What We Gain by Recognising the Role of Chance

At the Roulette Table in Monte Carlo (1892) by Edvard Munch. Courtesy Munch Museum/Wikipedia

Mark R Rank at Psyche: On 18 August 1913, at a casino in Monte Carlo, a roulette wheel was spun, and the ball fell on black. This is not unusual. The alternating red and black colours of a roulette wheel mean that, like a coin toss, there is roughly a 50-50 chance that the ball will land on either colour. But as the ball continued to land on black, again and again and again, gamblers rushed to the table, placing bets on red in the belief that the alternating colour must be coming up. Convinced that things would eventually balance out, gamblers raised their bets each time the ball landed on black. But they continued to lose. Improbably, the ball would settle on black a total of 26 times.

The ‘Monte Carlo fallacy’, also known as the ‘gambler’s fallacy’, is the belief that a string of bad luck must end. It is the belief that there is a sense of balance in how luck plays out. It explains why gamblers playing roulette mistakenly believe that one colour is overdue after a consecutive series of the other colour, even though the odds remain 50-50. But the relevance of the Monte Carlo fallacy goes far beyond the tendencies of gamblers in casinos.

Though anecdotal evidence for the fallacy is well established, only in recent decades have experts confirmed our belief that a string of bad luck must end. In a 2005 study, two US researchers studying decision-making, James Sundali and Rachel Croson, analysed gambling behaviour at casinos in Reno, Nevada. Among those who were making 50-50 bets in roulette, Sundali and Croson found that gamblers who had watched one spin of the wheel evenly divided their bets between red and black. However, as the wheel landed on red (or black) in consecutive spins, the betting changed significantly. After five consecutive reds, 65 per cent of the bets were placed on black, and after six consecutive reds, 85 per cent of the bets were on black. Though the sixth spin of a roulette wheel is not influenced by the previous five spins, gamblers still placed their bets as if it was.

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