If there are two pots with the same growth rate, and you can’t rebalance between them, you think you can beat the growth rate?
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And the objectionable assumption that I’m making is the infinite time horizon, right?
And I guess the assumption “I prefer A to B if A outperforms B with probability 1” but that seems really hard to object to (apart from objecting to the infinite time horizon)
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nope, there are a lot of bad assumptions!
1) infinite time horizon
2) the prob dist of the coins: your model relies on the claim that with p --> 1, ETH > $999999999999999 eventually
3) that you can't rebalance
4) that you can't choose a better way to trade
...cont'd
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5) that you assign prob 0 to blowing out to ~$0 and staying there with an AMM
6) that you lose only epsilon to each arb
7) (that you are log-maxing but while I think that's wrong it's not *stupid*)
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8) and, yes, the thing you said it's hard to object to.
you still haven't responded to
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Fair, I didn’t mean every assumption in the post about rebalancing portfolio growth, just in this separate hypo about pots. But I see why you think it’s an unrealistic scenario.
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wait but this separate hypo has to inherit all the stupid assumptions from the post about growth or else the hypo is wrong!
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No? The hypo is just about pots with some expected log growth. The pots are black boxes. No mention of rebalancing or anything
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At any rate this hypo is definitely a tangent—the reason I am harping on it is because you and Arthur said that I was unambiguously wrong on the math
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you're still assuming:
1) infinite time horizon
2) constant log growth factor in each pot
3) that those can scale to infinite value/size while staying exactly the same in terms of growth
4) that you can't rebalance
and that we're trying to maximize *asmptotic growth rate* - there are many strategies that give the *same* asymptotic growth rate, but e.g. higher E[log(wealth)]
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there are even strategies that have higher growth rate at every single step, but only eventually have the same growth rate in the limit (maybe, not 100% sure the limit is the same)
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Replying to @GaussianProcess @ArthurB and 3 others
The first has the same argmax f for every N, this is just 2p-1 as in regular Kelly
The second has decreasing argmax f as N increases
I don't know whether the limit is also 2p-1, but this seems at least plausible
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