Quote:
Originally Posted by KT_Purple
Not necessarily true. If we constantly adjust our bet size based on our bankroll we will eventually always win because our risk of ruin approaches zero and at some point we will theoretically always be in the black. In this sense Kelley can be seen as a reverse martingale. It's a surprising and counterintuitive result. A Kelley with an infinite br is a martingale
I’m confused about what you’re saying. What would Kelly say to bet playing a breakeven game?
Kelly maximizes the rate of bankroll growth. It doesn’t make sense to me that Kelly could recommend any bet size for betting strategies wtih 0 expected bankroll growth. Perhaps it would be more accurate to say Kelly “doesn’t care” whether you bet at 0 EV?
I can at least say that the Kelly bet size approaches zero as the edge approaches zero from the right.
Not talking about Kelly anymore, repeatedly betting any fraction of a finite bankroll at no edge leads to expected decline in the median bankroll. As the number of bets approaches infinity, the expected median bankroll approaches 0. Under the assumption that money has decreasing marginal utility, placing any sized net with neutral EV has negative utility.