Friday, January 01, 2010

Kelly Horse Race or Ziemba Roulette

In the spirit of the New Year, I offer the following thought-provoking argument:
Betting is often described as a competition between you and the "Crowd" (i.e. Pari-Mutuel market) on which you can better estimate the true distribution of odds in a particular sporting event. In that context, a good starting point is to ask Bill Benter's fundamental question of handicapping: what additional variables (if any) explain a significant proportion of the variance in results to date that is not already accounted for by the public odds (Wisdom of Crowds)? By keeping records, it is possible to determine whether or not you have been successful over time in so doing. However, it is not possible to know (in advance) if you have an overlay in an upcoming event. This is the fundamental flaw of handicapping and, eo ipso, the flaw of fundamental handicapping.
The alternative approach is technical trading and an often underestimated strategy is "Bold Play" and its variants. Bold play is recommended for subfair games (i.e. p < 0.5, assuming even money bet) and, given the high-level of taxation, one can argue that horse-racing qualifies. Without going into the mathematical details and assuming a little "poetic licence", bold play reduces to an algorithm comprising two rules:
__a) Bet amount to reach target bankroll in single event (e.g. one race); or
__b) Bet amount in current event to reach bankroll level from which it is possible to attain target bankroll in next event.
You will no doubt immediately recognize that it is possible to iterate rule b) over many events (e.g. complete race card) but, ideally, you want to minimize the number of iterations. This technical trading approach only requires information on current bankroll, target bankroll, number of remaining events, house limits, and access to the public odds.
In summary, the advice to use fundamental handicapping to find overlays which you then exploit using edge-based staking (Kelly, 1956) assumes a superfair game but if, in fact, the game is essentially subfair then technical trading is recommended using bold play (Ziemba, 2002) or one of its variants in as few iterations as is feasible given whatever constraints are in place (e.g. maximum stakes).