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<p>We take up a British TV game in its final round. Three contestants choose an integer from 0 to 10000 independently. One of the contestants wins if the chosen numbers are distinct and the chosen number of the contestant is in between the other chosen numbers. The winning amount is the winning number in British pounds. In this paper, we discuss distributions on {0, 1, 2, ..., 10000} the contestants can use for selecting numbers. We show that the Uniform Distribution is optimal maximizing the probability of selections being distinct. We generalize the problem to the continuous case.</p>

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Dissection of a British TV Game

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月29日

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  • Neelakshi Chatterjee,
  • Zhaochong Yu,
  • Nisha Sheshashayee,
  • Marepalli Bhaskara Rao

摘要

We take up a British TV game in its final round. Three contestants choose an integer from 0 to 10000 independently. One of the contestants wins if the chosen numbers are distinct and the chosen number of the contestant is in between the other chosen numbers. The winning amount is the winning number in British pounds. In this paper, we discuss distributions on {0, 1, 2, ..., 10000} the contestants can use for selecting numbers. We show that the Uniform Distribution is optimal maximizing the probability of selections being distinct. We generalize the problem to the continuous case.