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Author Topic: The advantage of going first  (Read 12663 times)

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rrenaud

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Re: The advantage of going first
« Reply #25 on: November 14, 2011, 08:10:07 am »
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Anybody who has just lost a game will go after anyone who has not just lost a game. If you win a lot, you disproportionately go 2nd.

I knew this, but I only just thought (which probably makes me slow): surely this means that stats drawn from isotropic will under-rate the value of going first? If player one is on average worse skill-wise than player two, this seems unavoidable. I wonder if there's any way to work out by how much it undervalues it?

Here is a reasonably simple (and IMO, elegant) way to deal with the second player is better skill bias.

http://forum.dominionstrategy.com/index.php?topic=20.msg438#msg438

Quote
The third column is the marginal difference between first and second player with the first player skill bias removed (eg, pair up two players, only take the same number of games from when player A was first as when player B was first, if they only played one game, it will be thrown out, if A was first once, and B was first 10 times, take the 1 game from A, and 1 game at random from B).
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hgfalling

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Re: The advantage of going first
« Reply #26 on: November 14, 2011, 10:55:04 am »
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Another way to crudely estimate this effect in percentage terms is the following.

Assume the following:
  • Every player has a true "win probability" x1 or x2 that is their %win against an average player in a long match where both players go first equally often, and these win probabilities are roughly normal over the population with some standard deviation s.
  • There is a true 1st player advantage t, and win probabilities are linear so that if x1 plays x2 and goes first, w(x1)=t+x1-x2+1/2.
Now suppose we sample two players x1 and x2 randomly from the game-population. Assume they played an average player in their last game. Then x1 goes first with probability (1-x1+x2)/2  and x2 goes first with probability (1+x1-x2)/2.
The win rate of the player who goes first overall is t+1/2 - (x2-x1)^2
This is equal to the overall reported "first player win percentage".
x2-x1 is normally distributed around zero, so the expected value of its square is twice the variance of each part, so E(x2-x1)^2 = 2s^2.
Sloppy quick looking at win pcts around rank 100 suggests s~0.08 or so, which means that the suppression of t from the player selection bias would be around 1.2% (win pct). So if overall CR data suggests that the first player wins 55-45 (what is the actual number?), an unbiased number would be perhaps 56-44 or so.

Now this model is pretty crude, but it would be easily adapted to monte carlo if someone had different priors on the composition of the playing population really wanted to know the answer to this. :)
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fellowmartian

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Re: The advantage of going first
« Reply #27 on: November 14, 2011, 12:42:23 pm »
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I like both of those ideas. The first makes me think of the idea of 'beating the spread'. We used to do that in an American Football game I used to play ('Paydirt'), which was supposed to simulate the teams and how good they'd been each year. If you were, say, San Francisco circa '97 playing Tampa Bay of the same year, you'd have to win by 20 points or so to actually 'win' (and of course, the Buccaneers player could claim a 'win' if they kept it tighter than that). It was elegant and quite cool.

A one per cent difference... sounds less than I'd have thought, but I guess even good players, in either win position, lose a reasonable amount, anyway (unless they're Paralyzed....).
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Fabian

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Re: The advantage of going first
« Reply #28 on: November 14, 2011, 06:01:04 pm »
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I'm curious what kind of win percentages (strong) players have in the different positions. I have a gut feeling that the difference in win% from positions 1 and 2 is bigger for me than for most. Here are my councilroom stats, look out of the ordinary to you (During most of this sample, I've played the strongest players I could find, then in the last couple hundred games, I've mostly played +-10 auto-match)?

Pos 1 525-273-15, 1.317
Pos 2 507-424-25, 1.089

My theory on why this might be is that strong players will tend to have a greater advantage going first than weaker players (this includes me of course) have. So if I mostly play strong players while going second, their lead in tempo will be tough to overcome since they make fewer mistakes, thus allowing for fewer chances to catch up. The same is true in reverse; while I face pretty strong players when going first, I'm guessing I give them fewer chances than the average player to catch up on my lead in tempo. Sound reasonable? Does this hold true for other peoples' numbers?

Also, looking at these numbers, it's depressing (but also good I guess, heh) to think how much more often I play second than first :)
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ackack

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Re: The advantage of going first
« Reply #29 on: November 14, 2011, 06:08:48 pm »
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My stats, mostly unrestricted automatch:

Table position 1   552-224-10        1.417
Table position 2   518-342-13        1.203
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mischiefmaker

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Re: The advantage of going first
« Reply #30 on: November 14, 2011, 06:30:24 pm »
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Almost entirely +/-15 automatch:

Table position 1   354-185-8   1.309
Table position 2   316-205-9   1.209

As an aside, you can find out this data for yourself (though you won't have the context of what kinds of games people play) just by searching for them on councilroom. For instance, some of the top players who also post here:

theory
Table position 1   796-406-23   1.318
Table position 2   686-581-38   1.081

jonts26
Table position 1   912-371-23   1.463
Table position 2   939-540-27   1.291

