Abstract
We define the bettor’s curse as the tendency for individual bettors to overvalue their private signals about the likelihood of events relative to the public information contained in market odds. In this study, we examine the extent to which betting behaviour is driven by the bettors’ curse.
Under Bayesian updating, private signals mechanically update posterior beliefs. Given correct priors and signal precision, posterior beliefs are unbiased. If market odds fully aggregate the private information of all bettors, then all relevant information is summarised by the posterior probability. Consequently, conditional on the posterior, betting behaviour should be identical regardless of whether a bettor observes the private signal or not. While private signals may be correlated with the true probability, they are not perfectly correlated and therefore not fully informative. In contrast, market odds—if efficient—perfectly reflect the true probability (up to the bookmaker’s margin).
In our experimental setting, individuals are not required to acquire private information themselves. Instead, we exogenously provide them with a private signal with known precision. Posterior beliefs are then computed based on all these signals and signal precision according to Bayesian rule and presented directly to participants in the form of market odds. This design removes the need for participants to perform belief updating themselves. Under the Bayesian benchmark, if individuals solely depend on the posterior probability, irrespective of the signal observed, their behaviour should be identical.
H1 (Bettors’ Curse): We hypothesise that when individuals observe private signals, they overweight these signals and perceive posterior probabilities as higher or lower than they objectively are, which lead their betting behaviour deviating from the Bayesian benchmark. On average, they place higher bets when they observe a private signal than when no signal is observed.
H2 (Directional Betting): If bettors overweight their private signals, betting behaviour should move in the direction indicated by the signal. In our experiment, odds are fair, so the expected value of betting on either outcome is zero, and there is no ex ante reason to favour one outcome over the other. However, if private signals are overweighted, participants will systematically bet in favour of the outcome suggested by their signal. Such directional behaviour indicates that bettors treat their private information as more informative than the information already incorporated into market odds.
H3 (Sole Dependence on Signals): If bettors fully disregard the information contained in market odds and believe that probabilities depend solely on their private signals, then, conditional on observing the same signal, they will place higher bets when the odds are more favourable (i.e., when potential payouts are higher).