An important consideration is that the hot hand and gambler’s fallacies appear at first to be opposite effects. While bettors may believe that long runs in the results of players or teams will continue (the hot hand), they simultaneously believe that long runs should end (the gambler’s fallacy). This begs the question: how can these two apparently opposite effects be explained?
One proposed explanation for both fallacies is the representativeness heuristic (Tversky and Kahneman 1971) in which decision-makers believe that sequences should be representative of the generating process. Decision-makers apply the “law of large numbers” too readily; that is, they believe in the “law of small numbers.” In other words, while the relative frequencies of outcomes approximate the generating process in the long run, people believe that this should also be the case in the short run.
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So the gambler’s fallacy is explained because people believe that unusually long streaks are not representative and so predict an alternation to make the sequence more representative. The hot hand is explained because people tend to over-infer from short sequences evidence of biased decision-making in betting markets 509 in a random process and decide that there is some underlying nonrandom process generating the sequence (Rabin 2002).
It is potentially problematic to explain opposite phenomena with the same principle. However, a solution was provided by Peter Ayton and Ilan Fischer (2004; see also Burns and Corpus 2004), who tested whether the type of random process employed to generate the result was consequential in whether decision-makers displayed the hot hand or the gambler’s fallacy. They hypothesized that when outcomes reflect human performance people believe in the hot hand, whereas when outcomes reflect inanimate mechanisms people believe in the gambler’s fallacy.
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This might explain why winning streaks of basketball and roulette players are perceived to exhibit long-run tendencies but outcomes of roulette games and lotteries are not. They conducted an experiment where they asked participants to play a simulated roulette-style game. Participants were first required to choose between red and blue and second were asked to rate their confidence in their prediction.
The results confirmed that while people are more likely to predict an alternation after a long run of either color they are also more confident in their own ability after a long run of successful predictions. Ayton and Fischer (2004, 1374) concluded that while the sequences of outcomes (red or blue) and predictions (win or lose) are each identical independent processes, “the two sequences are psychologically perceived quite differently; subjects simultaneously exhibited both.
Finally
The hot hand and the gambler’s fallacy.” In a second experiment they found that participants were more likely to attribute random sequences with low/high alternation rates to human performance/inanimate mechanisms. This line of experimentation goes some way to unravel the problematic nature of explaining two apparently opposite effects with the same heuristic. In summary, the
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