Estimating the number of reachable positions in Minishogi

TL;DR

This paper estimates the total number of reachable positions in Minishogi using random sampling, providing a key metric for understanding the game's complexity and aiding in its strong solving.

Contribution

The authors introduce a novel estimation method for reachable positions in Minishogi, bridging the gap between known bounds and enabling better game analysis.

Findings

Estimated number of reachable Minishogi positions: approximately 2.38×10^18

Demonstrated the effectiveness of uniform random sampling for position estimation

Provided insights into Minishogi's complexity for future research

Abstract

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 $2.38\times 10^{18}$.