通过匹配便士来测试随机性
Testing Randomness by Matching Pennies
摘要：
在配对便士游戏中，爱丽丝和鲍勃各拿一便士，在时钟的每一个滴答声中，他们同时展示硬币的正面或反面。如果他们都显示相同的一面，那么爱丽丝赢得鲍勃的便士;如果他们显示不同的一面，那么鲍勃赢得爱丽丝的便士。为了避免给对手获胜的机会，两个玩家似乎都没有别的事情可做，只能以相等的频率随机玩正面和反面。然而，虽然在这场比赛中不输是容易的，但不错过获胜的机会却不是。随机化你自己的移动可以很容易。识别对手的移动何时不是随机的可能是任意困难的。随机性的概念是博弈论的核心，但它通常被视为理所当然。智取的概念在博弈论中并不重要，但在博弈实践中却很重要。我们追求的想法是，这两个概念可以被有效地视为同一枚硬币的两面。
英文摘要：
In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they display different sides, then Bob wins Alice's penny. To avoid giving the opponent a chance to win, both players seem to have nothing else to do but to randomly play heads and tails with equal frequencies. However, while not losing in this game is easy, not missing an opportunity to win is not. Randomizing your own moves can be made easy. Recognizing when the opponent's moves are not random can be arbitrarily hard. The notion of randomness is central in game theory, but it is usually taken for granted. The notion of outsmarting is not central in game theory, but it is central in the practice of gaming. We pursue the idea that these two notions can be usefully viewed as two sides of the same coin.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
