Summary

Tricolor is a combinatorial board game invented in 1930 by the Belgian mathematician Maurice Kraitchik. Notable for its early use of a hexagonal tiling, stack-based piece mechanics, and capture rules influenced by tile colors, the game is an original object of study at the intersection of the history of mathematics, artificial intelligence, and computational game analysis. Despite its historical interest, Tricolor had not previously received a systematic computational study.

This thesis provides a first computational analysis of Tricolor. Its rules are formalized from historical sources and adapted into a precise model for automated simulation and AI experimentation. An efficient C++ game engine uses compact state and action representations to support fast move generation, state copying, and large-scale simulations.

Simulations estimate game duration, branching factor, game-tree and state-space complexity, player balance, and dynamic gameplay properties such as decisiveness, stability, and drama. The results characterize Tricolor as a game with a large search space, relatively long games, and unstable tactical dynamics. Strategic principles involving material control, positional power, stack concentration, and forced tactical sequences are then used to design a heuristic evaluation function.

Two classical game-playing agents are implemented and compared: an Alpha-Beta agent guided by the heuristic and a Monte Carlo Tree Search agent using random simulations. Both strongly outperform random play, while Alpha-Beta clearly dominates the basic MCTS agent under the tested conditions. This difference is linked to the high branching factor, long game duration, and delayed tactical consequences introduced by stacking and forced moves.

Beyond agent performance, the resulting framework provides a reusable tool for studying Tricolor through artificial intelligence, game history, mathematics, and cultural heritage research. The work illustrates how computational methods can contribute not only to playing historical games, but also to understanding and preserving them as mathematical and cultural objects.

Suggested citation

Bourceanu, A. F. (2026). Tricolor - Computational Analysis and AI Exploration of an Early Hexagonal Board Game. Master's thesis, Université catholique de Louvain (UCLouvain).