the table there are more spots favoring 3p though; but I think this is coincidental. That is, you can change this by changing the number of games played. And at the very top of course it favors 3p, which is not surprising as it's easier to get to first place in 3p, and at the top you need to get to first place.) There is a factor of 4/3 from the number of players, but this is expected. More players in a pod should generate more qualified players.
 
Quote
But the point is, a 3p pod is more likely to produce players at these higher point threshholds, even if any particular player may not be so much favoured. Which is important insofar as the 3p pods increase the threshold more quickly than 4p pods do.
Not sure this is right. As is tabulated 3p pod is more likely to produce 24 pts players but less likely to produce 22 and up. at 20-21 they are almost equal. Anyway this goes back to the same table. If you say that table favors 3p then ok, it favors 3p.

Quote
If I add an extra player to the pod, it is more likely that the top player in that pod will score worse, even with the added points injected. Certainly you see this at the top end, which is what is really important.
Not sure how you reach the conclusion with two cancelling factors (harder to win vs. more points at 2nd place), but this comes back to the question that whether the expected score of a player represents his skill well, across different number of players. This scoring method ensures that for an average player it will work. For player at higher end, it depends on the game itself, so yeah, maybe your feeling is right, but I didn't find convincing argument for that.
« Last Edit: June 26, 2012, 01:39:36 am by timchen »
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timchen

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #126 on: June 26, 2012, 02:32:47 am »
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I didn't find convincing argument for that.

I think I now find one. Just to exaggerate, suppose 4th position in a 4p game is just so bad that no one can win from that position. Now, using the scoring system (6-4-2-0) and (6-3-0), the expected score for a player who can score #1 x of the time and #3 y of the time (x+y<1), when he is not 4p, will score in average
(6x+4(1-x-y)+2y))*3/4 in a 4p game, and 6x+3(1-x-y) in a 3p game.

The former is 1.5(x-y)+3 and the latter is 3(x-y)+3. Notice that (x-y) is a measure of how good the player is. x-y=0 gives an average player. Indeed, if the game is tilted so much that at 4th seat you can't win, then 3p game is favorable for a good player. An average player is never affected. Note that for the analysis to work, the inability to win at 4th seat is the same for everyone.

While in practice it isn't so bad, I can imagine it's true that a good player's winning percentage is hurt more than an average player at 4th seat. So this picture should be qualitatively correct.

I guess for some this is trivial. I guess I've started from the wrong perspective.
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WanderingWinder

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #127 on: June 26, 2012, 09:30:40 am »
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An average player is never affected.
Can you clarify what the average player is never affected by? Because it seems obvious to me that an average player benefits from having a never-win player in his pod. And that by having everyone be terrible, he is going to qualify every time. And, moreover, that he's going to benefit more from having one never-win player in a 3p pod than in a 4p pod. So I'm sure I just don't get what you're saying with this claim.

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Re: Re: DominionStrategy Qualifying Day Results
« Reply #128 on: June 26, 2012, 09:49:54 am »
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Quote
Okay. Think I'm counting right again now? 3p pod means 216 order-invariant possible result lines, with 8 of these giving perfect scores, for a ~3.7% chance. 4p pod means 13824 lines with 216 of them giving perfect scores, for a rate of only 1.5625%. As the number of possibilities grows, though, it becomes increasingly difficult to count them, because there's LOTS of different cases, especially for the middle ones like 18 points.
So first you are trying to calculate the chance for a pod to have at least one player qualify, given some threshold.
Note that
8/216=1/27=1/81*3 (3 players each have 1/81 chance to win 4 straight games)
216/13824=1/64=1/256*4
is identical the first table you have given. Yes, if you go down further it will start to be different for obvious reasons (that is, the probability can not be larger than one so obviously you cannot just multiply that number by 3 or 4), but it is more due to the fact that when there are more than one player qualifying then a naive multiplication counts those instances multiple times. It is not due to the fact that sometimes one sequence can prevent another (for example, when one player scores 1111 the others can't.) Actually when there are mutual exclusiveness the probability will be that number multiply by the number of players.

A better question to ask perhaps is given a threshold what is the expected number of players per pod to qualify. This question can also be answered more easily. And more importantly, the answer to this question is the same as if we treat the record of each player as independent.
This is absolutely a worse question to ask, because it fails to model what actually happens - i.e. that the threshold to qualify is NOT fixed. Which was the whole point of my other calculation. Indeed, I can see no reason that this is better to ask, other than it is easier to calculate. Of course, this way, things will track pretty well with the chart above, but even so, let's take a look at your math...

Quote
The reason is as follows: let us denote the record for a player (ex. something like 1-4-3-2) R. R1 denotes the record of the first player, etc. Now in a 4p game, R1, R2, R3, R4 are four correlated random variables; say if R1=1111 then R2 cannot be 1234. Notice there are conditional probability as well; ex. given R1=1221 the chance for R2 to be 2134 will be different from not knowing R1=1221.

We can encode all this information in the joint probability density function P(R1,R2,R3,R4): P(1111,1234,R3,R4)=0, etc.
Let us also define the threshold function Q(R), basically when a record qualifies it returns 1. So for example if threshold=22, (with 6-4-2-0 scoring) then Q(1111)=Q(1112)=Q(1121)=Q(1211)=Q(2111)=1 and the rest is zero.

The expected number of qualified players is then <Q(R1)+Q(R2)+Q(R3)+Q(R4)>.

Now here is an important observation. When we know nothing about other players, the probability of say P1 to have a certain record is the same as our previous calculation, which let us call it p(R) (That is, assuming equally skilled players, the chance to score 1111 is 1/256, 1112 and the like 4/256, etc, etc.) In equations it reads

sum_(R2,R3,R4)P(R1,R2,R3,R4)=p(R1).

So, even though they are not independent (ie, P(R1,R2,R3,R4)!=p(R1)p(R2)p(R3)p(R4)), the marginal probability is the same. Intuitively, since you know nothing about others, correlations don't matter.
More or less, I am with you here. I maybe wouldn't phrase it like this, but I would certainly not say that this is wrong.

Quote
The expected number of player to qualify, then can be calculated as

<Q(R1)+Q(R2)+Q(R3)+Q(R4)>=<Q(R1)>+<Q(R2)>+<Q(R3)>+<Q(R4)>=4 <Q(R)>.

