Study and improvement of search algorithms in two-players perfect information games

TL;DR

The paper tackles the problem of evaluating whether game search algorithms generalize across a wide range of two-player, perfect-information, zero-sum games. It introduces a new variant, Unbounded Minimax with safe decision (UBFM_s), and conducts a large-scale empirical study across 22 games with diverse heuristic evaluations. The results show that UBFM_s outperforms all studied algorithms for short search times and achieves the best average performance for medium search times, while traditional Monte Carlo methods lag significantly. The findings establish UBFM_s as a robust, parameter-light option for general two-player game search and provide a thorough, reproducible experimental framework for future comparisons.

Abstract

Games, in their mathematical sense, are everywhere (game industries, economics, defense, education, chemistry, biology, ...).Search algorithms in games are artificial intelligence methods for playing such games. Unfortunately, there is no study on these algorithms that evaluates the generality of their performance. We propose to address this gap in the case of two-player zero-sum games with perfect information. Furthermore, we propose a new search algorithm and we show that, for a short search time, it outperforms all studied algorithms on all games in this large experiment and that, for a medium search time, it outperforms all studied algorithms on 17 of the 22 studied games.

Figures (10)

• Figure 1: Definition of symbols.
• Figure 2: Unbounded Best-First Minimax with safe decision algorithm ($\mathrm{UBFM}_{\mathrm{s}}$). It computes the best action to play in the generated non-uniform partial game tree starting from the root state $s$ with $t_{\mathrm{max}}$ as research time (see Figure \ref{['fig:def-symbol']} for the definitions of symbols ; at any time $T=\left\{ \left(v_{s,a},n_{s,a}\right)\,|\,s\in S\ \wedge\ a\in\mathrm{actions}(s)\right\}$). Note: tuples are lexicographically ordered.
• Figure 3: Transformation used to add a basic solver into a search algorithm. The transformation is based on a method $\mathrm{search\_tree\_construction\left(\right)}$ that builds the search tree and a method $\mathrm{search\_decision}\left(\right)$ that decides which action to play after building the search tree ($r_{s}$: resolution value of s ($0$ by default)).
• Figure 4: Unbounded Best-First Minimax algorithm $\mathrm{UBFM}$. It computes the best action to play in the generated non-uniform partial game tree starting from the root state $s$ with $t_{\mathrm{max}}$ as research time (see Table \ref{['tab:Index-of-symbols']} for the definitions of symbols ; at any time $T=\left\{ v_{s,a}\,|\,s\in S\ \wedge\ a\in\mathrm{actions}(s)\right\}$).
• Figure 5: Minimax algorithm with Alpha-Beta pruning. Parameter $d$ is the search depth.