Whatever the reason for these false intuitions, subsequent research has revealed that gamblers fallacy can have serious consequences far beyond the casino. The bias appears to be present in stock market trading, for instance. Many short-term changes in stock price are essentially random fluctuations, and Matthias Pelster at Paderborn University in Germany has shown that investors will base their decisions on the belief that the prices will soon even out. So, like Italys lottery players, they trade against a streak. Investors should, on average, trade equally in line with the streak and against it, he says. Yet that is not what we can see in the data.

The gamblers fallacy is a particular problem in the very professions that specifically require an even, unbiased judgement.

One team of researchers recently analysed US judges decisions on whether or not to grant asylum to refugees. Logically speaking, the ordering of the cases should not matter. But in line with the gamblers fallacy, the team found that the judges were up to 5.5% less likely to grant a case if they had granted the two previous cases a serious decline from the average acceptance rate of 29%. Consciously or not, they seemed to think that the chances of having the same judgement three times in a row was just too small, and so they were more inclined to break the streak.

The researchers next analysed bank staff considering loan applications. Once again, the order of the applications made a difference: the loan officers were up to 8% more likely to reject an application after they had already accepted two or more in a row and vice versa.

As a final test, the team analysed umpires decisions in Major League Baseball games. In this case, the umpires were about 1.5% less likely to call a pitch a strike if the previous pitch was also called a strike a small but significant bias that could make all the difference in a game. Kelly Shue, one the co-authors of the study, says that she was initially surprised at the results. Because these are professionals and they're making decisions as part of their primary occupation, she says. But they were still vulnerable to the bias.

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The simple maths error that can lead to bankruptcy - BBC News