That is, the expected number of qualified player per pod is just the chances you tabulated times the number of players.
But here you lose me. Certainly <Q(R1)+Q(R2)+Q(R3)+Q(R4)>=<Q(R1)>+<Q(R2)>+<Q(R3)>+<Q(R4)>. But this is not the same thing as 4<Q(R)>, because R1, R2, R3, and R4 are not independent! Sure, for R1, you can say that you don't know what the other players did, and thus it is R. But this fails to hold for R2, R3, and R4. Now, quite possibly this is still right somehow - I cannot say that I have definitively calculated it to be wrong. But you're making the claim without showing it sufficiently well to be true, at least for my standards.
Quote
Now as we see the difference of the chance between 3p and 4p is oscillating, which means that it does not favor 3p pods in particular. (I do agree if you look in detail at the table there are more spots favoring 3p though; but I think this is coincidental. That is, you can change this by changing the number of games played. And at the very top of course it favors 3p, which is not surprising as it's easier to get to first place in 3p, and at the top you need to get to first place.) There is a factor of 4/3 from the number of players, but this is expected. More players in a pod should generate more qualified players.
 
Quote
But the point is, a 3p pod is more likely to produce players at these higher point threshholds, even if any particular player may not be so much favoured. Which is important insofar as the 3p pods increase the threshold more quickly than 4p pods do.
Not sure this is right. As is tabulated 3p pod is more likely to produce 24 pts players but less likely to produce 22 and up. at 20-21 they are almost equal. Anyway this goes back to the same table. If you say that table favors 3p then ok, it favors 3p.
I wasn't saying that. My whole points were based on things you can't get from the table. However, now that I do look at the table, it's pretty clear to me that by-and-large, it does favour 3p. 4p gets a slight bump on exactly 16 and 22, but everywhere else, 3p has an advantage, and in some of these cases, quite a significant one.

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I moved all this discussion over into this topic, by the way.
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timchen

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An average player is never affected.
Can you clarify what the average player is never affected by? Because it seems obvious to me that an average player benefits from having a never-win player in his pod. And that by having everyone be terrible, he is going to qualify every time. And, moreover, that he's going to benefit more from having one never-win player in a 3p pod than in a 4p pod. So I'm sure I just don't get what you're saying with this claim.
That average player also cannot win when he is in 4th seat. So if you play a 4-game series with each player in each seat once he's score will not be affected. To put it more clearly, he's average score will be 3 per game (average to 4 when not at 4th seat, 0 when at 4 seat), which is the same as if there is no disadvantage at 4th seat.
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An average player is never affected.
Can you clarify what the average player is never affected by? Because it seems obvious to me that an average player benefits from having a never-win player in his pod. And that by having everyone be terrible, he is going to qualify every time. And, moreover, that he's going to benefit more from having one never-win player in a 3p pod than in a 4p pod. So I'm sure I just don't get what you're saying with this claim.
That average player also cannot win when he is in 4th seat. So if you play a 4-game series with each player in each seat once he's score will not be affected. To put it more clearly, he's average score will be 3 per game (average to 4 when not at 4th seat, 0 when at 4 seat), which is the same as if there is no disadvantage at 4th seat.
Oh, you're talking about fourth SEAT. I thought you were talking about having one player who was just really terrible no matter where he was.
Seating order will tend to bring everyone closer to average over time, no? (which obviously doesn't affect Mr. Average)

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But here you lose me. Certainly <Q(R1)+Q(R2)+Q(R3)+Q(R4)>=<Q(R1)>+<Q(R2)>+<Q(R3)>+<Q(R4)>. But this is not the same thing as 4<Q(R)>, because R1, R2, R3, and R4 are not independent! Sure, for R1, you can say that you don't know what the other players did, and thus it is R. But this fails to hold for R2, R3, and R4.
Your statement is kinda of funny. Suppose you accept it for R1. Note that when you calculate the expectation value for Q(R2), that term DOES NOT depend on R1, R3 and R4, in the same way that Q(R1) does not depend on the rest. This is why the expectation value only cares about the marginal probability. The correlation is encoded in the pdf P(R1,R2,R3,R4), but we have argued that the marginal probability for R1-R4 will all be the same as p(R). Technically, basically you plug in the above equality and then use this formula which you say you accept:

sum_(R2,R3,R4)P(R1,R2,R3,R4)=p(R1)
(and its permuted version)

 you then get the answer.

(To be perfectly clear I'll just calculate for example, <Q(R2)> here, the calculation is the same for every R)
<Q(R2)>=sum_(R1,R2,R3,R4)(Q(R2)P(R1,R2,R3,R4))
             =sum_(R2)Q(R2)sum_(R1,R3,R4)P(R1,R2,R3,R4)
             =sum_(R2)Q(R2)p(R2)
             =<Q(R)>.

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This is absolutely a worse question to ask, because it fails to model what actually happens - i.e. that the threshold to qualify is NOT fixed. Which was the whole point of my other calculation. Indeed, I can see no reason that this is better to ask, other than it is easier to calculate. Of course, this way, things will track pretty well with the chart above, but even so, let's take a look at your math...
You have to do things in steps. What you were calculating IS the probability of qualification given a threshold so I don't see why you are complaining. You have to know this first(or actually, know what I said is better to calculate first) then you can use the size of the tournament and the slots for the qualification along with this table to calculate the expected threshold and see if it favors 3p or 4p.

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I wasn't saying that. My whole points were based on things you can't get from the table. However, now that I do look at the table, it's pretty clear to me that by-and-large, it does favour 3p. 4p gets a slight bump on exactly 16 and 22, but everywhere else, 3p has an advantage, and in some of these cases, quite a significant one.
I am not disagreeing with you on this particular table seemingly favoring 3p. It depends really on where your threshold will sit. But the point is there is no reason for the threshold to prefer sitting on places that favors 3p, on the contrary of what you have said. Also, while this particular table has more 3p favoring thresholds I don't see this as a general trend. You can try to make a table of say 12 game-series I'll say it will be different, but still oscillating.

