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Expected Winning Probabilities in Sequential Truels under Uniform Distributions

机译:在均匀分布下顺序轨道中的预期赢得概率

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In this paper we examine the expected probabilities of survival of each of the three participants in sequential truels assuming uniform distributions for their marksmanships. We start by discussing the two most common sequential truels, one in which everyone has to attempt to eliminate someone on each turn, and the other in which the weakest marksman has the option to abstain. We conjecture that the expected winning probabilities in sequential truels cannot be calculated analytically, and so we estimate these probabilities using multiple computational approaches. We also calculate the expected winning probabilities of each of the participants for one fixed marksmanship at a time. At the end we show that as the three marksmanships approach 0, the sequential truel approaches the simultaneous truel and this explains some aspects of the sequential truel for small marksmanships.
机译:在本文中,我们将在销售统一分布的统一分布中检查三个参与者中每个参与者中每个参与者的预期概率。我们首先讨论两个最常见的顺序特鲁尔,其中每个人都必须尝试消除每个转弯的人,另一个是最薄弱的Marksman可以选择弃权。我们猜想不能分析顺序轨道中的预期获胜概率,因此我们使用多种计算方法估计这些概率。我们还每次计算每个参与者的预期获胜概率。最后,我们表明,随着三个枪手方法0,顺序干鲁接近同时创卷,这解释了小型射击的连续残忍的一些方面。

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