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We analyze the natural process of flipping a coin which is caught in the hand. We show that vigorously flipped coins tend to come up the same way they started. The limiting chance of coming up this way depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high‐speed photography are reported. For natural flips, the chance of coming up as started is about .51.
Diaconis et al. (2007) studied this question.