The Gambler’s Fallacy

coin tossThe Gambler’s Fallacy has led to the downfall of many a bettor. Consider this: the odds that a fair coin will come up heads ten times in ten flips are very low: 1/1,024, so you might feel safe betting against this happening. However, if a fair coin has been flipped nine times and come up heads every time, are the odds against it coming up heads on the tenth flip?

The odds on a fair coin flip are always fifty-fifty, and previous flips do not affect the odds of a future flip. Yet many people seem to believe that because the odds are so high against ten coin flips in a row coming up heads, that tails are “due” on the last flip. Conversely, some believe that a coin can be on a heads “streak” so heads become more likely.

The Martingale Strategy

rouletteFallacious reasoning also underlies the Martingale strategy. The strategy can be applied to various games of chance, but is most commonly suggested for roulette. The method is to pick a color, say black, and play that color repeatedly and consistently, doubling one’s bet whenever one loses. So the player bets one dollar on black. If the ball lands on black, then the player wins a dollar. If the ball lands on red, then the player bets two dollars on black next round. If she loses again, then she bets four dollars on black next round. Eventually, black must come up, and when it does, the player will recover her losses and be ahead by one dollar. This strategy may be successful in the short term, but will fail spectacularly at the point when an improbable-yet-certain long run of red outlasts the player’s available funds.

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