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Author Topic: First player advantage; was Donald mistaken?  (Read 10723 times)

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GendoIkari

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First player advantage; was Donald mistaken?
« on: November 08, 2011, 02:48:34 pm »
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Donald comments on first player advantage here: http://forum.dominionstrategy.com/index.php?topic=91.0. His comments seemed to make sense at first, but since reading that, I've read several other posts in other threads that talk about how much of an advantage going first is. The place where it seems to matter the most is when cursing or Ambassador is available; because the second player will have a curse shuffled in on his first shuffle far more often than the first player will; when both players have identical openings. A few questions:

  • What are the CouncilRoom statistics on this? Can it show a percentage of all games that were won by player 1?
  • Are there other factors aside from early cursing/Ambassador that give player 1 an advantage?

Also, it seems to me that the first player getting an additional turn should happen about half of the time in 2-player games, which means that this is a bit more than just a "potential" advantage... it's an advantage half of the time, which isn't insignificant. Can CouncilRoom show data on how often the first player got more turns than the second player? Is there a reason why it shouldn't be about half of the time? The only reason I can think of that it might not be is that if both players play essentially equally, then player 2 should be able to buy a Province each time player 1 buys a Province; which would cause the game to end after each player has had the same number of turns.
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ftl

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Re: First player advantage; was Donald mistaken?
« Reply #1 on: November 08, 2011, 03:31:26 pm »
+1

Early attacks of any sort, not just cursing. If we both open Militia, player 1 is less likely to get screwed out of a pre-second-shuffle Gold.
 
Running low on piles of any sort. In games where there's a race for some card, P1 has an advantage and is more likely to get that 6-4 split in their favor. (You might end up with the same number of turns in the game, but with P1 having had more turns of buying that key card which sets up the rest of the board.)

Mega-turn strategies. When you're aiming to have one huge turn, being the first one to get that turn is obviously a game-changer - even if the turn after, Player 2 COULD HAVE bought 6 provinces and a duchy, he can't do that if you launched your mega-turn first and bought 6 provinces and a duchy. That game may end with both players having an equal number of turns, but with player 1's advantage being a decider.

I don't know how to check Councilroom's stats for their entire player base. I  bet it's there I just don't know where it is. But if you look at any individual player, you can see their stats from different positions on the board. Theory, for example, wins 66% of his games when going first and 53% of his games going second, not counting ties. Pretty noticeable difference if you look at the numbers. (Your record is 48-15 in position 1, and 39-24 in position 2 - a pretty huge difference!)
« Last Edit: November 08, 2011, 03:36:00 pm by ftl »
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rrenaud

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Re: First player advantage; was Donald mistaken?
« Reply #2 on: November 08, 2011, 03:43:31 pm »
0

There have been a few threads on this.  This one is relatively long.

http://forum.dominionstrategy.com/index.php?topic=20.0
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rod-

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Re: First player advantage; was Donald mistaken?
« Reply #3 on: November 08, 2011, 04:08:27 pm »
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This topic was one that i took to heart and did some minor data analysis of.  The thread

http://forum.dominionstrategy.com/index.php?topic=54.msg723#msg723

Basic gist of it, since i'm really bad at talking about what data i'm presenting really means, is that the p1 win rate is .53 IF both players have an even number of turns, and .65 if they get the extra turn.  .55 games end with an uneven number of turns.  Strong attack cards such as Mountebank do not affect those numbers by much at all.  I didn't check militia and will probably do that right quick (The thought being that the first 3 turns are more important than the ones thereafter, and that mountebank is usually not bought on turn 1-2, where militia is) 

The net of that would be that the 1st player advantage is a real thing, amounting to around a 7% delta in winning percentage.  Of course, most people know that already.  What is more surprising is that the power cards don't seem to amplify that win percentage. 
(Although now that i look at the raw data, it seems that i have a little bit of noise included and will have to revise numbers somewhat)

Militia data: 
1p win %: .529
Uneven game %: .502
Uneven game 1p win %: .669

Moral of the story:  militia (being a strong attack that can always be opened with) Only slightly amplifies(if at all, .02 is a small number) 1p win percentage in games w/ uneven # of turns.

