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Is there an Unbeatable Chinese Chess Strategy? 3416
  • 友善列印版本

    10/2014

    Throughout history, chess masters from around the world have devoted much time and energy to determine an "unbeatable" strategy of moves to win in Chinese chess. While many believe no such strategy exists in the volatile game of chess, mathematics has proven otherwise!

     

    There is a finite number of moves in a game of chess. Perfect play by both players who are determined to win would always lead to a draw. Game theory dictates that in such a model, at least one player (either the player who moves first or second, or known as White or Black) can force a draw, although not necessarily a win. Take a look at the following game flow diagrams:

    Game 1

    Start à Loss/Draw

    In Game 1, neither move by the player will help him secure a win. Therefore the better outcome would be a draw

    Game 2

    Start à Draw/Loss/Win

    In Game 2, the player has three possible moves, one of which can secure a win. Therefore, the player can win this game

    Game 3

    Start àLoss/Loss

    It is a no-win situation for the player, while his opponent would win. Therefore, chess players know the endgame and the best outcome well before the first pawn is placed

    Now look at this game:

    White à Black à White wins; Black loses/Draw

    White à Black à Draw/White wins; Black loses/White loses; Black wins

    White à Black à White wins; Black loses/White wins; Black loses

     

    Scenario A resembles Game 1, with the best outcome for Black being a draw. Scenario B and C resemble Game 2 and 3 respectively, with the best outcome for Black being a win and a loss respectively. Therefore the game can be simplified as follows:

     

    White à Draw/White loses; Black wins/White wins; Black loses

     

    To White, it is the same scenario as Game 1 where he can win with move C. Therefore, by applying the same theory, which is the principle of mathematical induction, we can at least anticipate if White can force a draw in a chess game of three, four or up to 100 million moves; if not, then Black will surely win.

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