Note that Kelly is valid under the assumption that you know the true probabilities.
I object to the concept of “know the true probabilities”; probabilities are in the map, not the territory.
II do not know whether it is still valid when all you know is a noisy estimate of true probabilities—is it?
Is Kelly really valid even when you “know the true probabilities”, though?
From a Bayesian perspective, there’s something very weird about the usual justification of Kelly, as I discuss (somewhat messily) here. It shares more in common with frequentist thinking than with Bayesian. (Hence why it’s tempting to say things like “it’s valid when you know the true probabilities”—but as a Bayesian, I can’t really make sense of this, and would prefer to state the actual technical result, that it’s guaranteed to win in the long run with arbitrarily high probability in comparison with other methods, if you know the true frequencies.)
Ultimately, I think Kelly is a pretty good heuristic; but that’s all. If you want to do better, you should think more carefully about your utility curve for money-in-hand. If your utility is approximately logarithmic in money, then Kelly will be a pretty good strategy for you.
I object to the concept of “know the true probabilities”; probabilities are in the map, not the territory.
Is Kelly really valid even when you “know the true probabilities”, though?
From a Bayesian perspective, there’s something very weird about the usual justification of Kelly, as I discuss (somewhat messily) here. It shares more in common with frequentist thinking than with Bayesian. (Hence why it’s tempting to say things like “it’s valid when you know the true probabilities”—but as a Bayesian, I can’t really make sense of this, and would prefer to state the actual technical result, that it’s guaranteed to win in the long run with arbitrarily high probability in comparison with other methods, if you know the true frequencies.)
Ultimately, I think Kelly is a pretty good heuristic; but that’s all. If you want to do better, you should think more carefully about your utility curve for money-in-hand. If your utility is approximately logarithmic in money, then Kelly will be a pretty good strategy for you.