But more generally my point is that "maximize odds of winning" is not what really matters, and neither is "maximize the max upside"; both are "good" things to have but neither are perfect, and really this is just an argument between max(EV) and max(EV(log))
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No! I am not trying to maximize EV of anything!
I want to pick the strategy that beats yours 99.99% of the time. That’s my terminal goal
Kelly takes that input and spits out that I should maximize EV(log(wealth)), but that preference is the consequence, not the cause
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Understood -- I think it's a crazy goal that's not going to hold water if you really dig into it but acknowledged that's what you want to do!
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also, again this is all not necessary for my core arguments against the original paper; this is all a looooong tangent about risk tolerance
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Maybe one way to frame this: ignore the infinite time horizon point—imagine it’s a one-shot.
And ignore utility as a function of wealth—let’s just talk in terms of raw utility (the output of the utility function).
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If presented a gamble, I would not necessarily want to maximize EV(utility).
I am not indifferent between 99% chance of 0 utility and 1% chance of 100, and 100% chance of 1.
That preference is NOT a statement about my function of wealth->utility. Right?
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So my objection to the maximize-EV(wealth) heuristic is that over time it will tend inevitably to box me into an outcome where almost all of my utility is enjoyed by a version of me that lives in a vanishingly unlikely world—regardless of what my utility function on wealth is
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Your heuristic is that you prefer strategy A to strategy B if A has higher EV(utility). My heuristic is that I always prefer strategy B to strategy A if B leads to higher utility with probability (1 - epsilon)—regardless of how high my utility would be in the epsilon case.
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Now, whether Kelly actually outperforms your strategy with probability (1 - epsilon) does depend on some assumptions, including that we take the limit as t goes to infinity. But I think that is a separate disagreement
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Do you agree that it’s coherent (and indeed kinda reasonable) for me to prefer the gamble where my utility is almost surely higher, even if my average utility across all outcomes is lower because I miss out on a very rare outcome with astronomical utility?
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(I agree with )
There are 2 different threads here.
A) how risk seeking should you be?
B) should there exist some function F that you're trying to maximize the EV of?
on (A) I disagree with you but don't think it's obvious, and isn't the primary thing here.
(In particular I think the correct decision *is* to bite the bullet on twitter.com/danrobinson/st, but think that's not at all necessary for my argument here)
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Replying to @danrobinson @SBF_Alameda and @elliot_olds
So my objection to the maximize-EV(wealth) heuristic is that over time it will tend inevitably to box me into an outcome where almost all of my utility is enjoyed by a version of me that lives in a vanishingly unlikely world—regardless of what my utility function on wealth is
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Moving on to (B):
Say there are 3 possible outcomes; o_1 < o_2 < o_3
You have two options:
i) 100% o_2
ii) p_2 chance of o_1, (1-p_2) chance of o_3
for what p_2 are you indifferent between (i) and (ii)?
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