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arXiv · 2501.07463

A coin flip game and generalizations of Fibonacci numbers

Jia Huang
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Abstract

We study a game in which one keeps flipping a coin until a given finite string of heads and tails occurs. We find the expected number of coin flips to end the game when the ending string consists of at most four maximal runs of heads or tails or alternates between heads and tails. This leads to some summation identities involving certain generalizations of the Fibonacci numbers.

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Jia Huang. 2025-01-30. A coin flip game and generalizations of Fibonacci numbers. https://arxiv.org/abs/2501.07463

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