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Randal FTW

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Who goes first?
« on: June 16, 2011, 02:35:40 pm »
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I was reading the First Player Advantage thread and WanderingWinder made a post saying how people that win more often go second more often and im wondering how iso determines turn order.
« Last Edit: June 16, 2011, 02:37:28 pm by Randal FTW »
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Jack Rudd

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Re: Who goes first?
« Reply #1 on: June 16, 2011, 02:45:22 pm »
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I think it splits the players into two groups, "players who have just lost a game" and "other players", and whenever a member of one group plays a member of the other, the player who just lost a game goes first.
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theory

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Re: Who goes first?
« Reply #2 on: June 16, 2011, 03:05:33 pm »
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I think it splits the players into two groups, "players who have just lost a game" and "other players", and whenever a member of one group plays a member of the other, the player who just lost a game goes first.
Yeah.  More generally, when the game starts, everyone who has just lost a game goes before everyone who has not.  This means that if you just won, you can't log out and log back in to try to go first.
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rod-

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Re: Who goes first?
« Reply #3 on: June 16, 2011, 04:39:22 pm »
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This explains why i keep getting stuck with 3rd position in 3p games!  I think i have a new algorithm for deciding whether or not to play a 2er or 3er.  (I've just lost 3 straight 3p games by a cumulative total of 3 points, all from the 3rd position with one fewer turn than everyone else and 8$ in hand, so I'm pretty much done sitting there!) If only i'd known not to play quick 2s to fix my losing streak in between!
« Last Edit: June 16, 2011, 04:48:45 pm by rod- »
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vidicate

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Re: Who goes first?
« Reply #4 on: June 16, 2011, 04:48:47 pm »
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This explains why i keep getting stuck with 3rd position in 3p games!  I think i have a new algorithm for deciding whether or not to play a 2er or 3er
Ha! Play 2p til I lose, Play 3p til I win? Love it.
edit: I wonder if people already do something like this to "game the rankings".
« Last Edit: June 16, 2011, 04:51:00 pm by vidicate »
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rrenaud

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Re: Who goes first?
« Reply #5 on: June 16, 2011, 05:01:13 pm »
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Captain_Frisk takes out his losses on level 20+s.

If he just lost, he won't play anyone rated lower than level 20.
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rod-

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Re: Who goes first?
« Reply #6 on: June 16, 2011, 05:10:08 pm »
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Captain_Frisk takes out his losses on level 20+s.
If he just lost, he won't play anyone rated lower than level 20.

That's quite sporting. 
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theory

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Re: Who goes first?
« Reply #7 on: June 16, 2011, 11:44:01 pm »
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To be fair, most 40+ won't even play < level 20, so I think Frisk is a little more generous than most in even playing most level <20's.  It's rough to take the chance and play a level 9 who maybe isn't that good but has sure studied CouncilRoom and whacks you silly with a KC Mountebank on Turn 7.

The true way to game this is every time you win, play against an unregged player, resign immediately, then play regular games as P1.  But then you have a very ugly councilroom record...
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WanderingWinder

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Re: Who goes first?
« Reply #8 on: June 17, 2011, 12:21:15 am »
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I automatch against any reg. But I generally only accept challenges from 25+. Of course, I'm not 40+, though I was a couple of days last week. The only way I do anything to "game" the system at all really though is to almost always make sure I "win-quit".
I actually haven't looked at the math that close - is there a way to see what % you need to score to maintain a certain level difference? Obviously +/-0 is 50%, but is +1 like 51%, 60%, 90%, where? and +2, +3, so on. Is this out there somewhere?

rspeer

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Re: Who goes first?
« Reply #9 on: June 17, 2011, 05:03:17 am »
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I automatch against any reg. But I generally only accept challenges from 25+. Of course, I'm not 40+, though I was a couple of days last week. The only way I do anything to "game" the system at all really though is to almost always make sure I "win-quit".
I actually haven't looked at the math that close - is there a way to see what % you need to score to maintain a certain level difference? Obviously +/-0 is 50%, but is +1 like 51%, 60%, 90%, where? and +2, +3, so on. Is this out there somewhere?

