In most explorations of the Kelly Criterion I’ve seen, we’re deciding the % of our bankroll to apply to a bet under the assumption we will be repeatedly faced with the same bet many times.
I’m curious whether anything about the analysis changes if we relax this assumption e.g if each successive bet we face is drawn from some distribution (either indecently or not). In these cases does Kelly still focusing on maximising the log of wealth, or does this complicate things in a meaningful way
If this is too broad a question, any pointers to a good resource would be appreciated!