How many coin tosses would you need until you get n Heads or m Tails?

2025/12/08 by Janson, Svante, Martinez, Lucy, Zeilberger, Doron
Mathematics · Computer Science · #History and Theory of Mathematics #Advanced Combinatorial Mathematics #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.2512.07803

Abstract

We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching n Heads or m Tails. We also talk about the closely related problem of reaching n Heads and m Tails. This paper is accompanied by a Maple package that enables fast computation of expectations, variances, and higher moments of these quantities.

Citations

• First to reach n game

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• First to reach n game

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