The only thing that is beyond this table is when you weigh in the skills of the player. That is you have to consider players that win more often. As I've shown earlier with an example, as long as the expected score is the same for the player in question in 3p or 4p games, he will not be particularly favored. But if not, all this calculations are redundant. Obviously, when the expected score is different, he will in average score more in the format which he has a higher expected score. With a common threshold then of course he is going to have an advantage over there.
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Oh, you're talking about fourth SEAT. I thought you were talking about having one player who was just really terrible no matter where he was.
Seating order will tend to bring everyone closer to average over time, no? (which obviously doesn't affect Mr. Average)
Yeah, I guess it is sort of obvious. Sorry if I phrase it in a confusing way. But the point is that this effect indeed brings down the expected score for a good player, in this scoring scheme.

Actually, in principle one way to compensate this effect is to make it something like (6420) and (5 3 1) for 4p and 3p. (average not changing so the average player again is not affected. Good player will score less in a 3p game comparatively.) But somehow it is a terrible idea for a 4 game series. With threshold at 20 now in 3p games the player has to win all games to qualify!
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But here you lose me. Certainly <Q(R1)+Q(R2)+Q(R3)+Q(R4)>=<Q(R1)>+<Q(R2)>+<Q(R3)>+<Q(R4)>. But this is not the same thing as 4<Q(R)>, because R1, R2, R3, and R4 are not independent! Sure, for R1, you can say that you don't know what the other players did, and thus it is R. But this fails to hold for R2, R3, and R4.
Your statement is kinda of funny. Suppose you accept it for R1. Note that when you calculate the expectation value for Q(R2), that term DOES NOT depend on R1, R3 and R4, in the same way that Q(R1) does not depend on the rest. This is why the expectation value only cares about the marginal probability. The correlation is encoded in the pdf P(R1,R2,R3,R4), but we have argued that the marginal probability for R1-R4 will all be the same as p(R).
I believe this is what I fail to accept. Perhaps I said I accepted it above, but if that's the case, it was because I misunderstood what you were saying. My argument here is that R1, R2, R3, and R4 are not equal to each other, and in fact they can't be. Now, I'm getting lost a little bit inn your I'm-trying-to-write-math-using-only-plain-text, especially as I have not used multivariate probabilities in some years. I do NOT work in quantum physics as you do. I never liked using mathematical equations to describe things anyway - it is always much simpler to have some kind of example to explain your phenomenon, some concrete thing. It is just so difficult to keep so many abstractions in your head. Or at least it is for me.
So I will present a clear (clear to me, anyway) explanation of why R1, R2, R3, and R4 seem to me as they should not be equivalent to each other. (Obviously, if they are equivalent, then the Q will be equivalent as well - I am with you there).
So R1 is the first player's results. They can be anything, since we so far have no constraints (other, of course, than the fact that you can't do better than 1st place or worse than 4th, and the artificial no-ties constraint we've been using). But now, you go and pick R2. But now we have constraints. For every one of the four games, there is one result for the second player which he cannot achieve, because the first player already achieved it. And for the third player, there are two results he cannot achieve. The fourth player is entirely deterministic. If we are calculating the expectation value of R2...
Okay, I think I just got our problem. You are calculating the expectation value for each individual player? This is not what I am calculating. That is absolutely pointless - it's trivially obvious that every player will expect to score the same number of points, if we assume them to be of equal skill going in, and all games independent. I fail to see the need to use any math to prove this, and moreover,  I fail to see its importance. IS that what you're calculating?

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Quote
This is absolutely a worse question to ask, because it fails to model what actually happens - i.e. that the threshold to qualify is NOT fixed. Which was the whole point of my other calculation. Indeed, I can see no reason that this is better to ask, other than it is easier to calculate. Of course, this way, things will track pretty well with the chart above, but even so, let's take a look at your math...
You have to do things in steps. What you were calculating IS the probability of qualification given a threshold
No, that's what I did in the chart. What I was really trying to calculate though, was a function for what the threshold WILL BE. Which is what you need if you actually want to calculate the chance of qualifying, which is what we care about.
Quote
so I don't see why you are complaining. You have to know this first(or actually, know what I said is better to calculate first) then you can use the size of the tournament and the slots for the qualification along with this table to calculate the expected threshold and see if it favors 3p or 4p.
Well, yeah. But that's already done. I was moving on to the next step. I think we're totally just misunderstanding each other here.

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Quote
I wasn't saying that. My whole points were based on things you can't get from the table. However, now that I do look at the table, it's pretty clear to me that by-and-large, it does favour 3p. 4p gets a slight bump on exactly 16 and 22, but everywhere else, 3p has an advantage, and in some of these cases, quite a significant one.
I am not disagreeing with you on this particular table seemingly favoring 3p. It depends really on where your threshold will sit. But the point is there is no reason for the threshold to prefer sitting on places that favors 3p, on the contrary of what you have said. Also, while this particular table has more 3p favoring thresholds I don't see this as a general trend. You can try to make a table of say 12 game-series I'll say it will be different, but still oscillating.

The only thing that is beyond this table is when you weigh in the skills of the player. That is you have to consider players that win more often. As I've shown earlier with an example, as long as the expected score is the same for the player in question in 3p or 4p games, he will not be particularly favored. But if not, all this calculations are redundant. Obviously, when the expected score is different, he will in average score more in the format which he has a higher expected score. With a common threshold then of course he is going to have an advantage over there.

I still believe that, on top of the inherent gameplay factors and flaws in our assumptions, basically ALL of which help the players in 3p pods, there will be a general trend toward the favorability of 3p. Of course it depends on the thresholds, but what I am trying to argue above is that it is most likely for a threshold to sit somewhere which favors 3p. Of course you won't accept that, so fine, whatever. Don't think we're going to make progress on that. But at least, a 12-game series isn't what we're talking about HERE. Here we're talking about 4s

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Oh, you're talking about fourth SEAT. I thought you were talking about having one player who was just really terrible no matter where he was.
Seating order will tend to bring everyone closer to average over time, no? (which obviously doesn't affect Mr. Average)
Yeah, I guess it is sort of obvious. Sorry if I phrase it in a confusing way. But the point is that this effect indeed brings down the expected score for a good player, in this scoring scheme.

