2023年经济学人 如何预测抛硬币(1)（在线收听）

    How to predict a coin toss

    如何预测抛硬币

    Coins are fair.Their tossers, less so.

    硬币是公平的。它们的抛掷者就没那么公平了。

    Legend holds that the city of Portland, Oregon, was nearly called Boston.

    传说俄勒冈州的波特兰市差点被称为波士顿。

    A coin toss in 1845 between Francis Pettygrove, who hailed from a different Portland, in Maine, and Asa Lovejoy, from Boston (the one in Massachusetts) eventually decided the matter.

    1845年，来自缅因州另一个波特兰的弗朗西斯·佩蒂格罗夫和来自波士顿(马萨诸塞州的那个)的阿萨·洛夫乔伊之间的一次抛硬币最终决定了这件事。

    But things might have turned out differently, per Frantisek Bartos, a graduate student at the University of Amsterdam, if people were not such wobbly tossers.

    但是阿姆斯特丹大学的研究生弗兰蒂泽克·巴托斯认为，如果抛硬币的人不摇晃的话，事情可能会有不同的结果。

    Mr Bartos was interested in a prediction made by Persi Diaconis, Susan Holmes and Richard Montgomery, a group of American mathematicians.

    巴托斯先生对一组美国数学家佩尔西·戴康尼斯，苏珊·福尔摩斯和理查德·蒙哥马利所做的预测很感兴趣。

    In 2007 the trio analysed the physics of a flipping coin and noticed something intriguing.

    2007年，三人组分析了抛硬币的物理过程，发现了一些有趣的现象。

    Besides sending it somersaulting end-over-end, most people impart a slight rotation to a coin.

    除了让硬币上下颠倒外，大多数人还会让硬币稍微旋转一下。

    That causes the axis about which the coin is flipping to drift while it is in the air, a phenomenon called precession.

    这会导致硬币在空中抛掷时所围绕的轴发生漂移，这种现象被称为旋进。

    After crunching the numbers, the physicists concluded that a coin thrown by a human should exhibit a subtle but persistent bias.

    在计算了这些数字之后，物理学家们得出结论，人类投掷的硬币应该表现出微妙但持久的偏差。

    There was about a 51% chance that a coin would land the same way up as it had been prior to being thrown.

    大约有51%的几率，一枚硬币会以与投掷前相同的方式落下。

    If it was heads-up in the thrower’s hand, in other words, it would be slightly more likely to land heads-up too.

    换句话说，如果它在投掷者手中是头朝上的，那么它也更有可能头朝上落地。

    Or at least, that was the prediction.

    或者至少，这是预测的结果。