The St. Petersburg paradox: An experimental solution

The St. Petersburg paradox refers to a gamble of infinite expected value, where people are likely to spend only a small entrance fee for it. There is a huge volume of literature that mostly concentrates on the psychophysics of the game; experiments are scant. Here, rather than focusing on the psychophysics, we offer an experimental, “physical” solution as if robots played the game. After examining the time series formed by one billion plays, we: confirm that there is no characteristic scale for this game; explicitly formulate the implied power law; and identify the type of α-stable distribution associated with the game. We find an α=1 and, thus, the underlying distribution of the game is a Cauchy flight, as hinted by Paul Samuelson.