Actually, in principle one way to compensate this effect is to make it something like (6420) and (5 3 1) for 4p and 3p. (average not changing so the average player again is not affected. Good player will score less in a 3p game comparatively.) But somehow it is a terrible idea for a 4 game series. With threshold at 20 now in 3p games the player has to win all games to qualify!
Right. My entire point throughout all of this is that it's impossible to make a fair system.

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So R1 is the first player's results. They can be anything, since we so far have no constraints (other, of course, than the fact that you can't do better than 1st place or worse than 4th, and the artificial no-ties constraint we've been using). But now, you go and pick R2. But now we have constraints. For every one of the four games, there is one result for the second player which he cannot achieve, because the first player already achieved it. And for the third player, there are two results he cannot achieve. The fourth player is entirely deterministic. If we are calculating the expectation value of R2...
Okay, I think I just got our problem. You are calculating the expectation value for each individual player? This is not what I am calculating. That is absolutely pointless - it's trivially obvious that every player will expect to score the same number of points, if we assume them to be of equal skill going in, and all games independent. I fail to see the need to use any math to prove this, and moreover,  I fail to see its importance. IS that what you're calculating?
Yeah, I can see your problem here. That is why sometimes you do need some kind of abstraction.

What you are saying is completely true in the first paragraph. HOWEVER, as I said, I am calculating the expected number of players to qualify from a 4p prod, including the effect you listed in the first paragraph. So the point I am trying to show is that the correlation between the record of individual players does not change the expected number of players to qualify.

To give a concrete example, maybe I should just use numbers. If threshold=24:
(i) assume no correlations, each player has 1/256 chance to score 4 wins. The possible number of qualified players ranges from 0 to 4 though. The expected number of players to qualify from this 4 player prod. is just

1*4*(1/256)*(255/256)^3+2*6*(1/256)^2*(255/256)^2+3*4*(1/256)^3(255/256)+4*(1/256)^4=4*(1/256)=1/64.

The first half is just to count the number of qualified players times the chance for that to happen. The first equality you can either just calculate or prove by binomial expansions. Or you can use the physical argument that since four players are independent, the average number of players to qualify should be equal to the sum of the chance of each player to qualify.

(ii) now assume correlations. So only 1 out of 4 can qualify IN ANY GIVEN INSTANCE. You have calculated this, the chance for there is any player to acheive 4 wins is 216/13824=1/64. So the expected number of players to qualify is
 
1*(1/64)+2*0+3*0+4*0=1/64.

See, the point is that with or without the constraint between records, the expected number of players to qualify is the same. While I only use 24 as threshold and assume each player has equal skill, this statement is general, and works for any threshold and any player skill. The proof is what I have written there.

So the point that confuses you is I think, that the constraint is always there in any given instance. But when you average over all instances and see the average number of players to qualify from the pod, the constraint has no effect.

This point is indeed not intuitive, and that is why you need a little bit of abstraction to see it. Mathematically this is quite obvious though; it is just that the expectation value is the first moment so it does not care about correlations. If you try to calculate the variance of the number of qualified players in a pod given a threshold, then it will depend on this constraint.

Quote
Well, yeah. But that's already done. I was moving on to the next step. I think we're totally just misunderstanding each other here.
Ok, maybe you are trying to move to the next step. My point is that the calculation you've done midway (getting 216/13824 and other things) does not actually give new information, or move you to the next step. And what you say about the next step are pure speculations.

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I still believe that, on top of the inherent gameplay factors and flaws in our assumptions, basically ALL of which help the players in 3p pods, there will be a general trend toward the favorability of 3p. Of course it depends on the thresholds, but what I am trying to argue above is that it is most likely for a threshold to sit somewhere which favors 3p. Of course you won't accept that, so fine, whatever. Don't think we're going to make progress on that. But at least, a 12-game series isn't what we're talking about HERE. Here we're talking about 4s
1. I am trying to convince you your opinion is wrong. I give numbers and reasons behind it. It is not that I am not accepting any thing you say, it is just that you did not provide anything to support it. You know, your argument I feel is like this:
If it requires all wins to qualify, then 3p pods is definitely more favorable. And this generalizes.
The first part I agree. Sure you can also generalize this to situation with a fixed number of qualifying slots and a very large playing pool, since in this case it may require you to win it all. But it's not really true for the general case. I dunno how to tell you this in a different way except listing the probabilities/expected number to qualify as a function of the threshold. There is really no lock in effect for the threshold to always stay somewhere which favors 3p.

Well, I dunno if this will help, but the relation of fixing the threshold and fixing the number of qualified slots is pretty much the same as fixing the density or fixing the chemical potential. ie, you can calculate things using canonical ensemble or grand canonical ensemble, but the result in average will not change.

Quote
Right. My entire point throughout all of this is that it's impossible to make a fair system.
I thought your entire point is that for any fair system (to average players) 3p is generally going to be favorable for skilled players. I am saying this is not true, and there is no general trend toward 3p pods except at the very very top (all wins to proceed).
Heck, I don't even agree it is impossible to make a fair system. I think it is entirely possible. The problem we are facing here is some discretization error which is a technical problem instead of a fundamental problem. (Well it is funamental and inherit but I mean, that kind of thing is always there, can only be solved by a larger number of games. There is nothing fundamentally wrong to compare results from 3p and 4p games using some scale, if we disregard the inherit difference between 3p and 4p games and just consider it from how-many-people-can-win perspective, as we are doing here. And we can even compensate some of the inherit difference between the games by changing our point scale.
And we don't even need it to be perfectly fair. As long as the unfairness is quite a bit smaller than the intrinsic random factor, we are in good shape.
« Last Edit: June 27, 2012, 01:48:50 am by timchen »
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So R1 is the first player's results. They can be anything, since we so far have no constraints (other, of course, than the fact that you can't do better than 1st place or worse than 4th, and the artificial no-ties constraint we've been using). But now, you go and pick R2. But now we have constraints. For every one of the four games, there is one result for the second player which he cannot achieve, because the first player already achieved it. And for the third player, there are two results he cannot achieve. The fourth player is entirely deterministic. If we are calculating the expectation value of R2...
Okay, I think I just got our problem. You are calculating the expectation value for each individual player? This is not what I am calculating. That is absolutely pointless - it's trivially obvious that every player will expect to score the same number of points, if we assume them to be of equal skill going in, and all games independent. I fail to see the need to use any math to prove this, and moreover,  I fail to see its importance. IS that what you're calculating?
Yeah, I can see your problem here. That is why sometimes you do need some kind of abstraction.
No, I don't think so. The entire problem is BECAUSE you're using abstractions. BECAUSE of that, I don't know what you're talking about. Which leads to us misunderstanding each other. Which is the crux of our problems.
Quote

What you are saying is completely true in the first paragraph. HOWEVER, as I said, I am calculating the expected number of players to qualify from a 4p prod, including the effect you listed in the first paragraph. So the point I am trying to show is that the correlation between the record of individual players does not change the expected number of players to qualify.

