Gamblers' Rationality in Parimutuel Soccer Betting

A model for strategic behaviour in parimutuel gambles with unequal winning-probabilities is developed and applied to gambles based on soccer results. Assuming that the bookmakers' quotas reflect the true probability of each possible result of a soccer game, we are able to derive a formula for the expected payoff of a betting strategy (Tipp). Using recent (1996-99) data from the Austrian games Toto and Torwette we are able to calculate the optimal strategies for 90 Toto and Torwette rounds. It turns out that given the relatively high probability of a rollover, it is optimal to overbet favourite outcomes (as compared to the probability of their occurrence). Comparing optimal with actual gamblers' behaviour we find that overbetting is even more pronounced than predicted by the model. This means that gamblers bet too frequently on relatively probable results whereas less probable results are too infrequently chosen relatively to the optimal strategy.