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arXiv · 2312.09368

Leading All The Way

Peter E. Francis·Evita Nestoridi·Peter Winkler
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Abstract

Xavier and Yushi run a ``random race'' as follows. A continuous probability distribution $\mu$ on the real line is chosen. The runners begin at zero. At time $i$ Xavier draws $\mathbf{X}_i$ from $\mu$ and advances that distance, while Yushi advances by an independent drawing $\mathbf{Y}_i$. After $n$ such moves, Xavier wins a valuable prize provided he not only wins the race but leads after every step; that is, $\sum_{i=1}^k \mathbf{X}_i > \sum_{i=1}^k \mathbf{Y}_i$ for all $k = 1,2, \dots, n$. What distribution is best for Xavier, and what then is his probability of getting the prize?

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Peter E. Francis, Evita Nestoridi, Peter Winkler. 2023-12-14. Leading All The Way. https://arxiv.org/abs/2312.09368

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