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It is often debated that white has an advantage over black. Some even say that with perfect play on both sides, black simply cannot win. Is there any research that backs up this claim, or is it mere speculation by the greats such as Rauzer?

Also, if this has been or could be proven true, could the black pieces be given some sort of aid to make them equal to the white ones?

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White has the advantage because White is one move ahead. Therefore, with perfect play by each side White will checkmate Black just one move before Black checkmates White. But since White has checkmated Black, then Black will not get the chance to make that move to checkmate White, since the game will be over by then. One move too late for Black. – Nasser Feb 15 '13 at 23:44
@Nasser, I don't think you are using the standard definition of "perfect play". – Akavall Feb 16 '13 at 0:17
I think the Wikipedia article on the subject is pretty good. – EvilSpudBoy Feb 16 '13 at 0:50
Hmmm... I just pitted Chessmaster against itself and it was a draw. I like white better and win more games with it, but it could be psychological. When I was a kid after a year or so I never, ever lost a game of checkers if I played first and was pretty certain from playing so many games that it was impossible to beat me as long as I played first. I still believe that, except that I can't play checkers well enough after five decades to win every time and no longer remember how I did it. – user5686 Jan 17 at 9:58

8 Answers 8

These statistics come from a database of over 600,000 games:

White wins   37.35%
Black wins   27.41%
Drawn        35.23%

The stats suggest that White has a significant, measurable first-mover advantage. Not an overwhelming advantage, but better than the house advantage in any casino game.

Is that advantage structured into the game or psychological? Comparative stats on games between mature chess engines may help to decide that.

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The most comparable game to chess that has been solved is checkers, where it has been shown to be a draw given perfect play by the second player. The first move gives a player a very slight edge initially, but does that convert to a winning advantage?

Tablebases give us some insight into the debate. The vast majority of positions which are materially balanced result in draws. Positions that are somewhat dynamically balanced (say knight vs bishop) still result in draws a high percentage of the time, although the more powerful the remaining pieces are, the more likely first to move is the winner. (take for instance, KQRKQR endgames, the first to move wins 67% of the time).

Another important factor seen in tablebases is that most wins have a relatively short distance to conversion (or moves to force a win). There are extreme cases, for instance, the record had jumped from 292 moves in 1989 to 330, and then to 545 in 2006. The striking quality to me is that the gap between move lengths in these records jumps so much all at once, which suggests that it gets harder to force a win the more moves away from the end you are, because most positions that far away are draws. It would be a winning lotto ticket if starting from the opening position, it happened to be one of those extremely long won positions. To me, this is strong circumstantial evidence that chess will be another game shown to be a draw.

Unfortunately, it is currently impossible to generate a full 32 piece tablebase for chess, as there are more possible chess positions than atoms in the universe. Barring some breakthrough in quantum computing allowing all possible positions to be evaluated simultaneously, I doubt chess will ever be fully solved by man.

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The first move in chess affords a slight advantage. This is why pairing systems try to alternate a player between the white and black pieces. Some GMs are 'underrated' because over time, they have randomly been assigned the black pieces more often than is normal. They are at a slight disadvantage and thus lose an unnatural frequency.

I have never seen it demonstrated that with perfect play white (or black) will win.

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I think statistically it has been shown that White has the advantage, but as the saying goes, "The winner of chess is the player who makes the second to last mistake". White only has the advantage on the first move and this would not matter if they make a horrible second move. I would also say that White has more of an advantage at top level play because there are not likely to be too any mistakes, but at the lower level, being White or Black does not offer much of an advantage because there are probably many mistakes.

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One solution for equalizing a first-move advantage is the Pie Rule, AKA "I cut, you choose".

Under this rule, immediately after the nth move by White, the player that started as Black would have the option of either switching sides or proceeding with game as is. The number n is fixed in advance.

This rule is used in other boardgames, like Twixt, Havannah, or Hex, that have a more significant first-move advantage. With the Pie Rule, the first player must quickly give up the advantage lest it be seized by the second player.

