Two researchers looked at historical records of online betting on sporting events like animal racing or soccer matches. What was surprising was that the "hot hand" effect, or the increased probability of success after previous successive successes, was actually discernible. The opposite effect was also observable: a "losing streak" also existed for these kinds of bets and gamblers. One possible explanation is that this is a market which can reward skill in wagering-- it's inefficient. Researchers seemingly ruled this out by looking at the overall winnings of gamblers who had winning streaks vs the control who never had such a streak: the amounts of money each group made (on average) was nearly identical. Thus the gamblers who had winning streaks didn't seem to get it from skill, since over the course of their careers they won/lost the same amounts of money (as those without a streak). Researchers then examined the odds taken in bets being made on both winning and losing streaks. It appeared gamblers who were in the middle of a winning streak took bets with shorter odds, while those with losing streaks took bets with longer ones. In other words, those in the middle of a winning streak thought their luck might be nearing the end and got more conservative, while those in a losing streak thought their luck was about to turn around. This classic "gamblers fallacy" is correlated with the observed occurrence of the "hot hand"/"losing streak" effects.
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