标题： 阿斯图米安悖论的重新审视 显示英文标题

标题： Astumian's Paradox revisited

摘要： 我给出对之前发表在《科学美国人》上的游戏的简单分析，该分析展示了悖论性行为，即两个亏损的游戏随机结合会形成一个盈利的游戏。 该游戏模拟了一个随机游走，只需要两个状态，并由一阶马尔可夫过程描述。 显示英文摘要

摘要： I give a simple analysis of the game that I previously published in Scientific American which shows the paradoxical behavior whereby two losing games randomly combine to form a winning game. The game, modeled on a random walk, requires only two states and is described by a first-order Markov process.