#games: 98470
#games 2p wins: 46301
#games 1p wins: 52169
#games uneven turns: 49486
#games uneven turns 1p wins: 33139
#games uneven turns 2p wins: 16347
#games even turns: 48984
#games even turns 1p wins: 19030
#games even turns 2p wins: 29954

***this data is from a rather old tarball of rrenaud pointed me to, and doesn't include even cornucopia cards.  It's dated Jun 17 11. 
« Last Edit: November 08, 2011, 04:11:00 pm by rod- »
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rod-

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Re: First player advantage; was Donald mistaken?
« Reply #4 on: November 08, 2011, 04:13:29 pm »
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quick note:  I found a bug in the parsing filter i was using (had a pattern match in error 10% of the time) and only 50% of games end on uneven turns, not 55%.  Militia is, therefore, not even remotely abnormal.
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Jack Rudd

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Re: First player advantage; was Donald mistaken?
« Reply #5 on: November 08, 2011, 04:49:54 pm »
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So the first-player advantage in Dominion is slightly greater than that in chess. (I think it's about 55% for chess.) I reckon that's close enough that all the normal tournament formats can be ported over without trouble.
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DG

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Re: First player advantage; was Donald mistaken?
« Reply #6 on: November 08, 2011, 06:53:12 pm »
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Quote
The only reason I can think of that it might not be is that if both players play essentially equally, then player 2 should be able to buy a Province each time player 1 buys a Province; which would cause the game to end after each player has had the same number of turns.

This point was already mentioned for other key cards but it specifically applies to provinces so I'll repeat it. Let's suppose that both players have bought three provinces, two left in the supply, and can reasonably expect to buy one each turn. If player 1 draws badly he can just buy a duchy and player 2 still has a dilemma, since if player 2 buys the penultimate province then player 1 can buy the last province next turn and win by three points (this is the penultimate province rule). Player 1's deck would in fact have to perform badly twice to lose. So player 2 probably also has to buy a duchy and any advantage from his draw was wasted. However, if player 1 can buy a province he is in a safe position and will expect a tie at worst, while the second player will probably lose if they can only buy a duchy.

More generally, if player 1 falls behind in purchasing key cards they can use first turn advantage to equalize. If player 2 falls behind in purchasing key cards they never have the opportunity to catch up until player 1 fails as well.
« Last Edit: November 08, 2011, 06:56:24 pm by DG »
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biopower

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Re: First player advantage; was Donald mistaken?
« Reply #7 on: November 08, 2011, 11:07:04 pm »
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This point was already mentioned for other key cards but it specifically applies to provinces so I'll repeat it. Let's suppose that both players have bought three provinces, two left in the supply, and can reasonably expect to buy one each turn. If player 1 draws badly he can just buy a duchy and player 2 still has a dilemma, since if player 2 buys the penultimate province then player 1 can buy the last province next turn and win by three points (this is the penultimate province rule). Player 1's deck would in fact have to perform badly twice to lose. So player 2 probably also has to buy a duchy and any advantage from his draw was wasted. However, if player 1 can buy a province he is in a safe position and will expect a tie at worst, while the second player will probably lose if they can only buy a duchy.

More generally, if player 1 falls behind in purchasing key cards they can use first turn advantage to equalize. If player 2 falls behind in purchasing key cards they never have the opportunity to catch up until player 1 fails as well.

If player 1 falls behind, the first turn advantage doesn't always equalize. Player 2 can break PPR for a win if the scores are tied prior to buying the penultimate province, whereas Player 1 can only break PPR for a tie if the scores are tied prior to buying the penultimate province.
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timchen

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Re: First player advantage; was Donald mistaken?
« Reply #8 on: November 08, 2011, 11:37:19 pm »
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Basic gist of it, since i'm really bad at talking about what data i'm presenting really means, is that the p1 win rate is .53 IF both players have an even number of turns, and .65 if they get the extra turn.  .55 games end with an uneven number of turns.  Strong attack cards such as Mountebank do not affect those numbers by much at all.  I didn't check militia and will probably do that right quick (The thought being that the first 3 turns are more important than the ones thereafter, and that mountebank is usually not bought on turn 1-2, where militia is) 

Not sure about the meaning of the first two numbers. Assuming the game is competitive enough that the first player will not end the game unless he can win, and the second player will not end the game unless he can at least tie, the first number should be 0 and the second number 1. The deviation from this number probably measures either how players play sub-optimally or how many games ended up to have a substantial difference between the players so that the players will just end it anyway.

