A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations.
Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1-per-coin game with a 1% edge at a pretty good clip.
And what do you earn with perfect play in that situation? The princely sum of around $30 an hour.
A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy.
The Kelly criterion is almost never used as-is because it is very sensitive to probability of success, which is hard to know accurately and in many cases, dynamically changing. This is easy to see in an Excel spreadsheet. Changing the probability by even 0.01 percent can vastly shift the results. The article calls this out in the last paragraph.
The article mentions fractional Kelly is a hedge. But what fraction is optimal to use? That is also unknowable.
Finance folks, correct me if I’m wrong, but the Kelly Criterion is rarely used in financial models but is more a rule of thumb that says roughly if you have x $ and probability p, in a perfect world you should only bet y amount. But in reality y cannot be determined accurately because p is always changing or hard to measure.
All these probabilities and so on are basically unknowable so the real utility of this kind of thing for a hedge fund is converting a traders view into a suggested size so they take the amount of risk that they're being paid to take.
Here's a link to a bigger graph for the Blackjack Scenario:
https://github.com/obrhubr/kelly-criterion-blackjack/blob/ma...
I think it shows that Blackjack is not even theoretically winnable over time if you have to pay for information on the count in the form on minimum bets. The ideal case it that you bet $0.49 for every $1,000 in your investment pool when the count is extraordinarily high.
Even if you hack the casino's cameras so you know the count without having to be at the table, your reward is a growth rate that is very low per hand.
For the coin flipping scenario, what happens to the casino? Shouldn't they lose money in the long run as well? Or is it that they're under the kelly threshold with all the house cash?
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/