Author: Mike Hood
Date: 16:56:42 07/14/99
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The calculation of the maximum number of moves in a game of chess that you quoted is slightly too high. Earlier this year I calculated the longest game, taking into account the 50-move rule and the rule that a game is drawn when there is no longer enough material to checkmate. (I assume that the solution quoted is erroneous because of neglecting the second rule). I simply assume that it is possible to avoid a draw by repeating the same position three times. In the following description I shall call moves "basic moves" if a pawn is moved or a piece is taken. I shall call all other moves "waiting moves". The first simple calculation results in 6300 moves. There are 16 pawns that can each move 6 times. There are 30 pieces that can be taken. That means there are 126 basic moves. (96+30)*50 = 6300. To simplify matters I shall count in half moves from now on. This theoretical total of 12600 half moves cannot be reached for two reasons: 1) The pawns of the two players must pass one another. 2) If one side takes two pieces in a row (or moves two pawns) these two moves can be 100 half moves apart. If the two players take pieces alternately, the moves can only be 99 half moves apart. Therefore the solution must be reduced by several basic moves to allow the pawns to pass each other. Every time the initiative changes from one player to the other (ie first one player makes a basic move, then the other), the solution is shortened by one waiting move. Every time a basic move is lost the solution is reduced by 100 half moves. Every time the initiative is changed the solution is reduced by one half move. The best possible solution does without 8 basic moves, and the initiative is changed 4 times. This results in 11796 half moves. Many games are possible to reach this goal, but here is a relatively simple example: In the beginning of the game all moves are made with the Knights, until the other figures can move out. The first 8 basic moves each do without a basic move by using a pawn to take a figure (ie a pawn is moved and a piece is taken in the same move). Half move 100: The black pawn on b7 takes the Knight on a6 Half move 199: The white pawn on a2 takes the Bishop on b3 (change of initiative) Half move 299: The white pawn on d2 takes the Knight on c3 Half move 399: The white pawn on e2 takes the Knight on f3 Half move 499: The white pawn on h2 takes the Rook on g3 Half move 598: The black pawn on c7 takes the Bishop on d6 (change of initiative) Half move 698: The black pawn on f7 takes the Knight on e6 Half move 798: The black pawn on g7 takes the Rook on h6 In the next 44 basic moves Black moves his pawns. That brings us to half move 5198. Each pawn is promoted to a Knight. The initiative is changed, and White moves his pawns for the next 44 basic moves. That brings us to half move 9597. These pawns are also promoted to Knights. At this point each player has a Queen, a Bishop, a Rook and eight Knights. In the next 11 basic moves White takes all of Black's figures. That brings us to half move 10697. The initiative is changed, and black takes all of White's figures in the next 11 basic moves. That brings us to half move 11796. Since only the two Kings are left, the game is drawn after 5898 moves. Mike On July 14, 1999 at 18:09:37, Dann Corbit wrote: >From: >http://www.clark.net/pub/pribut/chessfaq.html > >We have: >Subject: [24] Trivia >How long is the longest possible chess game? >The basic idea is a player may claim a draw if fifty moves elapse without a >capture or a pawn advance. Ignoring the special cases where more than 50 moves >are allowed by the rules, the answer is after Black's 5948th move, White is able >to claim a draw. The simple calculation is (<Pawn_moves + - + ><Drawing_interval_grace_period) * <Drawing_interval, or (16*6 + 30 - 8 + 1) * 50 >= 5950; we're able to trim two moves from this total by observing that sequences >of Captures/Pawn_moves must have (at least) 4 alternations between the two >players. > >So no chess program need handle games longer than 5948 moves.
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