This Letter presents a numerical study across parameter space to calculate the aspect ratio (ratio of length to diameter) of a fair “three-sided coin”: a cylinder that when tossed, has equal probabilities of landing heads, tails, or sideways. The results are cast in the context of previous analytical studies, and the various mechanisms that govern the dynamics of coin tossing are compared and contrasted. After more than $7\times {10}^8$ tosses of coins of various aspect ratios, this study finds the critical aspect ratio to be slightly less than (but not exactly equal to) $\sqrt{3}/2\approx 0.866$.

中文翻译：

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三面硬币的厚度：分子动力学研究

这封信提出了一个跨参数空间的数值研究，以计算一个公平的“三面硬币”的长宽比（长径比）：一个圆柱体，被抛掷时，具有相等的着陆头，尾或侧面概率。结果是在先前的分析研究的背景下得出的，并且比较和对比了控制抛硬币动力学的各种机制。超过$7\times {10}^8$ 抛掷各种长宽比的硬币，本研究发现临界长宽比略小于（但不完全等于） $\sqrt{3}/\mathrm{2个}\approx 0.866$。