Welcome to MathOverflow

Question

1

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?

flag	asked Sep 17 at 14:30 Ian Calvert 105●3

4

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 at 14:54

1

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 at 16:39

Carlo Beenakker · Accepted Answer · 2012-09-17 18:28:52Z UTC

2

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").

edited Sep 17 at 18:28

answered Sep 17 at 15:45

Carlo Beenakker
5,796●10●20

2

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 at 16:15

2

The reference cited in this answer does not address the question posed. – TLss Sep 17 at 16:25

2

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 at 16:27

2

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 at 16:30

1

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 at 17:04

show 1 more comment

Ben · Answer 2 · 2012-09-17 16:34:04Z UTC

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.

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

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

2 Answers

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.