To give a concrete example, maybe I should just use numbers. If threshold=24:
(i) assume no correlations, each player has 1/256 chance to score 4 wins. The possible number of qualified players ranges from 0 to 4 though. The expected number of players to qualify from this 4 player prod. is just
1*4*(1/256)*(255/256)^3+2*6*(1/256)^2*(255/256)^2+3*4*(1/256)^3(255/256)+4*(1/256)^4=4*(1/256)=1/64.
The first half is just to count the number of qualified players times the chance for that to happen. The first equality you can either just calculate or prove by binomial expansions. Or you can use the physical argument that since four players are independent, the average number of players to qualify should be equal to the sum of the chance of each player to qualify.
(ii) now assume correlations. So only 1 out of 4 can qualify IN ANY GIVEN INSTANCE. You have calculated this, the chance for there is any player to acheive 4 wins is 216/13824=1/64. So the expected number of players to qualify is
1*(1/64)+2*0+3*0+4*0=1/64.
See, the point is that with or without the constraint between records, the expected number of players to qualify is the same. While I only use 24 as threshold and assume each player has equal skill, this statement is general, and works for any threshold and any player skill. The proof is what I have written there.

So the point that confuses you is I think, that the constraint is always there in any given instance. But when you average over all instances and see the average number of players to qualify from the pod, the constraint has no effect.

This point is indeed not intuitive, and that is why you need a little bit of abstraction to see it. Mathematically this is quite obvious though; it is just that the expectation value is the first moment so it does not care about correlations. If you try to calculate the variance of the number of qualified players in a pod given a threshold, then it will depend on this constraint.

Quote
Well, yeah. But that's already done. I was moving on to the next step. I think we're totally just misunderstanding each other here.
Ok, maybe you are trying to move to the next step. My point is that the calculation you've done midway (getting 216/13824 and other things) does not actually give new information, or move you to the next step. And what you say about the next step are pure speculations.

Quote
I still believe that, on top of the inherent gameplay factors and flaws in our assumptions, basically ALL of which help the players in 3p pods, there will be a general trend toward the favorability of 3p. Of course it depends on the thresholds, but what I am trying to argue above is that it is most likely for a threshold to sit somewhere which favors 3p. Of course you won't accept that, so fine, whatever. Don't think we're going to make progress on that. But at least, a 12-game series isn't what we're talking about HERE. Here we're talking about 4s
1. I am trying to convince you your opinion is wrong. I give numbers and reasons behind it. It is not that I am not accepting any thing you say, it is just that you did not provide anything to support it. You know, your argument I feel is like this:
If it requires all wins to qualify, then 3p pods is definitely more favorable. And this generalizes.
The first part I agree. Sure you can also generalize this to situation with a fixed number of qualifying slots and a very large playing pool, since in this case it may require you to win it all. But it's not really true for the general case. I dunno how to tell you this in a different way except listing the probabilities/expected number to qualify as a function of the threshold. There is really no lock in effect for the threshold to always stay somewhere which favors 3p.

Well, I dunno if this will help, but the relation of fixing the threshold and fixing the number of qualified slots is pretty much the same as fixing the density or fixing the chemical potential. ie, you can calculate things using canonical ensemble or grand canonical ensemble, but the result in average will not change.
I had this long response typed up, but then I realized, we're just making no progress here. We're each saying the same things over and over, and it's going nowhere. So there's not much point, is there?

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Quote
Right. My entire point throughout all of this is that it's impossible to make a fair system.
I thought your entire point is that for any fair system (to average players) 3p is generally going to be favorable for skilled players. I am saying this is not true, and there is no general trend toward 3p pods except at the very very top (all wins to proceed).
Heck, I don't even agree it is impossible to make a fair system. I think it is entirely possible. The problem we are facing here is some discretization error which is a technical problem instead of a fundamental problem. (Well it is funamental and inherit but I mean, that kind of thing is always there, can only be solved by a larger number of games. There is nothing fundamentally wrong to compare results from 3p and 4p games using some scale, if we disregard the inherit difference between 3p and 4p games and just consider it from how-many-people-can-win perspective, as we are doing here. And we can even compensate some of the inherit difference between the games by changing our point scale.
And we don't even need it to be perfectly fair. As long as the unfairness is quite a bit smaller than the intrinsic random factor, we are in good shape.
Disagree with you entirely there.

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I don't think I am saying the same thing. Isn't there an example for you to directly see what I am saying? How is that not concrete enough? Abstraction only helps when getting the proof. The example there is not abstract at all.

BTW, I don't think I misunderstand you. And I don't think you misunderstand me (in any consistent way anyway); it's more like you don't understand me.
« Last Edit: June 26, 2012, 05:57:38 pm by timchen »
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zxcvbn2

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Just as an FYI to theory and/or my opponents, I can't currently log in w/ my gmail account (This is the what happens when I try: http://imgur.com/uHa2y). If this issue doesn't resolve itself, like it has in the past, I'll be there under a different name (My Second Account).
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Your literal name is "My Second Account"?
Also, I'm guessing the man you really need to let know this is rrenaud.

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Just as an FYI to theory and/or my opponents, I can't currently log in w/ my gmail account (This is the what happens when I try: http://imgur.com/uHa2y). If this issue doesn't resolve itself, like it has in the past, I'll be there under a different name (My Second Account).

