Most studies of both pari-mutuel and fixed-odds betting markets have shown a systematic tendency for the expected return to bets at lower odds to exceed those at higher odds. Some work, however, has revealed in certain markets the absence or even reversal of this bias. We present a model which distinguishes two separate types of bettor, and use this to demonstrate how transactions costs, the extent of public information, and consumption benefits of betting can explain the disparities. Our empirical evidence, taken from a fixed-odds market, lends support to our theoretical conclusions.