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Asymmetric reformulation of draw rules in chess and its implications for game theory: Repetition as loss for White

Chong Qi

Abstract

Repetition-based draw rules in deterministic games like chess ensure termination but introduce strategic artifacts, allowing players to enforce draws independent of positional value. We propose an asymmetric modification: threefold repetition results in a loss for White if it is responsible for initiating it. This rule directly targets the persistent first-move advantage and removes low-effort draw strategies available to White. The new rule is expected to reduce draw rates, re-balance first-move advantage, and promote exploration in both human and artificial play. We outline a computational framework with existing and newly designed neural-network chess engines for the empirical validation of the proposal and analyze it from the perspectives of game theory and graph dynamics.

Asymmetric reformulation of draw rules in chess and its implications for game theory: Repetition as loss for White

Abstract

Repetition-based draw rules in deterministic games like chess ensure termination but introduce strategic artifacts, allowing players to enforce draws independent of positional value. We propose an asymmetric modification: threefold repetition results in a loss for White if it is responsible for initiating it. This rule directly targets the persistent first-move advantage and removes low-effort draw strategies available to White. The new rule is expected to reduce draw rates, re-balance first-move advantage, and promote exploration in both human and artificial play. We outline a computational framework with existing and newly designed neural-network chess engines for the empirical validation of the proposal and analyze it from the perspectives of game theory and graph dynamics.

Paper Structure

This paper contains 8 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The draw problem in chess
  3. Numerical evaluation of the asymmetric repetition rule
  4. Stockfish Self-Play Evaluation
  5. Neural network evaluation of the initial advantage and experimental fine-tuning
  6. Self-play chess engine under the modified rule
  7. Graph-theory formulation and equilibrium structure
  8. Conclusion and discussion

Figures (2)

  • Figure 1: Game outcome distributions and draw reason breakdowns for games retrieved from the latest issues of TWIC twic, comprising international tournament, including the 2026 Candidates Tournament, and competitive club games collected across a broad range of playing levels and events worldwide played in March, 2026.
  • Figure 2: Win rates for White and Black as a function of Stockfish search depth across the different experimental setups A--E, comparing the standard threefold repetition rule (solid lines) with the asymmetric repetition rule (dashed lines). In each panel, the shaded band between the solid and dashed lines of the same color illustrates the net effect of the ARR relative to the standard rules.