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.
Weird, somehow the links got merged together.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8046229/
https://royalsocietypublishing.org/doi/10.1098/rsos.200566
There’s a few papers on using prediction markets to determine which experiments are likely not to replicate. The prediction markets worked quite well. https://www.pnas.org/doi/10.1073/pnas.1516179112 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8046229/
https://royalsocietypublishing.org/doi/10.1098/rsos.200566
Someone should also talk to this guy: https://fantasticanachronism.com/2021/11/18/how-i-made-10k-predicting-which-papers-will-replicate/
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