In sports and in gambling there is a mistaken belief that a player who is performing better than normal will continue to play well, even if the odds suggest otherwise. This belief is especially strong in basketball. Players who have made several shots in a row are considered to have a “hot hand” and encouraged to continue to shoot – even to attempt very difficult baskets they normally cannot make.
A variety of scientific experiments have documented the fallacy of the hot hand in basketball. A player may make many shots in a row in the short term but his performance will eventually return to his long-term average. The law of statistics is not suspended.
Similarly, when gamblers are on winning streaks, they keep betting or even increase their wagers to take advantage of their good luck. Like in basketball, gamblers ignore statistics and mistakenly believe they are more likely to win a future bet because they have won previous ones.
Ignoring statistics while gambling is referred to as the Monte Carlo fallacy. The name derives from a 1913 incident in which black came up a record 26 times in a row in roulette.
[There] was a near-panicky rush to bet on red, beginning about the time black had come up a phenomenal fifteen times. In application of the maturity [of the chances] doctrine, players doubled and tripled their stakes. This doctrine leading them to believe after black came up the twentieth time that there was not a chance in a million of another repeat. In the end, the unusual run enriched the casino by millions of francs.
The Monte Carlo gamblers invented all sorts of reasons to explain the long run of black, failing to appreciate that each appearance of black was a random occurrence.
Amusingly, the hot hand and Monte Carlo fallacies can lead to contradictory conclusions. Imagine a gambler who bets on his lucky number and wins several times in a row. Under the hot hand fallacy, the gambler believes the number is likely to come up again and continues to bet on his lucky number. However, under the Monte Carlo fallacy the same gambler would believe the streak is likely to end and stop betting.
Obviously both predictions cannot be true at the same time but this contradiction is overlooked by most. It’s a reminder to us in our daily lives – emotions often overrule facts.