Estimating the number of reachable positions in Minishogi

To investigate the feasibility of solving Minishogi (Gogo Shogi) strongly, we need 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, we estimated 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 revealed that the number of reachable Minishogi positions is approximately $2.38 \times 10^{18}$.