On the other hand, I won't say a 7% first player advantage can really be felt in a single game. At least for me, having my single smithy at the end of the deck and then miss a shuffle (or worse, draw another smithy) feels a lot more painful than a head to head game when the first player edge out.
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DG

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Re: First player advantage; was Donald mistaken?
« Reply #9 on: November 09, 2011, 07:54:48 am »
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Quote
Player 2 can break PPR for a win if the scores are tied prior to buying the penultimate province

This is only true when player 2 has already outscored player 1 by a sufficient margin. If player 1 is allowed the lead before taking a turn he can just buy provinces knowing that the opponent can't match him.
The advantage of buying first is still there, it has just been overtaken by superior scoring.
« Last Edit: November 09, 2011, 10:29:26 am by DG »
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Empathy

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Re: First player advantage; was Donald mistaken?
« Reply #10 on: November 09, 2011, 10:10:22 am »
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quick note:  I found a bug in the parsing filter i was using (had a pattern match in error 10% of the time) and only 50% of games end on uneven turns, not 55%.  Militia is, therefore, not even remotely abnormal.

This analysis has an additional source of noise because second players are statistically better than first players. The first player advantage is *huge*.

First, why are second players on average better than first players? Because when you win a game, you play as player 2 in the next game.

The only way to compare first player and second player advantage is to work on the same player population. The easiest way to do that is just to pick a random player.

http://councilroom.com/player?player=WanderingWinder+

http://councilroom.com/player?player=Empathy

http://councilroom.com/player?player=Duh+Minion+

These examples illustrate well both my points. One is a top player with a lot of games, the second one is myself and the third one a lesser ranked player with a good amount of games.

First, the higher your winning probability, the more you play second. You can cheat your way through this rule by always ending on a win, and always playing after a loss (to maximize your games as first player). Sad but true.

Second, the difference in win rate  between first and second position *for a same player* is much higher than you would expect. In my case, it's the difference between a 0.7 and a 0.6 probability of winning.

Based on simulations or by picking players who have an equal number of first position and second position games, I think the number you got for first player advantage is 0.6 (though someone can correct me if I'm quoting the wrong number).

« Last Edit: November 09, 2011, 10:38:13 am by Empathy »
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rod-

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Re: First player advantage; was Donald mistaken?
« Reply #11 on: November 09, 2011, 10:47:34 am »
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The difference between 1st and 2nd for you and WW is still only 10%, which isn't an awful lot different than 7%.  It's certainly accurate that there are an uneven number of games with, say, WW playing 2nd vs playing 1st, but it's not *so* unevenly distributed. 

If you'd like to get a significant dataset that culls the entire set of games down to "only" N games with each player in each position to compensate, and still has around 100k games with each card, please go right ahead and do so.  However, I can't even pretend to write such a complicated script.  I'd be interested to see what it would do in cases such as Militia.

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DStu

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Re: First player advantage; was Donald mistaken?
« Reply #12 on: November 09, 2011, 10:52:05 am »
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btw. is there a good way to get lots of logs, like a monthly tarball or something? I know there is the daily one...
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DG

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Re: First player advantage; was Donald mistaken?
« Reply #13 on: November 09, 2011, 11:06:43 am »
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Attack cards such as militia extend the game and allow a better player more time to overtake first turn advantage, even if it means taking a hit on turn 3. Good players also defend better against attacks, or at least they should do.
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rrenaud

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Re: First player advantage; was Donald mistaken?
« Reply #14 on: November 09, 2011, 11:10:15 am »
+1

You could write a script that iterates over days in the month and does a wget or something similar.

Alternatively, you could use this script (which basically does that)

https://github.com/rrenaud/dominionstats/blob/master/scrape.py

and then rip out the command line handling imports, because it wants to be part of a standard dominion stats checkout.  That script prefers to get data from councilroom and then falls back on iso, so it means there is less load/bandwidth used for doug.  It's also smart about not downloading the same file twice, so you can periodically rescrape without worrying about wasting tons of bandwidth.

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