Biases in casino betting: The hot hand and the gambler's fallacy
Hmm…. how does” locus of control” influence “the hot hand” and “the gamblers fallacy”?
Abstract (Via SJDM)
We examine two departures of individual perceptions of randomness from probability theory: the hot hand and the gambler’s fallacy, and their respective opposites. This paper’s first contribution is to use data from the field (individuals playing roulette in a casino) to demonstrate the existence and impact of these biases that have been previously documented in the lab. Decisions in the field are consistent with biased beliefs, although we observe significant individual heterogeneity in the population. A second contribution is to separately identify these biases within a given individual, then to examine their within-person correlation. We find a positive and significant correlation across individuals between hot hand and gambler’s fallacy biases, suggesting a common (root) cause of the two related errors. We speculate as to the source of this correlation (locus of control), and suggest future research which could test this speculation.
Excerpts (Via SJDM)
The gambler’s fallacy is a belief in negative autocorrelation of a non-autocorrelated random sequence of outcomes like coin flips. For example, imagine Jim repeatedly flipping a (fair) coin and guessing the outcome before it lands. If he believes in the gambler’s fallacy, then after observing three heads in a row, his subjective probability of seeing another head is less than 50%. Thus he believes a tail is “due,” and is more likely to appear on the next flip than a head.
In contrast, the hot hand is a belief in positive autocorrelation of a non-autocorrelated random sequence of outcomes like winning or losing. For example, imagine Rachel repeatedly flipping a (fair) coin and guessing the outcome before it lands. If she believes in the hot hand, then after observing three correct guesses in a row her subjective probability of guessing correctly on the next flip is higher than 50%. Thus she believes that she is “hot” and more likely than chance to guess correctly.