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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?

  • 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
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    @Nasser, I don't think you are using the standard definition of "perfect play". – Akavall Feb 16 '13 at 0:17
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    I think the Wikipedia article on the subject is pretty good. en.wikipedia.org/wiki/First-move_advantage_in_chess – 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 '15 at 9:58

17 Answers 17

33

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

White wins   37.35%
Black wins   27.41%
Drawn        35.23%

http://www.chessgames.com/chessstats.html

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.

12

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 most comparable game to chess that has been solved is checkers" that is not even close to be the most comparable game to chess in any means: where did you take this from? – gented Jun 29 '17 at 16:07
  • @GennaroTedesco, agreed. I stopped reading this post after reading: "The most comparable game to chess that has been solved is checkers." – ScottyBlades Dec 4 '17 at 3:55
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    @GennaroTedesco What game, more comparable to chess than checkers, has been solved? – bof Dec 4 '17 at 7:04
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    @GennaroTedesco Among games which have been solved checkers is by far the most complicated and the one closest to chess. – bof Dec 9 '17 at 23:41
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    @ScottyBlades I was replying to your comment, where you said: "I stopped reading this post after reading: 'The most comparable game to chess that has been solved is checkers.'" Seeing you expressed strong disagreement with the statement 'The most comparable game to chess that has been solved is checkers,' I thought you must have some counterexample in mind, and I wondered what it could be. The negation of the statement 'The most comparable game to chess that has been solved is checkers' is 'Some game, more comparable to chess than checkers, has been solved.' – bof Dec 10 '17 at 0:42
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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.

5

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.

4

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.

3

There is not a single game where white wins because of the first move advantage. All wins for white are related to something else (e.g. blunders or more inaccuracies). If both sides play perfectly (i.e. achieving the most out of a move according to any decent algorithm), the game ends in a draw.

But it is difficult to play 50+ moves perfectly. Either side will go wrong sooner or later. Apparently this happens to black more. Maybe it is just psychological: chess players are told that White has the initiative from the start and that Black needs to respond to that initiative and try to equalize. Responding to the other players plan is more difficult. Based on a single move played and the current position, you need to understand what the opponent is trying to do. As long as mind reading is not allowed in OTB games, mistakes will happen.

The interpretation of the stats, are misleading at best. It assumes that difference in winning percentage can only be explained by the first move advantage, and that is demonstrably not true.

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    I also believe that the initial position is a draw with perfect play and that differences in winning percentage are due to the fact that white has the initiative and black has to play more accurate in order to equalize. Unfortunately it seems impossible to prove all this. – user1583209 Dec 4 '17 at 9:12
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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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    Some links to support the article's assertions would be well received. The point regarding Lasker is interesting if true. – thb Jan 10 '16 at 18:06
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This is an open problem, but historically:

Since 1851, compiled statistics support this view; White consistently wins slightly more often than Black, usually scoring between 52 and 56 percent. White's winning percentage is about the same for tournament games between humans and games between computers;

enter image description here

In the recent games played by AlphaZero against Stockfish:

With White AlphaZero [vs. Stockfish] scored a phenomenal 25 wins and 25 draws, while with Black it “merely” scored 3 wins and 47 draws. It turns out the starting move is really important after all!

enter image description here

So, if the performance of AlphaZero is evidence of what the best current possible play is, white does indeed have an advantage.

It would be interesting to see the statistics on white/black wins of AlphaZero playing against itself.


Source:

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Looking at the statistics shown by Sunanda above, it appears that white has some advantage. I feel it is more a question of human brain's (or machine's) capability to handle 8x8 squares to maintain that advantage for white or achieve equality or advantage) for black. With this in mind I tend to believe that white's advantage is more if the size of the board is say 5x5 or 6x6 (of course with some pieces removed from the board). The simple reason for my belief is that the game becomes a lot easier with smaller sized board. On the other side, if the board is large say 12x12, with some additional pieces and pawns, the game would be lot more difficult for white to have any advantage, because there would be many more possibilities for the moves at every stage of the game. First move advantage may actually cease to exist at some size of the chess board (as we move from small to large size for the board). This size at which it breaks has to be found out. To digress a little, some game designers have come up with chess variants to eliminate this supposed advantage. Google for Synchronous chess, parity chess and synchronistic chess to know the rules of these variants.

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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
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    This would be better as another question. – Elliot A. Jan 17 '16 at 14:21
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    The problem is that even if you have ten billion (10^10) games played, and assuming a branching factor of 3 (very conservative), after 10-20 full moves you will be following a single game in your database for the next 20 moves. – hkBst May 31 '16 at 8:36
  • Yeah, the branching factor sucks as hkBst says. If you looking at every game played by a 2700+ player since 2010, I think 1. a4 has the highest score with 100% win for white as played by MC against Radjabov in 2012. Even throwing out that anomaly, you'll quickly find others. You have to stay above that 100,000 mark to be accurate, and that's simply not possible in a game with any sort of significant branching factor. – Marty Neal Apr 24 '17 at 15:28
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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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Your question turns on the meaning of perfect play. If White starts with a Colle system and neither player offers any aggression I cannot imagine that the result is anthing but a draw. For one side to win, at some stage an ambitious move must be played to unbalance the position.. If it turns out that this move actually gave the advantage to the opponent then it could not have been perfect play. In the days of Alekhine and Capablance, many players expressed fear that Chess would experience a draw-death, Instead, the Kings Indian became popular

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In Chess White has an advantage or not depends upon who is playing and what opening is played on board . Man or Machine.There are statistics to prove and both disapprove . Playing white for Humans is more of a Psychological thing and for Machines it hardly matters .

