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hyku

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First player advantage
« on: June 13, 2011, 07:59:49 pm »
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I'd Like to discuss the inherent advantage of going first in dominion and if the rule for ties actually is enough to mitigate that. It seems to me that ties going to the person with the least turns is still not enough to makeup for going second (or third/fourth). Councilroom.com doesn't seem to have any data about who wins in relation to the turn so I'd like to know what people who have a lot of experience and games under their belt think. The second/third/fourth players do get to see what everyone ahead of them buys and be able to adapt but they'll face the attacks a turn earlier and in the endgame a loss of a turn is normally worth a province buy. So i was thinking that maybe there should be more advantage to going later and I thought of a couple variants that might help:

1) The second player starts with 1 VP chip, the 3rd player starts with 2 VP chips, and the fourth starts with 3 VP chips

2) Everyone gets the same amount of turns. So if the first player finishes a pile that would normally end the game, each other player gets to do one last turn.

I was thinking the best combination without making it a disadvantage to go first would be to keep the same rule about ties but add the first variant that each person after you has 1 VP more at the start.
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Teproc

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Re: First player advantage
« Reply #1 on: June 13, 2011, 08:26:46 pm »
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I always wondered about that but it turns out that CouncilRoom does have this stat available on the profile of each player, and the 1st player is consistently advantaged, so there you go (you can check the top player's profiles to verify this).

No idea how it is on multiplayer games but I don't see it being that different. The VP chip thing seems better than the other one, but I honestly don't think it's too big a deal either. It has a definitive effect, and not only on the fact that you can get one more turns, but also in that playing cards like Militia first gives you a pretty big advantage, but I do think it isn't that huge an effect that you need to invent house rules to circumvent it.
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Blaeu

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Re: First player advantage
« Reply #2 on: June 13, 2011, 08:40:55 pm »
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I have found that the 1st player does have an advantage, but only with specific attack cards (duh, I know).  With many tables, I find that any advantage disappears quickly since he can do nothing to actually impact my strategy.

However, anytime I do best of three, if a third game is needed I have the player with the most total VP from both games go first.  Doesn't really offset the advantage, but it makes the player earn it, more of less.
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theory

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Re: First player advantage
« Reply #3 on: June 13, 2011, 08:42:43 pm »
+2

The long and short of it is that first player advantage is an advantage, but not enough to justify an across-the-board rule change.  There are far more luck-dependent factors in Dominion: you can have first player every time if I get to determine how Turns 3 and 4 play out.

The problem really is that you can't identify how big the firstplayer advantage is ex ante.  Maybe it means 1VP win on pile exhaustion + 1 Estate; maybe it means a total VP blowout because they're the first to activate City/Wharf.  Maybe the Militia advantage turns out to be huge, maybe it's a wash.

If it's a huge concern for you guys, bid VP for first player.  I think in 99% of sets, ex ante, I would bid 0.

The real way to solve it is just to play multiple games...
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papaHav

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Re: First player advantage
« Reply #4 on: June 14, 2011, 12:33:12 am »
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Most province games with remodel/salvager I would be 1chip bid for first player...  nerfing "pile-endings" however really means taking strategy away from the game.

One possible solution for equitable attacks is to make militia/cutpurse effect the next hand (attacks your cleanup phase) but this is less fun to manage and IMHO dominion has much more strategic depth than most games.  Certainly not a case of coin-flip for first player wins the game...
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drg

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Re: First player advantage
« Reply #5 on: June 14, 2011, 01:07:53 am »
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The rule for ties does not come close to negating the first player advantage.  If you win because you got one more turn than your opponent, then you had an advantage.  Why would the first player end the game on a tie as they would lose the tiebreak? As Theory said, the advantage could get negated by random factors very early in the game, or it could just be magnified to make the 2nd player have no chance, which makes it very hard to quantify.

