Agreed. Utility is a flow, not a stock—it doesn’t carryover from decision to decision, so you can’t “lose” utility, you just find yourself in a state that is lower utility than the alternate you were considering. And there’s no reason it can’t be negative (though there’s no reason for it to be—it can safely be normalized to whatever range you prefer).
Either of these would make the Kelly strategy to minimize the chance of going broke and being barred from future wager irrelevant.
When talking about wagers, you really need to think in terms of potential future universe states, and a corresponding (individual, marginal) function to compare the states against each other. The result of that function is called “utility”. All it does is assign a desirability number to a state of the universe for that actor.
Attempts to treat utility as an actual resource in and of itself are just confused.
So, if you change the problem to be meaninful: say you’re wagering remaining days of life, which your utility function is linear in (at the granularity we’re discussing), Kelly is the clear strategy. You want to maximize the sum of results while minimizing the chance that you cross to zero and have to stop playing.
Dagon: You can artificially bound utility to some arbitrarily low “bankruptcy” point. The lack of a natural one isn’t relevant to the question of whether a utility function makes sense here. On treating utility as a resource, if you can make decisions to increase or decrease utility, then you can play the game. Your basic assumption seems to be that people can’t meaningfully make decisions that change utility, at which point there is no point in measuring it, as there’s nothing anyone can do about it.
The point of unintuitive high utilities and upper-bounded utilities I believe deserves another post.
Agreed. Utility is a flow, not a stock—it doesn’t carryover from decision to decision, so you can’t “lose” utility, you just find yourself in a state that is lower utility than the alternate you were considering. And there’s no reason it can’t be negative (though there’s no reason for it to be—it can safely be normalized to whatever range you prefer).
Either of these would make the Kelly strategy to minimize the chance of going broke and being barred from future wager irrelevant.
When talking about wagers, you really need to think in terms of potential future universe states, and a corresponding (individual, marginal) function to compare the states against each other. The result of that function is called “utility”. All it does is assign a desirability number to a state of the universe for that actor.
Attempts to treat utility as an actual resource in and of itself are just confused.
So, if you change the problem to be meaninful: say you’re wagering remaining days of life, which your utility function is linear in (at the granularity we’re discussing), Kelly is the clear strategy. You want to maximize the sum of results while minimizing the chance that you cross to zero and have to stop playing.
Dagon: You can artificially bound utility to some arbitrarily low “bankruptcy” point. The lack of a natural one isn’t relevant to the question of whether a utility function makes sense here. On treating utility as a resource, if you can make decisions to increase or decrease utility, then you can play the game. Your basic assumption seems to be that people can’t meaningfully make decisions that change utility, at which point there is no point in measuring it, as there’s nothing anyone can do about it.
The point of unintuitive high utilities and upper-bounded utilities I believe deserves another post.