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Most games that involve taking turns, with one player going first by lot or agreement, have some sort of advantage to going first. Tic-tac-toe, for instance, is a guaranteed draw for player 1, assuming correct play. Connect 4 is a guaranteed win for player 1, assuming correct play. The first move in Go is considered so powerful that player 2 receives a bonus of 5.5-7.5 points. The first-move advantage in Chess is less obvious, although statistically speaking White has an advantage of ~52-56%.

White's advantage is essentially that of time. He can count on starting ahead of Black and in theory should not go behind except by choice. He can even attempt to trade material for time.

Black's advantage is that of choice, or response. She can let White develop the game as he chooses, or she can force the game into a different line of play altogether. Presumably she knows her purpose in playing her responses to White, and can take advantage of White's loss of choice.

This being said, does it have meaning outside the highest levels of play? Is the game theoretically close enough that there isn't a way to equalize it 100%? (Related previous discussion suggests that the first move is "worth 25-45 rating points". However, the question didn't directly deal with the first-move advantage, instead referring to it tangentially in a discussion of handicaps.)

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"Black's advantage is that of choice, or response" - I'm not sure I'd refer to this as an actual advantage, or at least, it's no more of an advantage than White's choice of first move. It certainly doesn't seem like White's first move is a zugzwang situation, and on every move, each player gets an opportunity to determine the path the game takes. If anything, White has a bigger say in this, with choice of first move; in other words: a bigger advantage in terms of choice. –  Daniel B Nov 13 '12 at 13:08
    
I haven't abandonded the question, and I will accept an answer by the end of the week. :) Daniel, you're right, "choice" is slightly ambiguous. Picture it this way: After 1. e4 c5, White has no choice but to accept that he is playing at least one of the variations of the Sicilian. Or Black may instead choose to play 1. . . c6, and she now forces White to accept one of the Caro-Kann variations. In essence, White is choosing general classes of possibilities, but it is Black who decides how to direct those possibilities. Perhaps this choice is what keeps the first-move advantage "small". –  Jonathan Garber Nov 13 '12 at 16:11
    
From a game theory point of view, that's probably correct; in the sense that White has given Black some information - something to attack against. In some types of games, whoever moves first, loses... but this doesn't seem to be the case in chess. I've added an answer below which breaks down some stats (which I calculated quickly) for various rating groups. I hope it helps to answer the question. –  Daniel B Nov 13 '12 at 18:00
    
Actually, tic-tac-toe is also a guaranteed draw for player 2, assuming correct play. Chess may very well have the same status. To answer @DanielB, it is also possible (though highly unlikely, I agree) that W *is actually in zugzwang at move 1, and that black has a forced win (that would require losing tempi with a knight being a losing maneuver for W, which makes it even more unlikely, but I dont think the possibility has been discarded yet). –  Nikana Reklawyks Dec 2 '12 at 0:57
    
Yes, Tic-Tac-Toe is also a guaranteed draw for Player 2. I could have chosen a better example, but I figured that nearly everyone knows of it specifically and is aware that it's a draw with correct play. –  Jonathan Garber Dec 3 '12 at 13:31

5 Answers 5

up vote 17 down vote accepted

I think any real answer to your question will have to be statistical in nature. There's rationale behind the advantages and disadvantages of having the first move, but really, we'd be mostly guessing regarding how important these factors are.

With that in mind, I quickly ran some code to check what patterns I could pick up through the million base PGN library (check below for disclaimer / methodology):

ELO                  %W      %D      %B
1700: 56    games:  37.50 / 33.93 / 28.57
1800: 192   games:  34.38 / 35.42 / 30.21
1900: 736   games:  37.23 / 34.24 / 28.53
2000: 4682  games:  36.27 / 32.14 / 31.59
2100: 10568 games:  36.56 / 34.79 / 28.64
2200: 23486 games:  34.42 / 38.11 / 27.47
2300: 33444 games:  31.25 / 45.06 / 23.69
2400: 49706 games:  28.53 / 51.73 / 19.74
2500: 40264 games:  26.38 / 57.28 / 16.33
2600: 16946 games:  27.88 / 56.14 / 15.97
2700: 3581  games:  28.43 / 56.07 / 15.50
2800: 68    games:  27.94 / 55.88 / 16.18

As you can see, at the highest levels (around 2500 and above), the majority of games are draws (around 55%), and from the remainder, wins by White outnumber wins by Black with a ratio of around 1.75:1. A very significant advantage, indeed.

