Collapsi is strongly solved

Abstract

Collapsi is a two-player game of complete information released in June 2025 by Mark S. Ball of Riffle Shuffle & Roll. Played with two pawns on a toroidal board of 16 randomly mixed playing cards, players take it in turns to move based on the value of the card they sit on, with the game ending when a player has no legal moves. The number of possible deals after symmetry breaking is low enough, and the game tree shallow enough, to make an exhaustive analysis of the game feasible. A solver was written that can find an optimal move for a given board position in around 20 milliseconds. A search was applied revealing that the first player can force a win in 37.5% of deals, with the second player able to force a win in all others. In 6.4% of deals the losing player can prolong the game to the maximum length of 14 plies; a win can never be forced in fewer than 7 plies.