An explanation of each-way wagers in three models of risky choice

Punters may engage in betting on both a selection in an event to finish first or in one of the number of places, e.g. second, third or fourth. When the amounts staked with bookmakers at fixed odds on the win and place are equal, it is called an each-way bet. Each-way bets are apparently popular with punters but inconsistent with prominent models of wagering which assume gamblers are everywhere risk-seeking. In this note, we derive the conditions for win and place bets to be optimal in these three models of risky choice. The mathematical conditions for the each-way wager to be optimal, as opposed to a win and place wager with different stakes, are complicated and appear likely to occur rarely in practice. However, bettors obviously see the attraction in giving themselves two ways to bet on the one horse or two ways to win and betting each way. We suggest part of the ‘each-way’ betting attraction is that they are quick and easy to compute – a heuristic – to solve an otherwise complex betting strategy.