Estimating the number of reachable positions in Minishogi
This work addresses a specific gap in combinatorial game analysis for Minishogi, providing a concrete estimate that could aid in solving the game, though it is incremental as it refines bounds rather than introducing a new method.
The authors tackled the problem of estimating the number of reachable positions in Minishogi, a variant of Shogi, by using uniform random sampling to measure the proportion of legal positions, resulting in an estimate of approximately 2.38×10^18 positions.
To investigate the feasibility of strongly solving Minishogi (Gogo Shogi), it is necessary to know the number of its reachable positions from the initial position. However, there currently remains a significant gap between the lower and upper bounds of the value, since checking the legality of a Minishogi position is difficult. In this paper, the authors estimate the number of reachable positions by generating candidate positions using uniform random sampling and measuring the proportion of those reachable by a series of legal moves from the initial position. The experimental results reveal that the number of reachable Minishogi positions is approximately $2.38\times 10^{18}$.