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not sure I agree with you. Kelly says, if there is a positive expected value, there is an optimal amount to bet, which maximizes the growth rate of your stack

not sure I agree with you. Kelly says, if there is a positive expected value, there is an optimal amount to bet, which maximizes the growth rate of your stack per bet, if you were to bet repeatedly. If you overbet, your expected growth rate is negative... because over the long run, by the time you hit the jackpot you've lost too much of your stack to get back to even. Basically, I think Kelly says you can't just go by expected value, ie your edge, you have to look at your stack. Overbetting turns a +EV bet into a -EV bet and eventual loss of your whole stack. So 1) I don't think Kelly is a product of log utility, it just requires that you are trying to maximize your growth rate (As an aside, in many settings people are much more risk averse than log utility implies; and in many settings people don't have consistent cardinal utility, a time-inconsistent utility like prospect theory is more predictive) and 2) since you are presented with interesting bets every day, if not this particular one, Kelly generally applies, since if you don't heed it you fall victim to gambler's curse.

bluecalm 13y ago
Kelly bet amount just maximizes log(bankroll). Growth rate, utility, outcomes in series of bets etc. are just interpretations/uses of this fact.
- RockyMcNuts 13y ago
  hmmh... nitpick but log utility => maximizing the growth rate, but maximizing the growth rate maximizes utility for many different utility functions, in particular all constant relative risk aversion utility functions, of which log utility is one. so preference for maximizing growth does not imply log utility, could be linear utility too. (under a CRRA utility function, a risky income stream that varies between $1 and $2 gets the same risk aversion discount as one with a similar distribution that varies between $100 and $200, see e.g. http://ocw.mit.edu/courses/economics/14-123-microeconomic-theory-iii-spring-2010/lecture-notes/MIT14_123S10_notes04.pdf http://ocw.mit.edu/courses/economics/14-123-microeconomic-th... )
ronaldx 13y ago
> Kelly says, if there is a positive expected value, there is an optimal amount to bet Yes, and the optimal amount to bet here is for all practical purposes equal to zero. In short, you don't have a large enough stack to keep on taking this bet until it pays you back. I tend to agree with your wider point, that you can treat life as a long-term sequence of taking risky bets and use Kelly to approximate that. However, even if you did have an equivalent opportunity to this all day every day (which is itself hard to assert), Kelly is saying you definitely shouldn't take it here. If you don't have that repeated opportunity, Kelly-type thinking just leads to an even stronger conclusion - you definitely definitely shouldn't take it. Good luck to everyone if you're playing the lottery :) Until the numbers are drawn, you still have a chance ;)
- RockyMcNuts 13y ago
  yes, agree with you and OP! just Kelly makes the OP's advice not to play stronger, even if you get +EV, unless you're a millionaire you will overbet and go broke before you win !

bluecalm 13y ago

Kelly bet amount just maximizes log(bankroll). Growth rate, utility, outcomes in series of bets etc. are just interpretations/uses of this fact.

RockyMcNuts 13y ago
hmmh... nitpick but log utility => maximizing the growth rate, but maximizing the growth rate maximizes utility for many different utility functions, in particular all constant relative risk aversion utility functions, of which log utility is one. so preference for maximizing growth does not imply log utility, could be linear utility too. (under a CRRA utility function, a risky income stream that varies between $1 and $2 gets the same risk aversion discount as one with a similar distribution that varies between $100 and $200, see e.g. http://ocw.mit.edu/courses/economics/14-123-microeconomic-theory-iii-spring-2010/lecture-notes/MIT14_123S10_notes04.pdf http://ocw.mit.edu/courses/economics/14-123-microeconomic-th... )

ronaldx 13y ago

> Kelly says, if there is a positive expected value, there is an optimal amount to bet Yes, and the optimal amount to bet here is for all practical purposes equal to zero. In short, you don't have a large enough stack to keep on taking this bet until it pays you back. I tend to agree with your wider point, that you can treat life as a long-term sequence of taking risky bets and use Kelly to approximate that. However, even if you did have an equivalent opportunity to this all day every day (which is itself hard to assert), Kelly is saying you definitely shouldn't take it here. If you don't have that repeated opportunity, Kelly-type thinking just leads to an even stronger conclusion - you definitely definitely shouldn't take it. Good luck to everyone if you're playing the lottery :) Until the numbers are drawn, you still have a chance ;)

RockyMcNuts 13y ago
yes, agree with you and OP! just Kelly makes the OP's advice not to play stronger, even if you get +EV, unless you're a millionaire you will overbet and go broke before you win !