WanderingWinder
Table position 1   1792-898-56   1.332
Table position 2   1533-1223-32   1.117

chwhite
Table position 1   1280-697-40   1.303
Table position 2   1222-908-35   1.162

guided
Table position 1   601-245-10   1.416
Table position 2   665-356-16   1.298

allfail (timchen)
Table position 1   677-219-11   1.508
Table position 2   884-392-17   1.386

That list is not particularly scientific, just some forum posters who I happen to recall are near the top of the leaderboard consistently, but of that list, ackack, theory, and WW are all above .200 differential (and theory has an even bigger split than you do).
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DG

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Re: The advantage of going first
« Reply #31 on: November 14, 2011, 07:33:09 pm »
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I don't think that these figures are overly reliable since they cover all sorts of matches, including 3 and 4 players, and different skill opponents. My win rates for seat 1 and 2 are almost identical to guided's, but my seat 3 and 4 win rates are much higher than seat 1 and 2. There are some low ranked isotropic players who can't play well enough to beat pure money, even going first with good draws, so if you're a good player beating those guys continuously then your rating will get inflated for both seats.
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guided

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Re: The advantage of going first
« Reply #32 on: November 14, 2011, 07:54:48 pm »
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And another datapoint, for the account I've been playing the last few months, almost all veto-mode automatch, mostly +/- 20 since I got the account up to the high 30s in level.

Table position 1   152-56-9   1.442
Table position 2   149-68-6   1.363

I've noticed (on both accounts) I tend to have a smaller differential than most of the other folks here. Couldn't tell you why.
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mischiefmaker

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Re: The advantage of going first
« Reply #33 on: November 14, 2011, 07:59:49 pm »
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Well...it's true that we don't know who these players are playing against (a caveat I listed), although that's part of the reason I picked avid forum posters since a good number of them have expressed their playing preferences in the past.

As for the >2p case, here are the % of >2p games/total games that each of the players have played:

theory: <1%
guided: <1%
allfail: ~1%
WW: ~2%
chwhite: ~4%
jonts: ~12%

Of those, I think only jonts really has a relatively significant number of >2p games, and even in his case only about 7% of his position 1/2 starts come in games that are not 2p. What I'm trying to say is, >2p games probably don't distort the stats very much. Opponent skill, maybe, but my impression is that none of the players on this list are beating up on noobs.
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mischiefmaker

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Re: The advantage of going first
« Reply #34 on: November 14, 2011, 08:02:05 pm »
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guided, I wonder if playing mostly veto-mode helps narrow the differential, since as 2p you can often reject cards that give significant first person advantage.
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guided

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Re: The advantage of going first
« Reply #35 on: November 14, 2011, 08:27:56 pm »
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guided, I wonder if playing mostly veto-mode helps narrow the differential, since as 2p you can often reject cards that give significant first person advantage.
At a certain point I did start accounting for seating position with my vetos... but more in 1st seat than 2nd. In 1st seat I more highly prioritize reducing variance, killing most cursing attacks on sight for example, whereas in 2nd seat I'm somewhat more likely to let stuff like Sea Hag go through.
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chwhite

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Re: The advantage of going first
« Reply #36 on: November 14, 2011, 08:48:34 pm »
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Well...it's true that we don't know who these players are playing against (a caveat I listed), although that's part of the reason I picked avid forum posters since a good number of them have expressed their playing preferences in the past.

As for the >2p case, here are the % of >2p games/total games that each of the players have played:

theory: <1%
guided: <1%
allfail: ~1%
WW: ~2%
chwhite: ~4%
jonts: ~12%

Of those, I think only jonts really has a relatively significant number of >2p games, and even in his case only about 7% of his position 1/2 starts come in games that are not 2p. What I'm trying to say is, >2p games probably don't distort the stats very much. Opponent skill, maybe, but my impression is that none of the players on this list are beating up on noobs.

These days I mostly play automatch +-15 (with veto and point counter set to "don't care"), though I played +-20 for awhile when it first came out and still do that sometimes.  Before then, I'd avoid automatch because I figured it wouldn't be interesting for either of us to play level 0s, and of course if you go way back there are the games where I was a lower-ranked opponent myself.

There was a period of time where I would regularly be willing to play 3 and 4 player games with lower-ranked players then I'd accept a 2p game with, since I do like multiplayer, and most high-level players are 2p exclusively; this is probably why my 3p win rate is so high.  This kind of fell by the wayside when automatch was improved, but I still allow multiplayer games in automatch and enjoy playing them on the rare occasions they come up.
« Last Edit: November 14, 2011, 08:51:12 pm by chwhite »
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witchwitchwitch

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Re: The advantage of going first
« Reply #37 on: November 24, 2011, 04:29:46 am »
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IMHO going first is always an advantage, since with attack cards the first player may attack first (think about using Militia)
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