I prefer the equal turns variant when face to face, I think it's closer to being fair, especially if the game is ending on piles.  Some of my friends even add 'phantom provinces' so they are equal during the extra turns, but I'm less sure about this.
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rogerclee

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Re: First player advantage
« Reply #6 on: June 14, 2011, 01:29:30 am »
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It's certainly true that the first player advantage matters more on some boards than others, but it would be silly to conclude that it is not a big problem. Personally, according to CR, I win 5.75% more games as first player (I only play 2-player games, but against mixed opposition). For someone like theory, a top player who plays mostly against top players, he wins a whopping 12.3% more games as first player than second player (~66 vs ~54).
« Last Edit: June 14, 2011, 01:34:34 am by rogerclee »
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Nimmy

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Re: First player advantage
« Reply #7 on: June 14, 2011, 02:26:20 am »
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I did some statistics a few month ago based on one week of games in isotropic. This was before councilroom, so maybe you can do better statistics now.
(ties refer of course to players having the same number of VPs AND having played the same number of turns)


2 player games:
 21147 for player 1 (50.7%)
 19854 for player 2 (47.6%)
 701 ties ( 1.7%)

3 player games:
 1149 for player 1 (34.8%)
 1041 for player 2 (31.6%)
 1016 for player 3 (30.8%)
 91 ties ( 2.8%)
 (of the 91 ties:
32 ties between 1 & 2
 19 ties between 1 & 3
 37 ties between 2 & 3
 3 ties between all players)

4 player games:
 93 for player 1 (25.6%)
 102 for player 2 (28.1%)
 80 for player 3 (22.0%)
 74 for player 4 (20.4%)
 14 ties ( 3.9%)
 (of the 14 ties:
2 ties between 1 & 3
 2 ties between 1 & 4
 1 tie between 2 & 4
 4 ties between 2 & 3
 4 ties between 1 & 2
 1 tie between 1 & 3 & 4)
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rrenaud

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Re: First player advantage
« Reply #8 on: June 14, 2011, 02:45:57 am »
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I definitely think the average value of first player (.5 turn) should be more than 1 vp on average.  Consider a hypothetical end game turn, say turn 16.  You can probably pull a duchy.  So heuristically, you'd expect a turn to be worth at least 3, and first player advantage to be worth half a turn, so that would put it at 1.5 points.

Alternatively, in a 16 turn game, you expect to have at least 27 points (4 provs + 3 estates), which means the average value of your turns is 27 / 16 ~= 1.6.  Halving this would only give .8, but then the early turns are buildup, and the later turns are scoring, you the marginal value of an extra 'last' turn should almost certainly be greater than average of 1.6 points.
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painted_cow

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Re: First player advantage
« Reply #9 on: June 14, 2011, 06:04:05 am »
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Going first is a huge benefit. Top 10 players have like 10 - 15 % higher win chances than in second position. This is really a great plus.

In some games with like Peddlers, Grand Markets etc. its really important to gain the most of this cards. The second player is always behind and will lose the race to this cards likely. Even in "stupid" BigMoney-Province games you just can decide when to end the game.

But overall i dont think, that there should be any bids or point advantages for second player. In rare cases being second is a advantage too (countering the others stuff).
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Mean Mr Mustard

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Re: First player advantage
« Reply #10 on: June 14, 2011, 06:35:31 am »
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Yeah, like whe your oppenent opens potion and you buy a embargo ;)
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guided

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Re: First player advantage
« Reply #11 on: June 14, 2011, 11:42:27 am »
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First player advantage is certainly real, but most of the fixes people propose create huge distortions. Equal turns variants (with or without "ghost VP cards") are barely even the same game as Dominion, and there's no set of static numbers of VPs you could gift the other players that would be fair across a broad range of boards.

I am simply not bothered by turn order asymmetry in this game. It's short. Play another game and let the loser go first. Play a thousand games on isotropic and it evens out a hundred times over :P I definitely agree with theory that the luck of the turn-2 shuffle introduces much more asymmetry than turn order does.

If you really can't stomach any per-game turn order bias, bid for seating. Half-point increments, allow duplicate bids, and break tied bids by coin flip. I'd guestimate the value of 1st position in 2p games to be 0 or 0.5 points on most boards, to maybe a point or two on boards with Militia or certain other attacks.
« Last Edit: June 14, 2011, 11:45:54 am by guided »
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keithjgrant

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Re: First player advantage
« Reply #12 on: June 14, 2011, 12:39:05 pm »
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I came across an interesting alternative rule designed to help balance the first player advantage.  I haven't tried it myself, but I've always been intrigued:

Instead of actually playing the first two hands, allow every player the opportunity to choose the two cards (or one card) they would like to buy. Neither card may cost more than $5, and both cards combined cannot cost more than $7.  Shuffle them into your deck.  Then, the player who spent the least gets to go first.

