OPTIMAL EXCHANGE BETTING STRATEGY FOR WIN-DRAW-LOSS MARKETS

Since the Betfair betting exchange launched in 2000, sports gamblers have had a gambling forum quite different from the traditional bookmaker. Three features of betting exchanges in particular require new analysis methods extending the Kelly criterion originated by John Kelly (1956): (i) The ability to lay (i.e., bet against) a team as well as back it (ii) Negotiation of odds, where one can set one’s own odds and wait for another punter to match them, not just accept the market valuation at the time (iii) The bookmaker takes a fee as a fixed fraction of one’s net profit on a market, not as a hidden margin in each betting option’s price In sports where there are more than two possible outcomes, such as soccer (football), usually the prospective gambler will find that if he/she wants to bet on one team using the Kelly criterion, the same criterion will advocate laying against the other team. Basic Kelly betting offers no resolution to these correlated markets, and some punters at traditional bookmakers will instead seek a binary ‘handicap’ or ‘draw-no-bet’ market in order to find prices that they can immediately understand. This paper derives the criterion one should use when investing in a ‘win-draw-loss’ market, with the important feature that profits are significantly higher by combining back and lay bets than by relying on one or the other. The ‘draw-no-bet’ approach is shown to be optimal only in a narrow band of cases, where the advantage of having the draw result untaxed outweighs the profits to be gained by effectively backing it.