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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Replying to
So:
1) it's not literally *wrong* in that it doesn't make a math error
2) I disagree in general that Kelly is the right way for people to bet because I disagree with its assumptions
3) neither 1/2 are necessary for my argument: Kelly only works if you consider *all* your money
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There are other problematic assumptions snuck in here, e.g.
a) the paper assumes that you can only do one or the other forever and can't ever take profit if you don't use an AMM
b) the paper assumes that exponential increase in valuation can go on forever
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E.g. see what happens to the math if you assume:
a) The person is only using 25% of their money in this particular USD/coin pair and 75% outside of the system
b) you only expand out ~10 years
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I think it's also worth noting that if you had tweeted "AMM skeptics should consider what utility curves make sense for them and whether there are more cost efficient ways to manage their risk, in some extremely constrained cases AMMs might be a decent choice" I wouldn't disagree
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This is a relief—I fundamentally disagree (I was worried it was a mathematical rather than a philosophical disagreement!)
My log-wealth-maximization maximalism has absolutely nothing to do with differences in individual utility functions
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Replying to
I think there are likely some math disagreements snuck in there as well but I'm not sure -- e.g., would you agree that none of the paper holds if you have a linear utility function?
Say more about the second sentence? I'm not sure what point you're making.
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I would not agree with that!
This is a good representation of my beliefs: arxiv.org/pdf/1011.4404.
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equation 5.9 is wrong
the entire article hinges on it and falls apart irreparably as 5.9 does
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to give more color here (and to be clear 5.9 is the core mistake that all of the attempts to defy the distributive property of multiplication in order to over-sell Kelly make):
EV[SUM({x})] = SUM[EV{x}]
EV[PRODUCT({x})] != PRODUCT[EV{x}]
Alternately, the article could attempt to claim that they weren't trying to give advice, just to say what the median is.
This would be what's implied by "It is only necessary that all possible scenarios occur exactly with the appropriate frequencies during the sampling time."
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That quote itself is quite problematic: the *entire* argument behind doubling down relies on the claim that sometimes something other than the median thing happens.
But of course outliers *do* sometimes happen! And they're super asymmetric.
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