Double kelly criterion
No.13380074 ViewReplyOriginalReport
Quoted By: >>13380148 >>13380254 >>13380321
The Kelly criterion is a rule on how much to bet, mathematically. is there an adaptation of it for more than a single event?
The standard Kelly criterion is: . If the probability of some event happening is , and I can get times my money if it happens (including stake, e.g. b=1.4 means a $100 bet gives $40 profit).
But say I want to bet on two events with slight correlation, like "team 1 ahead by half-time" and "team 1 wins". I have the following 6 probabilities:
1) P(home team ahead and wins)
2) P(home team ahead but doesn't win)
3) P(home team behind but wins)
4) P(home team behind and doesn't win)
5) P(home team ahead)
6) P(home team wins)
If I'd treat them like independent events, I'd end up overbetting. If I'd treat them like 100% dependent, I'd bet less than I ought to. What's the solution?
I know I could do a mathematical optimization, but it feels like there should be a closed-form solution.
Would it be possible to break it up into 4 mutually exclusive bets and compute "phantom odds"?
The standard Kelly criterion is: . If the probability of some event happening is , and I can get times my money if it happens (including stake, e.g. b=1.4 means a $100 bet gives $40 profit).
But say I want to bet on two events with slight correlation, like "team 1 ahead by half-time" and "team 1 wins". I have the following 6 probabilities:
1) P(home team ahead and wins)
2) P(home team ahead but doesn't win)
3) P(home team behind but wins)
4) P(home team behind and doesn't win)
5) P(home team ahead)
6) P(home team wins)
If I'd treat them like independent events, I'd end up overbetting. If I'd treat them like 100% dependent, I'd bet less than I ought to. What's the solution?
I know I could do a mathematical optimization, but it feels like there should be a closed-form solution.
Would it be possible to break it up into 4 mutually exclusive bets and compute "phantom odds"?