On the complexity of Dark Chinese Chess

TL;DR

This paper analyzes the complexity of Dark Chinese Chess, a game with high strategic and informational complexity, by designing a self-play program to measure its game tree and information set sizes, highlighting its challenges for AI.

Contribution

It introduces a novel complexity analysis method for Dark Chinese Chess, including algorithms to compute game tree and information set sizes, advancing understanding of complex imperfect-information games.

Findings

Calculated game tree complexity of Dark Chinese Chess

Estimated average information set size for the game

Proposed algorithms for counting information sets

Abstract

This paper provides a complexity analysis for the game of dark Chinese chess (a.k.a. "JieQi"), a variation of Chinese chess. Dark Chinese chess combines some of the most complicated aspects of board and card games, such as long-term strategy or planning, large state space, stochastic, and imperfect-information, which make it closer to the real world decision-making problem and pose great challenges to game AI. Here we design a self-play program to calculate the game tree complexity and average information set size of the game, and propose an algorithm to calculate the number of information sets.