The ratio drops rapidly at lower levels, and by the time we are around 2000 in rating, it's closer to 1.2:1. From here, it doesn't seem to change much, and I don't really have data for under 1700 rating. Of equal importance is the percentage of drawn games - along with the White / Black win ratio, the number of draws drops significantly. I would interpret this data along the following lines (although I'm reading a bit into the data here):

White does have a tangible advantage, but needs to play very accurately to capitalise on it. At the "lower levels", tactics (and thus mistakes) play a far larger role, almost drowning out the underlying small advantage. It is still noticeable, however, even at the 1700 rating level, and with a small sample size. So, to answer your question: yes, the choice of colour is relevant even at lower levels, although much less so than at GM level.

Disclaimers and whatnot - I ran through the million base PGN library (+- 1.7 million games), and simply discarded any games with a greater than 50 rating points difference between the players, in order to select only games between similar strength players. Statistically, this shouldn't make all that much difference (the "unfair" games should have each other balanced out, given sufficient numbers), but there are a number of exhibition and simul games in that library which I was attempting to exclude from the data set. In any case, this is not meant to be strictly scientifically correct; it's just the results of a few minutes of programming.

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I would say the first move has a large advantage. I am not at the highest level (1), nor have I ever played against someone at the highest level, but I have played several GMs. I'll give two situations where I thought it was a large advantage. They relate to opening choice - which has a large impact on the rest of the game.

The first I had white against GM Khachiyan, and he played 1.d4 Nf6 2.c4 Nc6, which I only knew vaguely. But the temptation for a GM to "play to their class" is strong, and they are willing to play weaker openings in order to achieve this. The game continued 3.Nf3 e6 4.a3 d6 5.Nc3 g6 6.e4 Bg7 7.Be2 o-o 8.o-o Re8 9.d5. I wasn't too familiar with the opening, but I knew enough to play a3 when I did, and the same for d5. I came out of the opening with a slight plus, the game was a little bit of a see-saw, and we agreed a draw around move 30. I attribute it to the opening choice of my opponent, which was in my opinion guided by the colors.

The second I had black against GM Ivan Ivanisevic. The game opened 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.Qc2 o-o 5.Nf3.

I was out of book already, only knowing 5.e4 (not the strongest) and 5.a3, which is normal. So I figured, perhaps erroneously, that my chances lay in potentially transposing to the a3 lines, so I played 5...b6, which didn't work out so well after 6.e4! and white has a much favorable variation of the 5.e4 lines. White might even be close to winning with equal opponents, and with a GM against me it was a bit of a bloodbath. As black against a GM, you really have your work cut out for you, and taking chances like this (trying to transpose into something you know) is not something I would do as white.

1: I'll consider highest level to mean a situation where both players are top 20, and the game is not an exhibition, or it is a world championship.

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Chris, assuming that you are also chess.stackexchange.com/users/517/christopher-von-krogh, note that you can merge your currently separate user accounts: meta.stackoverflow.com/help/user-merge. Or if there's a problem with that, one of the mods can merge them for you. –  ETD Nov 12 '12 at 14:51
    
Ed Dean: Thank you for the tip. My profiles are now merged. –  Christopher von Krogh Jan 25 '13 at 20:26

Since you asked for experience apart from the higher level of plays, I can give you myself as an example, with a rating of ~1900 (FIDE rating is 1871) I've never felt at a disadvantage playing black or advantage playing white.

Most openings give a lot of play for both sides and small inaccuracies will tremple the advantage white might have before you'll even notice it.

I've never played for a draw just because I was black and I know players up to 2200 that feel the same. I don't know what you consider "highest level", but "weak" International Masters and Grandmasters already take this into account (of the 4 I got to talk to anyway).

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Historically, the first move advantage of White is a real one, as evidenced by the larger number of White victories in tournament play.

One way to balance this is to give Black "draw odds," that is, Black wins if the game goes into a forced draw.

That might tilt the playing field too much toward Black, so White might have to get a second (or third) "first" move to compensate.

But Go basically works along this principle, with the value of the first move having risen (in the eyes of the pros) from 5.5 to 7.5 points over time.

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In the Appendix of my article on "Pairwise comparison of chess opening variations" I made an estimate of white's first move advantage using controlled engine experiments. A sample size of 900 games was used. The mean estimated value of the first move advantage is 5.89% (with a 95% confidence interval of 4.4% to 7.4%). This means that white enjoys a 5.89% probability of winning because it is always one move ahead of black. Of course this advantage is easily squandered as for example in 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. Bxc6 instead of 4. Bxc6. Here is a link to the paper that contains the estimation of the first move advantage.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2472783

Your comments greatly appreciated.

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