2024/10/07 by Robert Steele, Daniel B. Larremore, Steele, Robert +1 · 2 voices
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Artificial Intelligence in Games #Computer science #Game Theory and Voting Systems #cs.GT #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2410.05551
openalex publication_date 2024/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and height six, in alternating turns. Misere Connect Four is played by the same rules, but with the opposite objective: do not connect four. This paper announces that Misere Connect Four is solved: perfect play by both sides leads to a second-player win. More generally, this paper also announces that Misere Connect k played on a w × h board is also solved, but the outcome depends on the game's parameters k, w, and h, and may be a first-player win, a second-player win, or a draw. These results are constructive, meaning that we provide explicit strategies, thus enabling readers to impress their friends and foes alike with provably optimal play in the misere form of a table-top game for children.