Conversation

SBF
@SBF_FTX
3) Let’s say you were offered a coin flip. 75% it comes up heads, 25% it comes up tails; 1:1 payout. How much would you risk?
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SBF
@SBF_FTX
4) There are a number of ways to approach this question, but to start: what do you want, in the first place? What’s your utility function?
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SBF
@SBF_FTX
5) In other words--how cool would it be to make $10,000? How about $1,000,000--is that 100 times as good? For most people the answer is ‘no, it’s more like 10 times as good’. This is because of decreasing marginal utility of money.
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SBF
@SBF_FTX
6) For the median US household, making another $10k helps them move to a more comfortable house, buy a newer car, and eat out more--not nearly the utility that you can get for $10k in the developing world, but still something.
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SBF
@SBF_FTX
7) But the 100th time you win $10k, it’s worth less. You’ve already bought a new car and moved to a fancier house. You could buy a few more new cars, but honestly who’s going to drive them? There are things you can do with it, but generally it’s just worth less.
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SBF
@SBF_FTX
8) One reasonable utility function here is U = log(W): approximating your happiness as logarithmic in your wealth. That would mean going from $10k to $100k is worth about as much as going from $100k to $1m, which feels…. reasonable? (this is what the Kelly Criteria assumes)
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petes
@petespetes
Replying to
@SBF_FTX
and
@SBF_Alameda
Kelly doesn't "assume" this. It calculates the optimal bet sizing for optimal growth given that you can keep making the same bet repeatedly. The implication that you should bet more with a more linear utility/happiness function is incorrect if you intend to keep gambling.
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