Collapsi is strongly solved

TL;DR

Collapsi, a two-player game with a small state space, has been exhaustively analyzed, revealing that the first player can only force a win in a minority of deals, with the game being strongly solved.

Contribution

This paper presents the first exhaustive analysis and strong solution of Collapsi, demonstrating its solvability and strategic outcomes.

Findings

First player wins in 37.5% of deals

Second player can force a win in remaining deals

Maximum game length is 14 plies

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.