That's good to know. Kelly is good if you know the probabilities AND they don't change.
If you don't know or if they can change, I expect the right approach has to be more complex than the Kelly one.
That's good to know. Kelly is good if you know the probabilities AND they don't change.
If you don't know or if they can change, I expect the right approach has to be more complex than the Kelly one.
As for the actual probability being different from the expected probability, that's not too difficult to account for. Just set up a distribution (more or less generous depending on your risk tolerance) for where you believe the actual probability may lie, and work out the integrals as necessary, recalling that you want to maximize expected log-value. It's not the trivial Kelly formula, but it's exactly the same principle in the end.
Almost all people can achieve at least 20 point accuracy with a few hours of training. Unknown probabilities are not so problematic as people make them out to be.
Probabilities are literally measures of uncertainty. It's okay for them to be uncertain. They always are.
Also, your estimate of the true probability doesn't have to be that exact, if your edge is big enough to begin with. Once I made great profits (betting with fake internet points) just by naively taking the sample proportion from a small sample. In fact, the event turned out to be more 'streaky' than a weighted coin flip, but it didn't matter, since everyone else there was betting on vibes.
In any case, it's not like there's just the trivial Kelly formula, and woe to you if its toy model doesn't apply precisely to your situation. It's a general principle that can be adapted to all sorts of scenarios.
For instance, casinos have different payout schedules for Blackjack based on minimum bet size and number of decks in the shoe. Payouts for single deck Blackjack are very small in comparison to multi-deck games, as well as requiring larger minimums (and they shuffle the deck after only a few hands).