A bit more explanation on what the Kelly Criterion is, for those who haven’t seen it before: suppose you’re making a long series of independent bets, one after another. They don’t have to be IID, just independent. They key insight is that the long-run payoff will be the product of the payoff of each individual bet. So, from the central limit theorem, the logarithm of the long-run payoff will converge to the average logarithm of the individual payoffs times the number of bets.
This leads to a simple statement of the Kelly Criterion: to maximize long-run growth, maximize the expected logarithm of the return of each bet. It’s quite general—all we need is multiplicative returns and some version of the central limit theorem.
A bit more explanation on what the Kelly Criterion is, for those who haven’t seen it before: suppose you’re making a long series of independent bets, one after another. They don’t have to be IID, just independent. They key insight is that the long-run payoff will be the product of the payoff of each individual bet. So, from the central limit theorem, the logarithm of the long-run payoff will converge to the average logarithm of the individual payoffs times the number of bets.
This leads to a simple statement of the Kelly Criterion: to maximize long-run growth, maximize the expected logarithm of the return of each bet. It’s quite general—all we need is multiplicative returns and some version of the central limit theorem.
That’s a really accessible (to me) explanation! Thank you.
Seconding shminux, found this explanation really helpful.