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/
[1] https://trends.google.com/trends/explore?date=today%205-y&ge...
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.
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.
"$1 per coin game" is this a game where you put in $1 to play and get paid either $2 or $0 with 50-50 probability (0 expected).
And the what does it mean %1 edge? Does it mean the probabilities are such that the expected payout is 1c per coin flip?
A million players each placing a single bet will have an expectation of losing the house edge.
A single player placing a million bets has an expectation of $0.
The fact that the aggregate and the single entity Experience different expectations despite both placing a million bets is what makes this ergodic.
Nassim Taleb also talks about this quite a lot: https://youtu.be/91IOwS0gf3g
TL;DR: while a single investment may be ergodic, portfolio management (the math behind weighting successive and concurrent investments/bets) is not, as it has a strong dependence on all prior states.
Ergodicity is less about memorylessness and more about the constraints on transitions into this or that state. A system is ergodic if "anything that can be an outcome, eventually will happen".
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.
The Kelly criterion is an optimization of capital growth (its logarithm) method/guide. Not using it doesn't change its correctness.
But yes you need to know the advantage/the edge you have. Like with pricing methods eg for European options for Black Scholes you need to know the volatility and there is no way to know it, you estimate. This is where all the adjusting for bias and ML comes in.
I don’t think it is used in this way. It swings too much with a given p.
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.