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

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

2012-09-17T14:30:04Z

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?

Answer by Carlo Beenakker for A Chess Question Of The Late Great W.T.Tutte

2012-09-17T15:45:23Z

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").

Answer by Ben for A Chess Question Of The Late Great W.T.Tutte

2012-09-17T16:34:04Z

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.