Single Conspiracy Number Analysis in Checkers

Abstract

Game playing provides the medium for a variety of algorithms to formulate play decisions that surpass human expert. However, the reasons that distinguish the winning and losing positions remain actively researched which leads to the utilization of the search “indicator”. Conspiracy number search (CNS) and proof number search (PNS) had been popularly adopted as the search indicators in MIN/MAX and AND/OR tree, respectively. However, their limitations had encouraged the need for an alternative search indicator. The single conspiracy number (SCN) is a search indicator inspired by CNS and PNS which measure the difficulty of getting MIN/MAX value over a threshold point for a current root node. Recently, SCN had been successfully applied in Chinese chess to analyze both the progress pattern and long-term position. In this paper, analysis of the SCN within the game of checkers is conducted where different SCN threshold values and varying depth of the search tree were considered. Checkers was chosen due to its smaller search space and contain a rule that affects the shape of the search tree. The experimental results show that the SCN values stabilize as the depth of the search tree increases whether the player is in winning, drawing or losing position.