AI 中文总结
本文拓展Cover猜数博弈策略，证明Alice可通过单次实验观测应用该策略，在Bob的实验未开展或细节未确定时，仍能以超0.5的概率猜对两实验结果的大小。
AI 中文摘要
Cover最初提出了一个博弈：Bob在两张纸上各写一个数，让Alice选一张查看。Cover证明（此前Blackwell似乎也证明过），Alice可采用包含随机数选择的策略，使得她猜对两个数中较大者的概率大于0.5，该推理的核心是Alice以相等概率选取任意一个数查看。本文研究Bob将两个数作为基于概率分布的实验结果（如轮盘赌的旋转）的情形，进一步拓展为Alice和Bob分别进行基于概率分布的独立实验：Alice完成一次自身实验后，可运用Cover的策略，在Bob选择进行一次实验时，猜测她的实验结果比Bob的实验结果更大或更小。本文的核心结果包括：1. 若两个数来自同一实验的观测值，Alice仅需观测一次实验结果并应用Cover策略，即可获得大于0.5的猜对较大值的概率，即便第二次实验尚未进行；2. 存在大量非平凡案例，其中Alice和Bob进行不同的实验，Alice仅需观测一次自身实验结果并应用Cover策略，即可获得大于0.5的猜对较大值的概率，即便对方实验的诸多具体细节尚未确定、且未进行过一次实验。
英文摘要
Cover originally proposed a game in which Bob wrote two numbers on pieces of paper and allowed Alice to pick one and look at it. Cover then showed, as Blackwell is thought to have shown previously, that Alice has a strategy involving the selection of a random number which enables her to guess correctly with a probability greater than 0.5 which of the two numbers was larger. Central to Covers reasoning was that Alice could have picked either number to look at with equal probability. In this paper, we investigate the situation in which Bob obtains the two numbers as the result of an experiment based on a probability distribution, such as the spin of a roulette wheel. We then modify this to envision Alice and Bob conducting separate experiments based on probability distributions. Alice conducts one trial of her experiment and uses Covers strategy to guess whether the result from her experiment will be larger or smaller than the result from Bobs experiment whenever he chooses to conduct a single trial of it. The following two results are among those in the paper. (1) If the two numbers are observations of the same experiment, Alice merely has to observe one trial and apply the Cover strategy to have a probability greater than 0.5 of guessing the larger value, even if the second trial has not yet been conducted (2) There are many nontrivial examples where Alice and Bob conduct different experiments, and Alice can observe one trial of her experiment and apply the Cover strategy to have a probability greater than 0.5 of guessing the larger value, even if many of the specifics of the other experiment have not yet been determined and a trial of it has not yet been conducted.
Comments29 pages, 2 figures