I see a lot of benefits to this: a) It speeds up the opening round by skipping the initial shuffle of the deck, b) Removes the luck factor that benefits anyone with a 5/2 split with the right tableau, and c) Gives the first turn advantage to the player whose deck should be mildly weaker than everyone else's.
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Thisisnotasmile

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Re: First player advantage
« Reply #13 on: June 14, 2011, 02:02:20 pm »
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I came across an interesting alternative rule designed to help balance the first player advantage.  I haven't tried it myself, but I've always been intrigued:

Instead of actually playing the first two hands, allow every player the opportunity to choose the two cards (or one card) they would like to buy. Neither card may cost more than $5, and both cards combined cannot cost more than $7.  Shuffle them into your deck.  Then, the player who spent the least gets to go first.

I see a lot of benefits to this: a) It speeds up the opening round by skipping the initial shuffle of the deck, b) Removes the luck factor that benefits anyone with a 5/2 split with the right tableau, and c) Gives the first turn advantage to the player whose deck should be mildly weaker than everyone else's.

And what if the costs are the same? Also, in which order are the cards taken? I'd happily sit there and wait for all of my opponents to take 2 cards so I know what strategy they are playing before making a decision about how to play my game. Maybe I'd even open militia/nothing on some boards simply to play first with a militia in my deck. Doesn't really fix the first player advantage, does it?
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Kuildeous

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Re: First player advantage
« Reply #14 on: June 14, 2011, 02:09:07 pm »
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That is intriguing. I've been trying to introduce a variant in my group where each person chooses whether he wants to open with 4/3 or 5/2. I argue that it cuts down on the first-turn luck since sometimes the 5/2 is horribly powerful or horribly horrible (especially if there are no 5s and 2s out there).

This "bidding to go first" is a very interesting proposition. One flaw I see with it is that Chapel/Silver would cost a total of $5, and it is stronger than most combinations that total up to $6 or $7. I'm sure there are other examples.

But, the idea that someone could open with two lesser cards (say, Haven and Embargo) in order to go first is something to think about.
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theory

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Re: First player advantage
« Reply #15 on: June 14, 2011, 04:14:08 pm »
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I came across an interesting alternative rule designed to help balance the first player advantage.  I haven't tried it myself, but I've always been intrigued:

Instead of actually playing the first two hands, allow every player the opportunity to choose the two cards (or one card) they would like to buy. Neither card may cost more than $5, and both cards combined cannot cost more than $7.  Shuffle them into your deck.  Then, the player who spent the least gets to go first.

I see a lot of benefits to this: a) It speeds up the opening round by skipping the initial shuffle of the deck, b) Removes the luck factor that benefits anyone with a 5/2 split with the right tableau, and c) Gives the first turn advantage to the player whose deck should be mildly weaker than everyone else's.

And what if the costs are the same? Also, in which order are the cards taken? I'd happily sit there and wait for all of my opponents to take 2 cards so I know what strategy they are playing before making a decision about how to play my game. Maybe I'd even open militia/nothing on some boards simply to play first with a militia in my deck. Doesn't really fix the first player advantage, does it?
Tied costs = the same situation you had before.

I rather like this idea, but mostly because of how it changes up the openings. Could make for some interesting starts.
« Last Edit: June 14, 2011, 04:40:05 pm by theory »
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rspeer

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Re: First player advantage
« Reply #16 on: June 14, 2011, 07:30:36 pm »
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I'm currently experimenting with my "Best and Worst Openings" code for CouncilRoom to take player order into account. In general, going first in a 2-player game seems to be worth about 3 points of TrueSkill.

I don't know if there's something wonky going on, though, or if playing Militia first is not as good as people think. I'm only halfway through chugging through all the games, but so far, buying Militia+Silver as player 1 of 2 is a level 0 opening (it's indistinguishable from the first-player baseline that's now 3 points higher), and buying it as player 2 of 2 is a level+2 opening! So contrary to the claim that Militia amplifies the first-player advantage, this seems to be saying quite to the contrary that it almost equalizes it.

