Retrograde Analysis of the KGK Endgame in Shogi: Its implications for ancient Heian Shogi

This paper explores evolutionary changes of Shogi (Japanese chess) using game-theoretic analyses by computer. Heian Shogi is an ancient game only briefly described in the literature. Therefore, it is impossible to know exactly how it was played. Through game-theoretic analyses of rules, we estimate the historical changes of this ancient game. Our method provides a new innovative approach to guess logically how these ancient games actually have been played. This paper focuses upon the game results of the KGK endgame on NxN boards, applying game-programming methods. Then it determines the size of the boards in which the side of King and Gold always wins except trivially drawn cases with the Gold being captured. Based on the analyses, we discuss the rules of Heian Shogi. We specifically provide a logical interpretation of the shift from the 8x8 board to the 9x9 board in the evolutionary history of Shogi.