Parrondo's paradox is the proposition that two losing strategies can, by alternating randomly, produce a winner. R. D. Astumian has recently created a simple board game to illustrate this counterintuitive phenomenon. We prove that the inherent symmetry of Astumian's game prevents it from achieving its purpose, and suggest amended versions that do. We also display the additional paradoxical effect of two slow, losing games combining into a fast, winning one. (C) 2004 American Association of Physics Teachers.
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机译：帕隆多的悖论是这样的命题，即两种失败的策略可以通过随机交替产生赢家。 R. D. Astumian最近创建了一个简单的棋盘游戏来说明这种违反直觉的现象。我们证明了Astumian游戏的内在对称性会阻止其实现其目的，并建议这样做。我们还展示了两场缓慢，失败的比赛组合成一场快速，获胜的比赛所产生的附加矛盾效应。 （C）2004年美国物理教师协会。
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