There are some openings that do seem to amplify the first player advantage. Chapel+Witch, for example, is level+10 for player 1 and level+7 for player 2. That three-level difference, plus another three levels for first-player advantage, would effectively put the first player 6 levels ahead in a game where both players open Chapel+Witch.

So are my results clearly flawed, or is the common intuition about Militia wrong?
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hyku

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Re: First player advantage
« Reply #17 on: June 14, 2011, 08:48:24 pm »
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That is some interesting results. All I can think of is that playing militia LATER is actually better somehow. Maybe because it can attack after the first player has done his second shuffle when the first player will already have 2+silvers and want golds? It happens more than 50% of the time that the second player will militia the first player after his second shuffle.
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rspeer

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Re: First player advantage
« Reply #18 on: June 14, 2011, 09:02:57 pm »
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My guess is that games where people are playing Militia last longer, and longer games are more equalizing.
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rrenaud

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Re: First player advantage
« Reply #19 on: June 14, 2011, 11:24:34 pm »
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Maybe it's worth adding a straight win/loss record to keep a sanity check?
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Zaphod

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Re: First player advantage
« Reply #20 on: June 15, 2011, 11:46:24 am »
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There is absolutely no question that the first player has an advantage.  Anyone who doubts can check his winning percentage from each position on http://councilroom.com.  That said, I think starting last can sometimes have an advantage as well, because you can see your opponent's opening strategy and adjust yours accordingly.  The first two buys are crucial, after all. Also, the player who starts last can play for a tie, knowing that if his opponent ends the game, he wins.
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WanderingWinder

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Re: First player advantage
« Reply #21 on: June 15, 2011, 12:45:38 pm »
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I just had someone complain to me about the tiebreaker. Apparently some people don't agree (though I definitely disagree with them).

Geronimoo

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Re: First player advantage
« Reply #22 on: June 16, 2011, 03:49:42 am »
+1

I found a neat and simple way to eliminate the first player advantage:

After deciding the player order, instead of everyone shuffling up their 7 Coppers and 3 Estates do this:

Player 1: normal starting deck
Player 2: puts one Estate in his discard pile, then shuffles deck and draws 5
Player 3: puts two Estates in his discard pile, then shuffles deck and draws 5
Player 4: puts three Estates in his discard pile, then shuffles deck (no need really :) ) and draws 5

This means player 2 can have a $4/$4 or $5/$3 opening, player 3 could start with $5/$4 and player 4 might get $5/$5. After the opening the game continues as normal.

Simulations have shown this will normalize the playing field for any 2-player game. 3 player games will also be balanced on most boards, but the 4-player game will sometimes not be normalized at all: imagine player 4 opening Mountebank/Mountebank while player one is stuck with Silver/Bishop...

If enough people are interested I could do an article on simulating different game variants that try to eliminate the first player advantage...
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grep

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Re: First player advantage
« Reply #23 on: June 16, 2011, 08:05:23 am »
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The advantage of first player heavily depends on the card set, and we cannot just give the second player a fixed amount of VP (like komi in Go).

For two players there exists a simple auction schema:
1. Player 1 chooses the amount of compensation VP tokens for playing first.
2. Player 2 chooses if she wants to play first or to get the pile of VP tokens.

See http://senseis.xmp.net/?AuctionKomi
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theory

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Re: First player advantage
« Reply #24 on: June 16, 2011, 09:04:28 am »
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It's really not even about the card set.  The same card set can play out totally differently: maybe City/Goons/Quarry ends in a pile ending, and maybe it ends on Colonies.  If it ends on a pile ending, maybe P1 gets a blowout win, and maybe P1 ekes out a 1VP win before either side gets their engine set up.

And this isn't even considering show-off games where someone deliberately buys only 1VP more than their opponent in a pile ending.

In other words, I think even if you have the average VP differential for when P1 gets an extra turn and wins (which I think rrenaud is planning to do), it's meaningless because those numbers vary so wildly, even if you were to replay the same set between the same players.  It's like trying to extract useful information from experiments conducted in randomly-varying conditions, with each experiment itself producing random data.
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