Ah, I see. The usual derivation of the Kelly criterion explicitly assumes that there is a specific sequence of events on which people are betting (e.g. stock market movements or horse-race outcomes); the players do not get to all bet separately on independent sources of randomness. If they could do that, then it would change the setup completely—it opens the door to agents making profits by trading with each other (in order to diversify their portfolios via risk-trades with other agents). Generally speaking, with idealized agents in economic equilibrium, they should all trade risk until they all effectively have access to the same randomness sources.
Another way to think about it: compare the performance of counterfactual Kelly and EV agents on the same opportunities. In other words, suppose I look at my historical stock picks and ask how I would have performed had I been a Kelly bettor or an EV bettor. With probability approaching 1 over time, Kelly betting will seem like a better idea than EV betting in hindsight.
Thanks, that way to derive it makes sense! The point about free trade also seems right. With free trade, EV bettors will buy all risk from Kelly bettors until the former is gone with high probabiliity.
So my point only applies to bettors that can’t trade. Basically, in almost every market, the majority of resources are controlled by Kelly bettors; but across all markets in the multiverse, the majority of resources are controlled by EV bettors, because they make bets such that they dominate the markets which contain most of the multiverse’s resources.
(Or if there’s no sufficiently large multiverse, Kelly bettors will dominate with arbitrary probability; but EV bettors will (tautologically) still get the most expected money.)
Ah, I see. The usual derivation of the Kelly criterion explicitly assumes that there is a specific sequence of events on which people are betting (e.g. stock market movements or horse-race outcomes); the players do not get to all bet separately on independent sources of randomness. If they could do that, then it would change the setup completely—it opens the door to agents making profits by trading with each other (in order to diversify their portfolios via risk-trades with other agents). Generally speaking, with idealized agents in economic equilibrium, they should all trade risk until they all effectively have access to the same randomness sources.
Another way to think about it: compare the performance of counterfactual Kelly and EV agents on the same opportunities. In other words, suppose I look at my historical stock picks and ask how I would have performed had I been a Kelly bettor or an EV bettor. With probability approaching 1 over time, Kelly betting will seem like a better idea than EV betting in hindsight.
Thanks, that way to derive it makes sense! The point about free trade also seems right. With free trade, EV bettors will buy all risk from Kelly bettors until the former is gone with high probabiliity.
So my point only applies to bettors that can’t trade. Basically, in almost every market, the majority of resources are controlled by Kelly bettors; but across all markets in the multiverse, the majority of resources are controlled by EV bettors, because they make bets such that they dominate the markets which contain most of the multiverse’s resources.
(Or if there’s no sufficiently large multiverse, Kelly bettors will dominate with arbitrary probability; but EV bettors will (tautologically) still get the most expected money.)