Solving 3 × 9 Quoridor with Independently Verifiable Strategy Certificates

Abstract

The paper solves two previously open configurations for the game Quoridor: the first player forces a win on a 3x9 board with both 9 and 10 walls. For the 10-wall variant, the exact minimax forcing horizon is mathematically proven to be 35 plies. Our results were independently reproduced by a structurally different, "lazy" secondary solver to ensure algorithmic accuracy, and we introduce a strategy-DAG certificate format (qcert-1) containing hundreds of millions of verified nodes. This allows the winning strategy to be exhaustively checked by independent, clean-room software, removing the need to trust the original search engines. Additionnaly, a no-stalemate theorem is established for boards with a height of 3 or greater (sharp at height 2), which closes a semantic loophole that could have altered the verdicts.