I stumbled upon a research paper the other day called “Issues related to sports gambling“, written by three well-known academics Robin Insley, Lucia Mok and Tim Swartz from Simon Fraser University in Burnaby, British Columbia, Canada.
The authors look at various issues related to sports wagering, such as
i) an expression is obtained for the distribution of the final bankroll using fixed wagers with a specified initial bankroll,
ii) fixed percentage wagers are considered where the Kelly method is extended to the case of simultaneous bets placed at various odds; a computational algorithm is presented to obtain the Kelly fractions, and
iii) they consider the problem of determining whether a gambling system is profitable based on the historical results of bets placed at various odds.
Section 5 (“Is a gambling system profitable?”) of the paper can be particularly interesting for sports betting fans.
The main conclusion of the authors (based on their “extensive personal simulations”) is that it is better to begin with the Kelly system using a bankroll of x1 = $400, and if the bankroll drops below x2 = $200, add the final $100 to the bankroll.
The idea is to ‘kickstart’ the system since a very small bankroll grows slowly with fixed percentage wagering. It would be interesting to see if optimal values for x1 and x2 could be obtained. Again, as long as the prescribed value of Kelly wagering exceeds $3000, you would maintain $3000 betting.
The results that the authors have presented in this paper are readily applicable to sports betting. The real difficulty is coming up with a winning system.