You Can Load a Die, But You Can't Bias a Coin
Dice can be loaded—that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal. However, it is not possible to bias a coin flip—that is, one cannot, for example, weight a coin so that it is substantially more likely to land “heads” than “tails” when flipped and caught in the hand in the usual manner. Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air. We describe a student activity with dice and coins that gives empirical evidence to support this property, and we use this activity when we teach design of experiments and hypothesis testing in our introductory statistics courses. We explain this phenomenon by summarizing a physical argument made in earlier literature.