Is the Gambler’s Fallacy Really a Fallacy?

Abstract

The behavior known as the gambler’s fallacy is exhibited when gamblers increase their wager after a series of losses.  The conventional interpretation of this behavior is that, after a series of losses, the gambler views the probability of winning as increasing.  However, if the probability is independently and identically distributed (as it normally is), previous losses do not affect the probabilities of subsequent gambles, hence the fallacy.This paper suggests an alternative explanation for the gambler’s fallacy behavior.  It holds that the gambler views the probability of a series of (outcomes resulting in) losses as very small.  Therefore, from an ex ante perspective, consumers strategize that if they lose, they will increase their wagers because a long series of losses is unlikely.  A simulation demonstrates the rationality of the gambler’s fallacy behavior by showing positive winnings when the theoretical expectation is $0.This same behavioral assumption is also behind the St. Petersburg Paradox.  The difference is that the low probability of a series motivates people to gamble with the gambler’s fallacy, but motivates people not to gamble with (or more accurately, not pay very much for) the St. Peters Paradox.  If anything, the gambler’s fallacy is a fallacy regarding the adequacy of the consumer’s bankroll, rather than a fallacy regarding a change in the probability of winning.