This paper investigates the reason why expected returns to identical bets placed at different odds vary significantly and systematically from one another. It is hypothesized that the cause is the existence for bettors of positive transactions costs. Two different arenas, fixed odds and spread betting markets, distinguished by different levels of transactions costs, are identified which offer competing bets about similar outcomes. The bias is examined in each arena and compared. Our results lend support to the hypothesis that the incidence of transactions costs on the bettor is at least a contributory factor in explaining the bias observed against bets placed at higher odds.