I don't understand what you mean.  Can you rephrase in a way that includes several unbroken paragraphs of mathematical arguments?
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zxcvbn2

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Your literal name is "My Second Account"?
Also, I'm guessing the man you really need to let know this is rrenaud.

That's correct. I'm sitting in the tournament lobby right now. I'll PM rrenaud, thanks.
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So I have just a few questions about the Semifinals/ Finals. I hope I'm not pestering you too much.

First of all, how will the semifinal matches be decided? Will they be seeded, random, by qualifying day?

Second, what is the actual format of the match? Is it just one game winner take all?

And lastly, what kind of timeframe do we have to complete those games?I know it was very soon, but when exactly are the games to be completed?

Thanks in advance! :)

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Semifinals will likely be seeded in some form, though we will probably rotate the games.

I think we'll do something similar: everyone plays 4 games.  Can be persuaded otherwise though.

Finally, it must finish between June 30 and July 2.  No exceptions.

Let's also discuss 3p v 4p.  On the one hand, we had two 24pt qualifiers from 3p pods.  On the other, what more can you ask of them than winning all their games?  Also, dghunter went 1-1-1-3 but couldn't advance because he was in a 3p pod.

Finally, let's discuss the points system.  Do we keep it in place for Day 3 - Day 4 or revert back to wins?
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Captain_Frisk

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Semifinals will likely be seeded in some form, though we will probably rotate the games.

I think we'll do something similar: everyone plays 4 games.  Can be persuaded otherwise though.

Finally, it must finish between June 30 and July 2.  No exceptions.

Let's also discuss 3p v 4p.  On the one hand, we had two 24pt qualifiers from 3p pods.  On the other, what more can you ask of them than winning all their games?  Also, dghunter went 1-1-1-3 but couldn't advance because he was in a 3p pod.

Finally, let's discuss the points system.  Do we keep it in place for Day 3 - Day 4 or revert back to wins?

I'm in favor of points, but I tend to favor more reward for winning.  1st place - 2nd place > 3rd place - 4th place.  5-3-1-0

As for 4p vs 3p... I strongly encourage drafting warm bodies out of the general lobby to round it out.

If all players had equal skill and there was no seating advantage: A player has a .39% chance of getting a perfect score from a 4p pod.    Same conditions - a player has a 1.23% chance of getting a perfect score from a 3p pod... that's over 3 times as good - not to mention that the 3p games are going to be more skill based - so it will be easier for a higher skilled player to advance well out of there.

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WanderingWinder

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I still think 3p is a massive advantage over 4p, I think the established math bears that out, and would even moreso in a more generalized case, though I guess there are some who disagree with that - and I don't think anyone's going to actually go do all that math.

On the other hand, I think a much bigger effect will be in place when you take into account the different skill levels of the players. It is much easier for a highly skilled player to demonstrate superiority in a small series of 3p matches than in a small series of 4p matches. You have a lot more control over what happens in every individual game, and the games also last longer. I think this is further compounded by the seating order effect being a good bit larger in 4p than in 3p. Overall, it is not clear to me that it is easier to 1-1-1-2 in a 4p than to 1-1-1-1 in a 3p (in fact, I suspect the opposite is true), or even to 1-1-1-1 in a 3p than to 1-1-2-2 in a 4p (which seem close to me; of course this is subjective, as it's extremely difficult to measure this - impossible on the data we have).
So I would try to avoid different pod sizes as much as possible.

I like points in general, and apparently this is what's happening at nationals/worlds? I'd suggest that format, if possible, because this qualifies for that. Of course, my preferred 4p point system would be something along the lines of 6/3/1/0.

Of course, if you do just wins, this gives an even huger advantage to any 3p guys....


Edit: cleaned up a stray line at the end.
« Last Edit: June 27, 2012, 10:42:27 am by WanderingWinder »
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Powerman

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Could you add an extra field to the signup sheet that says "indicate preferred choice: 3p or 4p" and then place people that way, with the number of qualifiers proportional to the number of players in each?  (IE: if it's half and half, 2 qualifiers from 3P and 2 qualifiers from 4P)  You might have to juggle around a few people, but assuming you can either get it to be half-half or 1:3 (3:1) this could alleviate any problems of competing between 4P and 3P.
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theory

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Quote
Of course, my preferred 4p point system would be something along the lines of 6/3/1/0.

Of course, if you do just wins, this gives an even huger advantage to any 3p guys....
If we're doing
Isn't this a contradiction?

Could you add an extra field to the signup sheet that says "indicate preferred choice: 3p or 4p" and then place people that way, with the number of qualifiers proportional to the number of players in each?  (IE: if it's half and half, 2 qualifiers from 3P and 2 qualifiers from 4P)  You might have to juggle around a few people, but assuming you can either get it to be half-half or 1:3 (3:1) this could alleviate any problems of competing between 4P and 3P.

I'd prefer not to do that, since that makes dropouts and no-shows even worse.
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theory

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Here is my concern about how we're addressing the 3p-4p unfairness: are we trying to make it "fair" not by removing advantage/disadvantage, but by giving a 50/50 chance of a big advantage and a 50/50 chance of a big disadvantage? 
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Quote
Of course, my preferred 4p point system would be something along the lines of 6/3/1/0.

Of course, if you do just wins, this gives an even huger advantage to any 3p guys....
If we're doing
Isn't this a contradiction?

The reason this isn't a contradiction is because I posted no 3p points system. I really don't think you can make a sufficiently fair one of those - pretty sure the one last night is very unfair, but on the other hand, I can't think of one and have yet to see one that isn't.

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I still think 3p is a massive advantage over 4p, I think the established math bears that out, and would even moreso in a more generalized case, though I guess there are some who disagree with that - and I don't think anyone's going to actually go do all that math.
Completely untrue. I have shown you enough math how you should do it and you just ignore it. Especially if you are talking about equal player skills.

@frisk: if you've read my previous posts, yes, it is 3 times easier to score 1-1-1-1 in 3p game assuming equal player skills. But that is still above the threshold we have for the two days.