Generally from the opening itself if you take any powerful Chess Engine Fritz/ StockFish/Komodo they will show a Score slight advantage of +0.3 to +0.7 even if the most accurate Openings are played .

If it is Sicilian then the Score will incline more and if it is Petroff then the Score will be less . Please remember Petroff is the only defence where White has not been able to find a real advantage . So it really depends upon the Opening and the Player who plays White .

I will take the best instance of WCC matches from Lasker, Alekhine, Capablanca to Carlsen where both Players have got equal number of matches with both white & black and the mightiest Player have always won with their respective chosen openings.

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Bobby Fisher said that black has an advantage, but his mentee Adam Robinson reported that Fisher later said white has the advantage:

"I don't understand why you played that, because you said black is better in your book, and he said 'I did?', I said, 'yea you did', and he said, 'Oh, I was wrong. White is better' and he crushed me."

"Fisher conducted the longest con in sports history...A long con is when a confidence man sets you up and the payoff is years away...Fisher when he was growing up played always pawn to king 4 as his first move and had a very limited opening repertoire, and he always played the same opening moves and he defied the Russians and he defied the world to beat him...So from the age of 12 til the age of 29 he played exactly the same opening moves. What was curious for me was that when I was with him 2 months before the match began I noticed he was studying games outside his opening repertoire...Sure enough against Spasky...now mind you, spasky was supported by the Russian chess machine, dozens of the worlds top players who were all russian were supplying Spasky with analysis of all of Fishers old games. But then he played an entirely new opening repertoire...And they didn't know what to do, they were totally flummoxed."

-Adam Robinson

26 minutes in

https://www.youtube.com/watch?v=oSyMmleisQM

Some people I have talked to in the past (no direct quotes available). argue that fewer people study black's plays as much as whites, and therefore white's more frequent winning is a self-fulfilling prophecy.

  • Hi! Welcome to Chess SE. Could you please provide a reference for your quote? – Pablo S. Ocal Dec 4 '17 at 4:28
  • @PabloS.Ocal, how is that? – ScottyBlades Dec 9 '17 at 20:07
  • Much better, your answer is now trustworthy. – Pablo S. Ocal Dec 10 '17 at 15:23
  • @PabloS.Ocal, did you downvote it? – ScottyBlades Dec 10 '17 at 20:03
  • I did not. The answer without the reference lacked necessary information and the downvote probably came before the edit. – Pablo S. Ocal Dec 11 '17 at 5:37
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Wondering if this may have something to do with white possibly having a greater ability to push the game down a line of play for which white has spent more time preparing. This may mean that Black is more likely to run into time constraints as they are have to spend more time figuring out the right response. Play at a high level seems to some extent to be to follow common lines of play for first set of moves and to then to try to push game into a less common line of play where you may have spent more time preparing/which you are more used to playing/where you have an advantage. To extent to which this is easier for white, there may be some advantage.

  • Actually, the common feeling is that while White may decide between an open or closed game (1. e4 vs. 1. d4), Black will choose the actual opening, and has a greater ability to push the game down a certain line of play. – Glorfindel Nov 16 '18 at 21:47
  • @Glorfindel There's some truth to that. If White plays e4, Black gets to decide whether to play, for example, the French. But on the other hand, if he does, it's then White who gets to decide whether to play the advance variation, the exchange variation, or something else - and that choice can result in different types of games as well. – D M Nov 16 '18 at 22:12
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By virtue of the first move, white has the initiative. Black's goal must thus be to first blunt the initiative if he is to have a chance. In other words he must first play to equalize and then try to gain the initiative if he is to have a chance to win. Barring mistakes on either side, the game should then be a draw.

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Though taking it from a suggested article, there is a great need to point it out literally as it is the best argument.

"The first-move advantage is founded more in psychology than in reality." - Andras Adorjan

Explanation of above conjecture:

First-move advantage doesn't just exist in Chess but approximately in all games but theoritically (pychologically). This is often neat. Come, play football! Let team A (say) start the game then, if, both teams A and B play perfect games (equal play), A is going to have first Goal. But this is certainly all theoretic. This has very small to do with Reality (as it happens nearly never) since, one team is always going to play different from other. This either results in a Draw (before penalty shootout) or a win/lose.

The point is, "theoretically, things seem much different as they look practically". This is why the problem is a chess theorists' problem and not of chess players!

  • Adorjan hadabook to sell! – Philip Roe Dec 9 '17 at 18:55

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