A Combinatorial Game Mathematical Checkmate Control Procedure for a Class of Chess Endgames

摘要

In this paper a checkmate control procedure for a class of chess endgames is given. The class of chess endgames considered are those chess games that are built around a trebuchet, are just formed by pawns and, whose configuration can be decomposed as a sum of independent subgames restricted to belong to one of the following cases: ⅰ) Zero or fuzzy games, and ⅱ) Positive or negative games where the winner has the possibility of driving the game to case (ⅰ). In addition some tempos are allowed. The main contribution consists in answering the question of how a chess player checkmates knowing that he is in a winning position using combinatorial game mathematical tools. By a winning position in a game it is understood a position where one of the players makes the last move in that game and as a consequence forces his opponent to start playing in the next game and so on, until at the end plays first in the trebuchet and loses the chess game.