Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess (2009.04374v2)

Abstract: It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero provides an alternative in silico means of game balance assessment. It is a system that can learn near-optimal strategies for any rule set from scratch, without any human supervision, by continually learning from its own experience. In this study we use AlphaZero to creatively explore and design new chess variants. There is growing interest in chess variants like Fischer Random Chess, because of classical chess's voluminous opening theory, the high percentage of draws in professional play, and the non-negligible number of games that end while both players are still in their home preparation. We compare nine other variants that involve atomic changes to the rules of chess. The changes allow for novel strategic and tactical patterns to emerge, while keeping the games close to the original. By learning near-optimal strategies for each variant with AlphaZero, we determine what games between strong human players might look like if these variants were adopted. Qualitatively, several variants are very dynamic. An analytic comparison show that pieces are valued differently between variants, and that some variants are more decisive than classical chess. Our findings demonstrate the rich possibilities that lie beyond the rules of modern chess.

• The paper's main contribution is using AlphaZero to objectively assess game balance in alternative chess variants.
• Quantitative analysis revealed that Torpedo Chess boosted White's expected score from 51.8% to 56.8% and reduced draw rates from 88.2% to 71.9% in rapid games.
• The investigation uncovers novel tactical strategies in both Torpedo and Self-capture Chess, offering valuable insights for future AI research and game design.

Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess

The paper "Assessing Game Balance with AlphaZero: Exploring Alternative Rule Sets in Chess" by Nenad Tomasev et al. investigates the potential of using AlphaZero as a tool for assessing new chess variants. The authors explore the efficacy and implications of alternative rule sets to determine their merit to the chess community. They focus specifically on two variations: Torpedo Chess and Self-capture Chess.

In the course of their investigation, the authors train multiple AlphaZero models, each adapted to a different chess variant, learning through self-play. Each model played approximately 10,000 rapid games and 1,000 slower games, providing a substantial dataset for qualitative analysis.

Torpedo Chess

Torpedo Chess extends the pawn's ability to move two squares forward from any position, not just from its starting square. This rule modification significantly shifts game dynamics, enhancing tactical complexity and altering strategic play.

Quantitative Findings: Torpedo Chess presented a more decisive gameplay compared to classical chess. The expected score for White in rapid games increased from 51.8% to 56.8%, while the draw rate decreased from 88.2% to 71.9%.

Qualitative Assessment: This variant tends to increase the power of pawns, especially passed pawns, making the game more tactically driven. Defensive structures are naturally fortified to counteract the tactical threats posed by the enhanced mobility of pawns.

Self-capture Chess

In Self-capture Chess, players can capture their own pieces. This rule provides novel strategic possibilities, such as breaking through blockades or providing new defensive maneuvers.

Qualitative Assessment: Kramnik highly values this variant, suggesting it enriches chess by allowing new tactical motifs and winning strategies, particularly in endgames, without drastically altering the opening phase. For instance, in certain endgame positions traditionally considered drawn, the self-capture option enables the stronger side to maneuver more effectively, leading to potential wins.

Practical and Theoretical Implications

This exploration with AlphaZero opens new frontiers in chess research by systematically evaluating alternative rules, with implications extending into AI strategy development and competitive gameplay. It also provides practical insight into designing balanced and engaging game variants that could enhance the spectator experience and strategic diversity.

Speculation on Future Developments

Continued use of AI systems like AlphaZero in exploring game variants could lead to systematic ways of evaluating game balance and complexity, possibly influencing future designs of turn-based strategy games, not limited to chess.

This paper contributes to an understanding of game dynamics and their computational evaluation, illustrating the potential of AI technologies in augmenting human creativity and strategic exploration in games.