Kelly Can't Fail

Interesting side note on Kelly:

In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008.[1] The paradox was named for Todd Proebsting, its creator.

https://en.wikipedia.org/wiki/Proebsting%27s_paradox

Quoting the same page: One easy way to dismiss the paradox is to note that Kelly assumes that probabilities do not change.

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.

In particular, then the right approach has to be more risk averse than Kelly would recommend. In reality, most probabilities can only be estimated, while the objective probabilities (e.g. the actual long run success rate) may well be different and lead to ruin. That's also what makes the title "Kelly can't fail" more wrong than right in my opinion.

For the issue in Proebsting's paradox, one simple approach I've found successful is to gradually accumulate your full bet as the betting lines progress to their ultimate positions. This works even in illiquid markets where your bets affect the lines, since it gives the other participants less room to suddenly react to what you're doing. (Though you always have the slight worry of a huge last-second bet that you can't react to, eBay-auction style.)

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.

I think the problem with estimating a distribution is the same, it might simply not match reality (actual unknown success rates, actual unknown variance of your estimation of success rates being correct). In particular, if you are too optimistic relative to reality, Kelly betting will lead to ruin with high objective probability.

There are people who can verifiably estimate unknown probabilities with accuracy finer than 5 percentage points. These are called superforecasters.

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.