It's trying to maximize EV[log(money)] instead of EV[money].
This is probably wrong in and of itself as an assumption to make.
But if you *do* want to make that assumption, then e.g. you have to consider all of your assets that don't have anything to do with the pool.
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Proponents of the Kelly criterion almost never use it with their own money.
Do you think most people’s preference is actually to maximize log(wealth)?
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The Kelly criterion does not assume that you prefer to maximize log(wealth). It assumes that you would prefer having more wealth to having less wealth, and it guides you to the strategy where you have more wealth than any other strategy in 99.99...% of worlds (in the long run)
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Causation is tricky, but Kelly is mathematically equivalent to maximizing log(wealth), so assuming one gives the other.
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I think you're being a bit glib with the second half there? Like I could equally say "maximize linear EV assumes you'd prefer having more wealth than less wealth, and it guides you to the strategy where you are able to get the largest possible wealth by a factor of 999999999..."
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Hmm I don’t think EV(wealth) maximization actually maximizes wealth in the best possible world, right? It doesn’t reach the highest peak
What EV(wealth) maximizes is sum of wealth across all possible worlds
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Peak-maximization would mean buying lottery tickets and such even at negative EV
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so in every example we've been talking about they *are* the same.
they don't have to be but they usually are.
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agreed that negative lottery tickets are different here but every approach gets that one right!
but in e.g. st petersberg, hold USDC vs hold ERC20 token vs LP, classic Kelly question, etc., the max EV = max upside strategy = bet it all every time on the max EV option
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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))
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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