Junyeop Yim
The FIDE Laws of Chess effective from 1 January 2023 terminate a game automatically upon fivefold repetition or after 75 consecutive moves by each player without a pawn move or a capture. Legal games of 17,697 plies were previously known, and a scheduling analysis of the pawn moves and captures gave an arithmetic upper bound of 17,699 plies, but games of 17,698 or 17,699 plies were not excluded. We close this gap. Partitioning play at pawn moves and captures yields at most 118 segments. Each segment has length at most 150 plies, and each change in the colour of successive segment endpoints reduces this bound by one ply. We prove that a game with all 118 segments must incur at least three such changes. Hence every game has at most $150 \cdot 118 - 3 = 17{,}697$ plies, and the known constructions are optimal. Moreover, in every maximum-length game, all sixteen pawns make six one-rank moves and promote.