Quote
On the other hand, I think a much bigger effect will be in place when you take into account the different skill levels of the players. It is much easier for a highly skilled player to demonstrate superiority in a small series of 3p matches than in a small series of 4p matches. You have a lot more control over what happens in every individual game, and the games also last longer. I think this is further compounded by the seating order effect being a good bit larger in 4p than in 3p. Overall, it is not clear to me that it is easier to 1-1-1-2 in a 4p than to 1-1-1-1 in a 3p (in fact, I suspect the opposite is true), or even to 1-1-1-1 in a 3p than to 1-1-2-2 in a 4p (which seem close to me; of course this is subjective, as it's extremely difficult to measure this - impossible on the data we have).
So I would try to avoid different pod sizes as much as possible.
Well, I think your reasons are fine and sound, but still, the estimation seems a bit off to me. If you really think so, I think you can request yourself to be in a 3p pod but forfeit the chance to qualify unless you score 1-1-1-1. IMHO saying it is easier than 1-1-2-2 in 4p is somewhat crazy. I would say it is just a lucky day for 3p pod winners last night. Or to put another way: think about a 2p game. Must be easier to score a 4-0 record right? Still not that easy, even against random opponents!

Quote
I like points in general, and apparently this is what's happening at nationals/worlds? I'd suggest that format, if possible, because this qualifies for that. Of course, my preferred 4p point system would be something along the lines of 6/3/1/0.
This is absurd. In most cases this is the same as only counting wins. And I thought you don't like that? (1-1-2-2  now scores the same as 1-1-1-4. And you know, if you can get 3 wins in a 4p game usually you can avoid that 4. That makes 3 wins strictly better than 2 wins. It's ok, but I think it will be more luck dependent.)
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timchen

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Of course, my preferred 4p point system would be something along the lines of 6/3/1/0.

Of course, if you do just wins, this gives an even huger advantage to any 3p guys....
If we're doing
Isn't this a contradiction?

The reason this isn't a contradiction is because I posted no 3p points system. I really don't think you can make a sufficiently fair one of those - pretty sure the one last night is very unfair, but on the other hand, I can't think of one and have yet to see one that isn't.
Your opinion is that 3p games and 4p games cannot be compared. But I figure you are not really thinking about it.

 
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timchen

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Here is my concern about how we're addressing the 3p-4p unfairness: are we trying to make it "fair" not by removing advantage/disadvantage, but by giving a 50/50 chance of a big advantage and a 50/50 chance of a big disadvantage? 
I don't think in a 3p pod the good player has 50% chance to score 1-1-1-1. All in all I think if you score 1-1-1-1 you are worthy of being qualified. And you cannot change that with any scoring system. (like, if with some scale even 1-1-1-1 cannot qualify it is just outright unfair.)

So the inherit advantage of 3p vs. 4p game at the very top is something that cannot be changed by any point scale. Fortunately we are not there yet: the threshold is 1-1-1-2 for 3p and 1-1-2-2 for 4p. This means while the chance of scoring 1-1-1-1 is 3 times higher in 3p games it does not translate into a real world advantage (compensated by the chances at 4p to score 1-1-1-3 and 1-1-2-2.)

Then the question becomes whether it is too harsh to throw away 1-1-1-3. But here I am with WW. (What a rare thing to see recently! lol) I think under current format good players in 3p are favored. If you score a last place there, well, bad luck. But worse things can happen in 4p.
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zxcvbn2

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One thing to note about my games that I think does add to the conversation was that it was 3 players with one of them really low-ranked. I think after we got frustrated and assigned pods randomly, we made it a lot more likely for something like this to happen.

benji, our lvl 3 third player, was pretty much out of contention for 3 games (so it was just me and Mic Qsenoch, or in one game just me after connecting tournament-province first). In the other game, he makes a stupid end-game error, buying the last province with an estate when he could have gone duchy-duchy and played for the win.

My point is, when you have one low-ranked player in a 4p group, the effect is a lot smaller than it is in a 3p group, and I think that made it much easier in my group.
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ednever

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Two random ideas:

1- two pools. Divide total group in 2. Then round up/down to ensure one group divisible by 4 and one by 3. Two people move on from each group (or divide the group into 4. And only one moves on from the 1/4 group

2- theory and/or rr play to round numbers up to 4 per pod. I'm even fine if they end up qualifying. But if that makes people uncomfortable then, if they win the spot goes to the next highest

Ed
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theory

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Yesterday our cutoff was 20 points.  That means that if you are in 3p, you have to score 1-1-1-1 or 1-1-1-2; 1-1-1-3 will DQ you (as poor dghunter found out).

In 4p, you must score 1-1-1-1, 1-1-1-2, 1-1-2-2.  So the most unfair outcome is that a 4p 1-1-2-3 or 4p 1-2-2-2 will lose out to 3p 1-1-1-2.

I think I'm OK with that.
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zxcvbn2

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Semifinals will likely be seeded in some form, though we will probably rotate the games.

I think we'll do something similar: everyone plays 4 games.  Can be persuaded otherwise though.

Finally, it must finish between June 30 and July 2.  No exceptions.

Let's also discuss 3p v 4p.  On the one hand, we had two 24pt qualifiers from 3p pods.  On the other, what more can you ask of them than winning all their games?  Also, dghunter went 1-1-1-3 but couldn't advance because he was in a 3p pod.

Finally, let's discuss the points system.  Do we keep it in place for Day 3 - Day 4 or revert back to wins?

I worry about being able to get all sixteen players to agree on a two-hour time slot within 2-3 days. :/ I think it would probably be best to avoid rotating those games (as much as I was in favor of it for the prelims), so only four people have to schedule games.
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rrenaud

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The real problem was that I can't operate a spreadsheet, especially under time pressure.  Open .csv, edit, save (in spreadsheet format rather than csv), run script consuming CSV, don't see diff, freak out.  That was approximately my behavior last night, with a couple of loops. 

We should be able to just have 0 3p games.  See a hard problem, find ways to avoid solving it.  It's the engineering way.
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timchen

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One thing to note about my games that I think does add to the conversation was that it was 3 players with one of them really low-ranked. I think after we got frustrated and assigned pods randomly, we made it a lot more likely for something like this to happen.

benji, our lvl 3 third player, was pretty much out of contention for 3 games (so it was just me and Mic Qsenoch, or in one game just me after connecting tournament-province first). In the other game, he makes a stupid end-game error, buying the last province with an estate when he could have gone duchy-duchy and played for the win.

