Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Take a look at my predictions: the final two choices of mine are the same as the first two of my opponent. My goal is to cut them off at the pass. Sure, one player could win on the very first three flips of the coin (a 12.5 percent chance for each person), but after that, the winning run of heads and tails will be preceded by a run of three that overlaps it. I want to choose that preceding group. For something like TTT, it either has to be the first three flips, or it will definitely be beaten by HTT coming directly before it. A midsequence run of three tails will always have a head directly before it, giving HTT before TTT. The game is rigged. This is a game known as Penney ante (named for its inventor, Walter Penney), and it has been used to separate humans from their cash for years. In the game of Penney ante, people get thrown because every option of three heads and tails has a different combination that is more likely to win. It is unsettling that there is no best option to pick that is more likely to win than all the others. But this exact oddity is the basis of the game rock-paper-scissors. Any option picked can be beaten by one of the other options.