The Kelly criterion is an elegant, but often misunderstood, result in decision theory. To begin with, suppose you have some amount of some resource, which you would like to increase. (For example, the resource might be monetary wealth.) You are given the opportunity to make a series of identical bets. You determine some fraction of your wealth to wager; then, in each bet, you gain a fraction with probability , and lose a fraction with probability .[1]
In other words, suppose is your wealth after bets. We will define , and we will suppose for simplicity that . Then , where is a random variable defined as:
Now suppose that, for some reason, we want to maximize . By linearity of expectation, . Hence, we... (read 1196 more words →)
No -- you should bet so as to maximize E[U]. If U(W)=logW, and you are wagering W, then bet Kelly, which optimizes E[logW]=E[U]. However, if for some reason you are directly wagering U (which seems very unlikely), then the optimal bet is actually YOLO, not Kelly.