Adapting AlphaZero for Three-Player Hexagonal Chess

Vasiljević, Jan (author), Bajec, Marko (mentor), Pirker, Johanna (comentor), Sadikov, Aleksander (comentor)

This thesis adapts the AlphaZero framework for Three-Way Chess, a three-player variant defined by hexagonal geometry and complex coalition dynamics. To address the lack of software frameworks, a high-performance training ecosystem was developed for resource-constrained hardware. A transformer-based architecture incorporating relative positional embeddings was introduced to capture the board's unique spatial relationships. Methodological validation in Three-player Hex demonstrated that canonical input representations and geometric embeddings significantly enhance learning efficiency. In Three-Way Chess, the agent autonomously discovered advanced tactics but initially adopted a passive survivalist strategy to avoid drawing aggression. Refining the objective with material incentives corrected this behaviour, resulting in competitive performance against human opponents. These findings suggest that the efficacy of self-play in non-zero-sum multiplayer environments depends on the underlying game structure and may require additional fine-tuning.

• Language: English
• Keywords: multiplayer chess, AlphaZero, transformer, deep reinforcement learning, non-zero-sum games, game theory
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2025
• PID: 20.500.12556/RUL-177428
• COBISS.SI-ID: 263051523
• Publication date in RUL: 23.12.2025

Secondary language

• Language: Slovenian
• Title: Prilagoditev AlphaZero za trostranski heksagonalni šah

Abstract

Magistrska naloga obravnava prilagoditev ogrodja AlphaZero za varianto heksagonalnega šaha za tri igralce, ki jo definira zapletena dinamika zavezništev. Zaradi pomanjkanja odprtokodnih rešitev je bilo razvito visokozmogljivo ogrodje za učenje na strojni opremi z omejenimi viri. Za učinkovito modeliranje specifične geometrije heksagonalne plošče je bila uvedena arhitektura na osnovi transformerjev, ki vključuje relativne pozicijske vložitve. Metodološka validacija na primeru igre Hex za tri igralce je pokazala, da kanonične vhodne predstavitve in geometrijske vložitve bistveno izboljšajo učinkovitost učenja. Pri šahu za tri igralce je agent samostojno odkril napredne taktične motive, vendar se je sprva naučil pasivne igre, da ne bi postal tarča napadov. Prilagoditev sheme nagrajevanja z materialnimi spodbudami je izboljšala vedenje in posledično privedla do konkurenčne igre proti človeškim nasprotnikom. Izsledki nakazujejo, da je učinkovitost učenja s samo-igranjem v okoljih za več igralcev z neničelno vsoto odvisna od osnovne strukture igre in pogojno zahteva dodatne prilagoditve.

• Keywords: večigralski šah, AlphaZero, transformer, globoko spodbujevano učenje, igre z ne-ničelno vsoto, teorija