# A Chess Question Of The Late Great W.T.Tutte

In "Graph Theory As I Have Known It", p.12, Knights Errant, Tutte mentions as an aside the chess question " does either Black or White have a certain win from the initial position, given perfect play by both sides".

Is there any literature on that possibility of a Black win, that is the possibility of the initial chess position being mutual zugzwang? What is the earliest reference to the question?

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I do not know the earliest reference to the question - I've wondered about it myself - but I believe this question is far, far outside the realm of current computational techniques and power. I just don't think there is anything even on the horizon that would make answering this question tractable. –  TLss Sep 17 '12 at 14:54
This looks like a chess question, not a math question. Also, it's quite well-known. Whenever someone asks whether chess is close to solved, one of the responses is that we don't even know that black doesn't have a forced win. –  Douglas Zare Sep 17 '12 at 16:39

## 2 Answers

The question "does either Black or White have a certain win from the initial position, given perfect play by both sides" was first addressed by Wilhelm Steinitz in his 1896 "Theory of Perfect Play" (Chapter 6 of Modern Chess Instructor). He concluded that "by proper play on both sides the legitimate issue of a game ought to be a draw".

You can find a quite detailed overview of the literature since Steinitz in Wikipedia. The advantages of Black over White seem to be largely psychological ("underdog").

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Actually, if you look at opening databases, and condition on games being decisive (that is, not a draw), black seems to be running a massive disadvantage, so the underdog thing is of limited benefit, it seems... –  Igor Rivin Sep 17 '12 at 16:15
The reference cited in this answer does not address the question posed. –  TLss Sep 17 '12 at 16:25
Just to be clear, the results of practical play are not relevant to the question of the theoretical status of a Black win. –  TLss Sep 17 '12 at 16:27
For that matter, I highly doubt one could prove using current techniques that from the initial position with Black's queen removed, that Black has no win. Doing so would, in fact, be a major advance in the state of the art. –  TLss Sep 17 '12 at 16:30
Almost everyone who plays competitive chess would view White as having some practical advantage over Black, other thins being equal. Well, maybe Adorjan would disagree... –  Yemon Choi Sep 17 '12 at 17:04

In my decade of chess-playing, I have never come across anything remotely resembling an answer to this question. If the perfect play question had already been answered by example, chess would be an exercise in memorization -- the absolute perfect path(s) of the game could all be played out down to the endgame, and whoever deviates first loses material. In the event that one side has a forced win, the other side would always be the one forced to lose material. Brute-forcing a solution to chess is nowhere near possible at the moment, given the amount of possible game positions (~ $10^{43}$, according to Claude Shannon). I've never heard of any sound way to argue this question other than brute-force.

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That $10^{43}$ excludes promotions. –  Douglas Zare Sep 17 '12 at 16:43
Why the definite article before "perfect play"? It's imaginable that either e4 or d4 (for example) can be the opening move of a "perfectly played game (and similarly, for many positions, it's imaginable that there is no one best move). Actually, when I was more active in chess, I used to like opening with Nf3 as White, and it's not clear to me that that is inferior to e4 or d4. –  Todd Trimble Sep 17 '12 at 18:24
I believe the meaning is the "perfect play question" not "the perfect play" question –  Lee Mosher Sep 17 '12 at 23:42
Ah, thanks Lee. Happily, I see "path(s)" in the next line, so this would support that reading as well. –  Todd Trimble Sep 18 '12 at 0:05