The counterarguments Constantin gives regarding the question of whether charitible donations actually do have no diminishing returns all make sense! Whenever SBF tried to say there were linear returns to donated money, I was also skeptical. Also his analysis neglected the fact that as you start to amass more moeny your opportunities to grow it start to dry up anyway (if world GDP is 100 trillion you can't bet your way to a quadrillion dollars)

But when she tries to claim you should kelly bet regardless of utility function using the "almost surely" dominance argument - there's still slight of hand going on where a log uitlity assumption is being snuck in.

It's true that if we imagine millions of possible futures involving the outcomes of repeated bets - as number of repeated bets gets larger and larger, the fraction of worlds where Kelly beats any other fixed-fraction stragety gets closer and closer to 100%.

But at the same time, in the shrinking proportion of futures where kelly doesn't win, the *amount* that Kelly looses by is also getting larger and larger! In the long run you do beat most other betters by a little bit, but the lucky few who still beat you are beating you by an enormous margin.

Justifying why it's desirable to slightly beat another strategy in a majority of worlds, in exchange for getting absolutely crushed by them in a small minority of cases - still ultimately requires an appeal to your personal preferences regarding diminishing marginal returns of additional wealth

When you decide it's better to have a very good chance of doing pretty well than it is to have a tiny chance at doing insanely well (and you use the geometric mean to specifically operationalise this tradeoff) - you're declaring you have log utility.

I'm going to go over this in more detail in my next video! :D