The more common solution, since draws are acceptable in Chess, is to play multiple games, with players alternating sides.

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I have analyzed the statistics of the top players in history, and the top chess engines of the last few years, and found that white has a distinct winning and scoring advantage except for one player (Lasker, who was about 1% better with black!). The stats are:

Top players of history: white wins 7.5% more than black, white scores (wins plus draws x .5) 2.5 % more than black Top chess engines to date: white wins 37% more than black white score 34% more points than black

For comparison, the stats for: All players (several million games in public databases): white wins 13% more, and scores 8.5% more Hundreds of 1000's of games from available chess engine games for last 8 years (over 1500 engines): white wins 15% more than black, and scores 14% more than black.

The higher caliber of human player, or higher rating of the chess engine, the higher the advantage for white (ranged from 1 to about 40%). For me, this is pretty good evidence that white has a big advantage, since both the top players and basically ALL the engines achieve more wins and points as white. The best engines rarely, if ever, lose as white, but lose more often as black. Yes, engines draw more than top humans (about 50% compared to 20-30% for humans) but the remaining games are won most often by white. The top human players ranged from 1-22% more wins with white, while the top computers ranged from 6.5-44% more wins by white.

Of course, since chess isn't 'solved' then we can't be sure, but the top players, who look ahead 20-30 play, and the top computers, who look ahead 30-50 ply easily now, are a good indication that white has a definite advantage. Perfect play by both sides is still a mystery, though! :) John

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The Perfect Game of Chess Statistically, Move by Move:

Has anyone ever compiled high level (2700+ rating), large number (100,000+ games) statistics on the most winning chess moves, move by move?

This would be to "build" the statistically strongest game of Chess we could uncover.

To do this I would propose starting with move 1. to see which move gives the highest percentage of wins for White. In this case I would suspect 1. e4 but I don't KNOW this.

Then seeing which move gives the highest percentage of wins for Black in answer to White's first move. Then start the process all over again for move 2., then move 3. and so on until the game ends with each move being statistically the strongest. This would eliminate most opening variations and dealing with only the statistically strongest move.

World Champion Emmanuel Lasker said a perfectly played game of chess would probably be boring and end in a draw.

I would expect the end result of this "statistically strongest" game to also be a draw.

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This would be better as a comment than an answer. – dfan Nov 14 '14 at 21:40

Some here have stated that white has a one-move advantage, which is certainly incorrect.

White has a half-move advantage. It is true that before each black move, white is ahead one move. However, after each black move, equal moves have been made by each side. Averaging all decision points in the game yields a .5 move advantage.

Also, it is easy to see that there are a number of ways to give up a move immediately in most real-world games, if having it were not actually an advantage.

If we take a simple example of a mirrored game, where black attempts to duplicate every move of white's, white will rapidly be ahead material. You could argue that being ahead material is not an advantage in some configurations, but having the choice to take that material, having more control of the outcome, certainly is.

You might find the previous concept absurd, but let's look at it from another perspective. Given every possible exactly mirrored board position, it seems intuitive that more of them would be mate-in-one for the first to move. (I have not done this calculation, but it would be an interesting and probably achievable search to run.) If we broaden this to all possible configurations, it seems intuitive that mate-in-one would on-average be more accessible to the first to move. Etc. And we need not follow this trail too deeply, either. Forced mate-in-six is a challenging find for most humans.

Many people have played many games of chess, some without any preconceived notions. If a clear way to neutralize white's opening advantage with certainty had been played, it would be well-documented by now. In fact, much opening strategy exists in chess surrounding this concept. See chess "tempo".

In endgames a well-known concept is zugzwang, where a clear disadvantage exists to having to move. However, this disadvantage exists because of the lack of choice, not because of having first choice; the move a player must make is disastrous (or more accurately the disaster has already occurred). Reiterating tbischel's comment, chess may never be solved by man. Because of this, we play games forwards, rather than backwards, as humans - and because of THAT, having the first move is an advantage.

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