I'm looking at racing in Hong Kong and would like to apply the Kelly criterion to my probability estimates of the races.
I've seen a few algorithms for solving the kelly optimized bet percentages for mutually exclusive outcomes, but was never able to get something that looked correct.
To start with, all of the algorithms calculate a "score" and then sort things by that "score". I've see the score represented as "edge", as "odds * implied_odds", as "expected value", etc. Not sure which is ideal.
Is there a good resource, sample code, or good algorithm outline somewhere?
Looking at things further, it gets more complicated.
In HK, they don't post the odds, but the "dividend", which I believe includes your original dollar bet. So a horse paying 4/1 is really running at odds of 3/1. Then, the track take is 18%, so if my math is correct, the implied odds is:
(1 - trackTake) / (dividend - 1) = .82/dividend/1
1) The dividends posted are for a HKD 10 stake. So a horse shown at 50 is currently 4/1. If you are not American there are several bookmakers that do offer fixed odds on Hong Kong racing.
2) It is difficult to use Kelly when betting into a Pari-Matuel pool because the final odds are unknown. Your edge is derived from those odds.
Thanks FLC. That confirms my understanding of the "dividend" there. I have worked out something with a reasonable hit rate. The challenge now is bet allocation.
Three choices are:
1) Kelly (or fractional Kelly)
2) Bet 1 unit on any horse with a positive EV (based on my prob calculation.)
3) Bet 1 unit on any horse where my calculated prob is greater than the implied prob.
A better approach might be to bet to win x units. Risking 1 unit when a horse is even money and the same amount on a horse which is 10/1 would not be very sensible. No matter what approach you take however you still face the issue of not knowing what the final odds will be.
Of course the final odds are not known until after the race. (Or technically the second betting closes.) However, baring a huge move, I believe that the odds generally settle a few minutes before the race starts. There may be some last minute fluctuation, but large moves are rare.