My point is, when you have one low-ranked player in a 4p group, the effect is a lot smaller than it is in a 3p group, and I think that made it much easier in my group.
Yeah, seeing this reminds me a thing.

How did the seeding work yesterday?
If we put players closer to average to 3p pools it can work a lot better. And this doesn't seem to hurt anyone's chance.
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theory

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I worry about being able to get all sixteen players to agree on a two-hour time slot within 2-3 days. :/ I think it would probably be best to avoid rotating those games (as much as I was in favor of it for the prelims), so only four people have to schedule games.


Is it unequivocally awful if we just make the four players that advance each day play their games with each other?
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zxcvbn2

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I worry about being able to get all sixteen players to agree on a two-hour time slot within 2-3 days. :/ I think it would probably be best to avoid rotating those games (as much as I was in favor of it for the prelims), so only four people have to schedule games.


Is it unequivocally awful if we just make the four players that advance each day play their games with each other?

I mean, the people who win on the first couple of days are more likely to be better players than the last couple of days, theoretically. I personally don't think it's a bad idea, though.
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timchen

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I would prefer some rotation. 16 players, one afternoon in the weekends should be enough time.
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Captain_Frisk

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I mean, the people who win on the first couple of days are more likely to be better players than the last couple of days, theoretically. I personally don't think it's a bad idea, though.

Unless more and more people keep showing up. 
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I would prefer some rotation. 16 players, one afternoon in the weekends should be enough time.

I would prefer to not play allfail or WW.
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I worry about being able to get all sixteen players to agree on a two-hour time slot within 2-3 days. :/ I think it would probably be best to avoid rotating those games (as much as I was in favor of it for the prelims), so only four people have to schedule games.


Is it unequivocally awful if we just make the four players that advance each day play their games with each other?
You could just have the 16 work out their availabilities, then group them thusly. I think the biggest concern is getting the games in here.
Fixed pods in the semis are way less bothersome to me than in the prelims, because essentially it's just whoever does best in your group makes it through, as opposed to 'random I have to outperform people which I have NO control over'.

yuma

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Is it such a bad idea to limit the pods to 4-player only? This of course means cutting out 1-3 people who were the last to register. But that is a penalty for waiting until the last minute. Or advertise that one more--or two or three--last minute registrant is needed at a first come first serve basis.

I would advocate for completely removing 3P as an option and then we get rid of the whole controversy. Yes, we are left with the "should we be able to include everyone" question. But to that the answer shouldn't always be yes. Real life games have caps and limits, so can this. If players really want to compete in this tourny--they should register early. If they don't... well register early next time.
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timchen

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The problem is that there will be no shows. And if you cut it off in the order of registration live so that people may wait and then realize that they cannot play... that doesn't look too good.
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zxcvbn2

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So I have an idea for doing semis-finals after seeing how WW-IP played their match. What if the four players play until a player falls X points behind the leader. This reduces the chances of any player who has zero chance of winning the group deciding who moves on, because if you don't stand a chance you aren't playing. It would take more games to decide, but games would get shorter as we go from 4p-3p-2p.

I'm just throwing that out there.
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So I have an idea for doing semis-finals after seeing how WW-IP played their match. What if the four players play until a player falls X points behind the leader. This reduces the chances of any player who has zero chance of winning the group deciding who moves on, because if you don't stand a chance you aren't playing. It would take more games to decide, but games would get shorter as we go from 4p-3p-2p.

I'm just throwing that out there.

It would match more closely to the WW-IP match scoring if the four players played a set number of games (say 6 games, as in WW v. IP), and if the winner doesn't win by more than X points (predetermined by the "fairness math"), then the players within X points of the leader continue playing (either in 2, 3 or 4 P format).  The match ends when the leader wins by more than X points, or after a longer number of matches (say 12 games), the player in the lead wins the war of attrition.

I am up for something like this, but I think the idea needs the fixed number of games (to nix eliminations based on bad/good initial draws).
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So I have an idea for doing semis-finals after seeing how WW-IP played their match. What if the four players play until a player falls X points behind the leader. This reduces the chances of any player who has zero chance of winning the group deciding who moves on, because if you don't stand a chance you aren't playing. It would take more games to decide, but games would get shorter as we go from 4p-3p-2p.

I'm just throwing that out there.
I think eliminations are a very bad idea. First and most importantly, you're changing the format, which is not something that is good. Now, instead of needing to be a good 4p player, you have to be good at all of them. Which isn't necessarily bad, but that wasn't laid out from the start, and this is qualifying for a pure 4p event. Also, there's fewer points up for grabs after an elimination, which means you're giving extra advantage to people who get the early wins.

theory

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Semifinalists will compete against each other.  The Day 1 semifinalists will play 4 games against each other, and so on. 

I have contacted the Day 1 and Day 2 semifinalists.
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timchen

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Oh no... I have to play WW...
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theory

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Sorry :)  You will settle your math arguments with Dominion!

More seriously, I spoke to some of the semifinalists.  It is just too hard to try to coordinate 16 people to narrow down into 1 in 4-5 days.
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toaster

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Semifinalists will compete against each other.  The Day 1 semifinalists will play 4 games against each other, and so on. 

I have contacted the Day 1 and Day 2 semifinalists.

Did you contact everyone?  I didn't receive anything from you.
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theory

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I thought I emailed you.

I guess I could PM too...
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toaster

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Oops, looks like I didn't use the email address I thought I did, either that or you pulled my email address from the forum instead of my registration...nevermind  :P
« Last Edit: June 28, 2012, 11:19:18 pm by toaster »
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Mic Qsenoch

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In the semifinals, will the winner of each pod advance or the top four based on some point system as in the previous rounds?
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theory

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Both -- in your group of 4, only one will advance, and it'll be based on the points system.  Though I doubt there'll be a difference between "points" and "most wins" when you're talking about a single group of 4.
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Sorry :)  You will settle your math arguments with Dominion!

More seriously, I spoke to some of the semifinalists.  It is just too hard to try to coordinate 16 people to narrow down into 1 in 4-5 days.
I don't actually have any math arguments with timchen. I haven't found any piece of math he's done wrong, that I can recollect. It is what goes into the math that I question.
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