Professional gambler here. I haven’t really studied the formal theory behind the Kelly Criterion, but I’m certainly aware of the practical import. It doesn’t rely on having a logarithmic utility function for money; it makes a much stronger claim, which is that it maximizes long-term results, and I believe it has been formally proven to do so.
Overbetting Kelly results in a much higher risk of ruin, which reduces long-term results even if your utility function for money is linear, as SBF claims.
I see there seems to be some disagreement on this point… let me quote the conclusion of Kelly’s original paper:
”The gambler introduced here follows an essentially different criterion from the classical gambler. At every bet he maximizes the expected value of the logarithm of his capital. The reason has nothing to do with the value function which he attached to his money, but merely with the fact that it is the logarithm which is additive in repeated bets and to which the law of large numbers applies. “
Good point! My understanding is that SBF’s argument was that the right thing to average wasn’t serial rounds of oneself (where the money to play with would be determined by past rounds), but parallel-universe versions of oneself (i.e., of 100 parallel universes with SBF trying his strategy, what % would lead to him being super-rich?).
Professional gambler here. I haven’t really studied the formal theory behind the Kelly Criterion, but I’m certainly aware of the practical import. It doesn’t rely on having a logarithmic utility function for money; it makes a much stronger claim, which is that it maximizes long-term results, and I believe it has been formally proven to do so.
Overbetting Kelly results in a much higher risk of ruin, which reduces long-term results even if your utility function for money is linear, as SBF claims.
I see there seems to be some disagreement on this point… let me quote the conclusion of Kelly’s original paper:
”The gambler introduced here follows an essentially different criterion from the classical gambler. At every bet he maximizes the expected value of the logarithm of his capital. The reason has nothing to do with the value function which he attached to his money, but merely with the fact that it is the logarithm which is additive in repeated bets and to which the law of large numbers applies. “
https://archive.org/details/bstj35-4-917/page/n9/mode/2up?view=theater
Good point! My understanding is that SBF’s argument was that the right thing to average wasn’t serial rounds of oneself (where the money to play with would be determined by past rounds), but parallel-universe versions of oneself (i.e., of 100 parallel universes with SBF trying his strategy, what % would lead to him being super-rich?).