Well, it's not just about how many games you win, it's who you beat. Just like in chess or other games with a global ranking system. But there's a related question I'm curious about too: how does a given TrueSkill difference translate into win probability?
I can attempt to answer this by running TrueSkill on my copy of the CouncilRoom database, which might not be exactly the same as when DougZ runs it but should be close. And I'm not running through all the games, just letting it converge until I get bored.

Now, you can compare skill values, or you can compare levels (minimum proven skill values). There's a lot of uncertainty when you compare levels, because people who haven't "proven themselves" have levels far lower than their actual skill. I ran it, though, and to summarize the results:
If you're up by 5 levels, you have about a 60% chance of winning. At 10 levels up, you have about a 2/3 chance. And it hovers around a 2/3 chance as the difference gets higher, up until it gets lost in the noise.

From TrueSkill's point of view, it's more meaningful to compare the players' mean skills, not their levels. And these probabilities are interesting enough that I'll make a table of them.

diff  win prob.
0     50.0%
1     54.2%
2     57.6%
3     60.0%
4     63.5%
5     68.6%
6     71.5%
7     75.5%
8     78.7%
9     82.2%
10    82.6%
11    87.7%
12    90.8%
13    93.9%
14    97.6%
15    97.3%
16    98.6%
>=17  100%-ish

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WanderingWinder

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Re: Who goes first?
« Reply #10 on: June 17, 2011, 08:42:21 am »
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I automatch against any reg. But I generally only accept challenges from 25+. Of course, I'm not 40+, though I was a couple of days last week. The only way I do anything to "game" the system at all really though is to almost always make sure I "win-quit".
I actually haven't looked at the math that close - is there a way to see what % you need to score to maintain a certain level difference? Obviously +/-0 is 50%, but is +1 like 51%, 60%, 90%, where? and +2, +3, so on. Is this out there somewhere?

Well, it's not just about how many games you win, it's who you beat. Just like in chess or other games with a global ranking system.
This is exactly what I was asking about. And I meant to say level difference in the mean, not the levels as posted on the leaderboard. But you did what I was looking for anyway, but these numbers don't make sense with each other quite - easiest way to see that is by looking at difference ranges 13-16, but if you just look at the differences between consecutive numbers, you get a sequence that doesn't make a lot of sense:
1-0      4.2
2-1      3.4
3-2      2.4
4-3      3.5
5-4      5.1
6-5      2.9
7-6      4.0
8-7      3.2
9-8      3.5
10-9     0.4
11-10   5.1   
12-11   3.1   
13-12   3.1   
14-13   3.7   
15-14   -0.3   
16-15   1.3   
17-16   1.4ish   

theory

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Re: Who goes first?
« Reply #11 on: June 17, 2011, 08:43:39 am »
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This is quite interesting.  I wonder if WanderingWinder might have been asking a slightly different question: i.e., if I am of level X and I play 100 games against someone of level X +/- delta, how many do I need to win in order to keep my current level?  Or are these two questions the same?
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WanderingWinder

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Re: Who goes first?
« Reply #12 on: June 17, 2011, 08:49:44 am »
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theory, that is what I'm wondering about, but it should be the same question if the rating system jives at all with my understanding of rating systems from chess.

rrenaud

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Re: Who goes first?
« Reply #13 on: June 17, 2011, 10:21:08 am »
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From TrueSkill's point of view, it's more meaningful to compare the players' mean skills, not their levels. And these probabilities are interesting enough that I'll make a table of them.

diff  win prob.
0     50.0%
1     54.2%
2     57.6%
3     60.0%
4     63.5%
5     68.6%
6     71.5%
7     75.5%
8     78.7%
9     82.2%
10    82.6%
11    87.7%
12    90.8%
13    93.9%
14    97.6%
15    97.3%
16    98.6%
>=17  100%-ish



What did you do here?  The player variance matters a lot in terms of pushing probabilities toward 50% regardless of mean difference.  I don't see how you can reasonably ignore variance and still get output from trueskill.
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Kuildeous

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Re: Who goes first?
« Reply #14 on: June 17, 2011, 10:25:43 am »
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I didn't realize Isotropic had an algorithm for determining start player. That's pretty neat.

