Deriving the Kelly Criterion to Maximise Profits

I had never paid much attention to Effective Altruism or SBF before FTX blew up, but when that happened I spent some time reading old EA forum posts and SBF tweets and interviews. One of the things that absolutely shocked me was the dismissal of the Kelly criterion by SBF and other EAs. The argument was that the Kelly criterion was only rationalized by a logistic utility function, and if you were going to use your money for altruistic purposes a linear utility function is more appropriate (at least up into the trillions of dollars) because you can help twice as many people with $200 billion as you can with $100 billion.

This argument was used--by SBF and others--to justify truly absurd risk taking. I don't think it's an exaggeration to suggest that this misunderstanding may have been one of the primary drivers of Alameda's (and hence FTX's) downfall. For a group with as many smart people as EA and as many people obsessed with existential risks as EA not to have started screaming en masse when SBF suggested he would take a 51-49 bet on doubling utility or deleting all known life out of existence[1] is insane.

The mathematical misunderstanding is one part of it. Kelly betting dominates any other betting strategy in the sense that as the number of bets increases the probability that the Kelly better will have more money than someone following any other strategy approaches 1. You don't need a logarithmic utility function. If I bet Kelly and you follow some other strategy, eventually I will almost surely end up with more money and more utility than you.

I suspect another part of it is a misunderstanding by SBF (and perhaps others) of Jane Street's trading strategy. Jane Street encouraged their traders to be "risk neutral", which can be expressed as maximizing expected utility with a linear utility function. They wanted their traders to be willing to take big risks. But any individual trader is only working with a tiny fraction of Jane Street's capital, so even if they're risking all the money they've been given to work with on a bet that's still a small bet relative to the entire company. SBF seems to have taken that same risk neutral idea and applied it to the entirety of Alameda/FTX's available capital (and indeed expressed a willingness to apply it to the combined utility of the entire world), with predictably disastrous results.

[1] https://elmwealth.com/a-missing-piece-of-the-sbf-puzzle/

What a great example of Dunning-Kruger as applied to elites. I remember the spike of interest in DK bias during the pandemic [1], largely as a way of explaining how uneducated folks could be so confidently incorrect about vaccination strategies. In reality it can strike in any social strata -- like a bunch of professional traders wielding billions of dollars, smugly misunderstanding Kelly.

[1] https://trends.google.com/trends/explore?date=today%205-y&ge...

I don't want to denigrate the whole community or anything as quite a lot of thought-provoking and interesting reading has come out of it over the years, but I can't help but recall very serious defense of the notion of quantum immortality on LessWrong after Eliezer's fairly convincing rants that any serious scientist has to conclude multiple worlds is the only sensible interpretation of quantum mechanics. If you honest to God take this to its logical conclusion, then wiping out all life in your particular branch of the multiverse may very well be the right move if it doubles utility in 51% of all possible universes.

I don't actually buy that argument and think it's insane, but it would not remotely surprise me if SBF believed it, and if you do, then you don't really observe the Kelly criterion. You take the ruin for the larger team of other yous that collectively wins. If the density of quantum branches in which he funded colonization of the galaxy is greater than the density in which he is serving life in prison, it was worth it.

In some way, I think everyone was so used to founders saying dumb things for attention that nobody realized SBF was actually going to do it..