General Mathematics

    

A Brief Study on Solitaire Modulo 3

Authors: Mattia Furlin

In this short article, we will discuss a card game, from now on namely Solitaire modulo 3. After having described how it works, through a probabilistic calculation, we will arrive at determining the probability of victory. In particular, we will use the rook polynomials, which will allow us to finally obtain a closed form for calculating the probability of winning at Solitaire modulo 3. Finally, we will study the case where the number of cards in play is much more greater than the number of constraints present in the game format. Under this assumption, the Solitaire modulo 3 mechanism becomes asymptotically equivalent to a binomial distribution.

Comments: 5 Pages.

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[v1] 2026-01-22 21:20:43

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