In F2F games, we start our first game randomly (I personally like shuffling a hand of N-1 Curses and a Gold and have players draw cards to see who goes first).

After that first game, the rule is that the first player is the one to the left of the winner of the previous game. Since going first is an advantage, the winner can struggle in the next game.
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DStu

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Re: Who goes first?
« Reply #15 on: June 17, 2011, 10:33:50 am »
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I automatch against any reg. But I generally only accept challenges from 25+. Of course, I'm not 40+, though I was a couple of days last week. The only way I do anything to "game" the system at all really though is to almost always make sure I "win-quit".
I actually haven't looked at the math that close - is there a way to see what % you need to score to maintain a certain level difference? Obviously +/-0 is 50%, but is +1 like 51%, 60%, 90%, where? and +2, +3, so on. Is this out there somewhere?

Well, it's not just about how many games you win, it's who you beat. Just like in chess or other games with a global ranking system.
This is exactly what I was asking about. And I meant to say level difference in the mean, not the levels as posted on the leaderboard. But you did what I was looking for anyway, but these numbers don't make sense with each other quite - easiest way to see that is by looking at difference ranges 13-16, but if you just look at the differences between consecutive numbers, you get a sequence that doesn't make a lot of sense:
1-0      4.2
2-1      3.4
3-2      2.4
4-3      3.5
5-4      5.1
6-5      2.9
7-6      4.0
8-7      3.2
9-8      3.5
10-9     0.4
11-10   5.1   
12-11   3.1   
13-12   3.1   
14-13   3.7   
15-14   -0.3   
16-15   1.3   
17-16   1.4ish   


Don't know what exactly you mean that doesn't make sense, but if is the oszilating and even negative values in the table, I think that's mostly noise. You don't have so many games in the ~15-Differences, and often the has not "converged" in the sense that either the skill of the player really changes, or trueskill has not adjusted the skill yet correctly. So if a new player 25+-23 (Level 2) plays against and old player 9+-7 (Level 2), that seems like a fair game in the Lobby, but it that's as well a 16 diff as if a 51+-7 (Level 44) plays against a 35+-7 (Level 28). While in the second example the prob. is quite high that the "Skill-difference" is really ~15, in the firstone it might be significantly higher or lower. Don't know which one is more likely or which games happen more often on isotropic.

The Trueskill system is not designed to give you a "win probability" given the "mean", but to give you the win probability given "mean" AND "variance". As we integrate out the variance here the noise can be expected to be much higher, and bias can be introduced by effects like new players entering with 25,25 in the system espescially in the combination with the mechanism by which players choose against whome they play (which will mostly be influenced by the level, not by mean and variance directly). So if you look at the table and fit a line, I think you can say that with each additional difference in the level, your winchance de/increases by 3-4%, at least until somewhere in the 10-15th.

PS@offtopic: Thanks theory, reloading does help.

edit:
Quote
What did you do here?  The player variance matters a lot in terms of pushing probabilities toward 50% regardless of mean difference.  I don't see how you can reasonably ignore variance and still get output from trueskill.
I think if the database is high enough, the variance should just integrate out and you get the avarage win probability given the difference of the mean (integrated over the "variance distribution of isotropic"). That is some kind of output, question is how much this matters for one individual player.
I think you are right, the more interesting table would 3/4-dimensional and show win-probability given (mean difference, variance pl1, variance pl2). Or for the beginning just restrict to variance of both player ~$(typical value for $type player on isotropic).
« Last Edit: June 17, 2011, 10:41:15 am by DStu »
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Randal FTW

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Re: Who goes first?
« Reply #16 on: June 17, 2011, 11:08:19 am »
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thanks for the responses, i like what the thread evolved into as well
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WanderingWinder

