[proamdev123]

> I haven't even found an explanation of why uncertainty about probabilities requires betting more conservatively than Kelly would recommend.

It’s because the risk of ruin increases quickly if you overestimate optimal f, as calculated by Kelly criterion. So OVER-estimating f, dramatically increases your risk of bankruptcy, while UNDER-estimating f only results in not optimizing your returns.

If you’re not certain of your probabilities because (you’re estimating unknowns), you’d prefer having sub-optimal gains over going bankrupt.

[cubefox]

I guess something like that is indeed the reason. However, as stated (in terms of "risk of ruin") the argument doesn't quite work. Because even if the probabilities are known with certainty, betting the Kelly optimum would increase the risk of ruin compared to betting less. But Kelly betting would nonetheless be better.

[cochne]

The thing about Kelly is that it assumes risk of ruin is zero because you never bet your entire bankroll. It assumes you can always bet a fraction of a fraction of what you have remaining.

[cubefox]

Sure, but you can get arbitrarily close to zero over time.