AI 中文总结
本研究针对2023年国际棋联规则下的国际象棋对局最大步数问题，通过对局分段分析证明合法对局最大步数为17697步，填补了此前未排除17698、17699步对局的空白，且最长对局构造最优。
AI 中文摘要
2023年1月1日生效的国际棋联（FIDE）国际象棋规则规定，对局在五回合重复或双方各连续走75步未走兵或吃子后自动终止。此前已知合法对局步数为17697步，通过对兵移动和吃子的调度分析得出算术上界为17699步，但未排除17698或17699步的对局。我们填补了这一空白：将对局按兵移动和吃子划分，最多产生118个段，每个段的步数最多为150步，且连续段端点的颜色变化每发生一次，该上界减少1步。我们证明，包含全部118个段的对局必须至少发生3次此类颜色变化，因此每局最多有150×118−3=17697步，且已知构造的对局是最优的。此外，在每局最长对局中，全部16个兵各走6步并升变。
英文摘要
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.
Comments11 pages. Companion repository: https://github.com/junyeobe0315/longest-chess-game (version 1.2.0; archived at doi:10.5281/zenodo.21929234). Ancillary files include the 17,697-ply reference game (PGN) and a self-contained C verifier