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Re: Who goes first?
« Reply #17 on: June 17, 2011, 11:36:35 am »
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Don't know what exactly you mean that doesn't make sense, but if is the oszilating and even negative values in the table, I think that's mostly noise.
Yeah, but if the noise is so big, the data is next to worthless.

livious

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Re: Who goes first?
« Reply #18 on: June 17, 2011, 01:11:20 pm »
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I'd like to see it switched to just a random player goes first.  It discourages re-matches since the winner knows they're definitely going second vs a... dunno 1/4 to 1/3 chance of going first if they play somebody else.  And other weird matching effects.
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theory

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Re: Who goes first?
« Reply #19 on: June 17, 2011, 01:16:46 pm »
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I'd like to see it switched to just a random player goes first.  It discourages re-matches since the winner knows they're definitely going second vs a... dunno 1/4 to 1/3 chance of going first if they play somebody else.  And other weird matching effects.
From what I understand, dougz goes to great lengths to make sure Isotropic plays by the Dominion rules as written.  And them's the rules: player who just won goes last.
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Thisisnotasmile

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Re: Who goes first?
« Reply #20 on: June 17, 2011, 01:17:40 pm »
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I'd like to see it switched to just a random player goes first.  It discourages re-matches since the winner knows they're definitely going second vs a... dunno 1/4 to 1/3 chance of going first if they play somebody else.  And other weird matching effects.

But the official rules state "When playing multiple games, the starting player is the player to the left of the winner of the last game". If you're having a rematch, you're playing multiple games. Thus, the winner of the previous game should go last.

(ninja'd but posting anyway)
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rrenaud

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Re: Who goes first?
« Reply #21 on: June 17, 2011, 01:22:14 pm »
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I'd like to see it switched to just a random player goes first.  It discourages re-matches since the winner knows they're definitely going second vs a... dunno 1/4 to 1/3 chance of going first if they play somebody else.  And other weird matching effects.

I think this is a nice point.  In order to maximize your "trueskill", If you've just won, don't rematch.  If you've just lost, go for it!
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rspeer

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Re: Who goes first?
« Reply #22 on: June 17, 2011, 02:07:37 pm »
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From TrueSkill's point of view, it's more meaningful to compare the players' mean skills, not their levels. And these probabilities are interesting enough that I'll make a table of them.

diff  win prob.
0     50.0%
1     54.2%
2     57.6%
3     60.0%
4     63.5%
5     68.6%
6     71.5%
7     75.5%
8     78.7%
9     82.2%
10    82.6%
11    87.7%
12    90.8%
13    93.9%
14    97.6%
15    97.3%
16    98.6%
>=17  100%-ish



What did you do here?  The player variance matters a lot in terms of pushing probabilities toward 50% regardless of mean difference.  I don't see how you can reasonably ignore variance and still get output from trueskill.


Well, I certainly can get output, I'm just ignoring one of the dimensions in order to get a concise table that one can use as a rule of thumb. Yes, variance is important.


To take this thread even further afield: does anyone know how the automatcher works? Does Isotropic just set up the first available game, or does it try to wait for a good match based on skill? (TrueSkill was designed to suggest matches, not just to output skill ratings.)
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rrenaud

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Re: Who goes first?
« Reply #23 on: June 17, 2011, 07:14:32 pm »
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So the table you posted is this?

Run trueskill for each game g between p1 and p2
  let d = abs(diff(mean(p1), mean(p2))
  associate win or loss with d

Then print win/total for each d?

I agree that makes sense, it basically the average win probability given level difference over all games on isotropic.
« Last Edit: June 17, 2011, 08:08:48 pm by rrenaud »
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rspeer

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Re: Who goes first?
« Reply #24 on: June 17, 2011, 08:14:43 pm »
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So the table you posted is this?

Run trueskill for each game g between p1 and p2
  let d = abs(diff(mean(p1), mean(p2))
  associate win or loss with d

Then print win/total for each d?

I agree that makes sense, it basically the average win probability given level difference over all games on isotropic.


Yep, you got it.
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