Combinatorial Game Theory Meets Deep Learning:Efficient Endgame Analysis

The endgame stage of Go presents a unique challenge for scientific research. Contrary to previous stages, in the endgame the key to a successful analysis is board decomposition into smaller, independent local positions. Go players typically analyze these positions separately and prioritize moves based on their value. In this paper, I introduce a novel program that automates this decomposition-based analysis for the endgame stage of Go. AlphaZero has revolutionized Computer Go, by applying a generic move-selection mechanism, based on neural network judgments and the MCTS search algorithm. However, it does not specifically address the complexity of endgame in the aforementioned manner. On the other hand, by leveraging the decomposition-based analysis, my program reaches decisions in the endgame with relatively little computation. Additionally, it offers insights for Go practitioners by providing accurate move value evaluations. Notable prior work on automated endgame analysis was done by Martin Müller (1995). His program Explorer checked all possible variations in every undecided position and aggregated the results based on an algorithm inspired by the Combinatorial Game Theory (CGT). However, due to the exponential growth of the number of variations, Explorer’s application was limited to small, tightly bounded local positions. In contrast, my program leverages a neural network to predict optimal local moves, dramatically reducing the number of variations that need to be explored. Provided that the neural network’s predictions are correct, the program can accurately evaluate move values by considering relatively few variations, just like human Go experts do. Thanks to this approach, it is the first program capable of analyzing large, unbounded local positions, which are commonly encountered in real games. The neural network was fine-tuned from a pre-trained AlphaZero reimplementation on the task of optimal local move prediction. Training data was gathered from KataGo self-play games, utilizing KataGo’s network to perform board decomposition.