why I like chess

May 27, 2008, 8:24 AM |

  A finite game is a game with a finite number of nodes in its game tree.A game of perfect information is a game where every information set is a single node and nature has no moves.In 1913 the famous mathematician Ernst Zermelo proved that in chess,either the first mover has a winning pure strategy,or the second mover has a winning pure strategy,or either player can force a draw.This proof was generalized by Harold Kuhn(1953),who proved that every finite game of perfect information has a pure strategy Nash equilibrium.

    So chess is formally a trivial game!But we know that this is not the case.Only brilliant and highly trained minds,or powerful computers play chess well.The reason for this discrepancy between game theory and reality is that game theory assumes that agents can process any amount of information at zero cost.The average chess game involves about eighty moves,and the average number of possible choices at each move is about thirty,so there are roughly 30.30 80 times differrent chess games.So even the most powerful computer in the universe probably couldn't use backward induction to find a Nash equilirium to chess.