Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2507.16823

Collapsi is strongly solved

Michael Young
View original source ↗Read source document ↗Export metadata ↓

Abstract

Collapsi is a two-player game of complete information released in 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 77.7% of deals, with the second player able to force a win in all others. In 3.5% 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.

Explore related subjects

math.HO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Michael Young. 2026-07-29. Collapsi is strongly solved. https://arxiv.org/abs/2507.16823

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Come for the vibe, stay for the math

This article describes our experiences in mathematical outreach over the past decade. We talk about specific activities, but also general principles that we've learned along the way.

math.HO↗
arXiv2026

From foundations to applications: reverse mathematics and philosophy

Reverse mathematics is a branch of mathematical logic dedicated to determining the minimal set existence principles necessary and sufficient to derive ordinary mathematical theorems about concrete structures like the real line. Since the mid-1970s, reverse mathematics has developed a systematic classification of the strength of theorems in areas of mathematics ranging from real and complex analysis to infinitary combinatorics. This essay will place reverse mathematics in its historical and philosophical context, and reveal its relevance to central issues in the philosophy of mathematics, from the foundational programmes of Hilbert and Brouwer to contemporary debates about realism, determinacy, and applicability of mathematics. In doing so, it will discuss the role of computability theory in measuring the strength of set existence principles, as well as related questions about idealisation when these principles are applied in the physical sciences and in philosophy.

math.HO↗