(I’m going to nix the cost of the ticket as it’s just a constant)
Depends. Do you want to sum the probability weighted payoffs? EV is fine for that. The probability weighting deals with the striking “really, really low” odds (unless you want to further reweight the probabilities themselves by running them through a subjective probability function), and the payoffs are just the payoffs (unless you want to further reweight the payoffs themselves by running them through a subjective utility function). Either or both of these changes may be appropriate to deal with your own subjective views of objective reality, but that’s what they are—personal transformations. However, enough people subscribe to such transformations that EU (expected utility, or see cumulative prospect theory) makes sense more widely than just for you. We indeed perceive probabilities differently from their objective meanings and we indeed value payoffs differently from their mere dollar value.
Now, if you just want a number that best represents the payoff structure, we have candidate central tendencies—mean is a good one (that’s just EV). But since the payoff distribution is highly skewed, maybe you’d prefer the median. Or the mode. It’s a classic problem, but it’s finding what represents the objective distribution rather than what summarizes your possible subjective returns.
(I’m going to nix the cost of the ticket as it’s just a constant)
Depends. Do you want to sum the probability weighted payoffs? EV is fine for that. The probability weighting deals with the striking “really, really low” odds (unless you want to further reweight the probabilities themselves by running them through a subjective probability function), and the payoffs are just the payoffs (unless you want to further reweight the payoffs themselves by running them through a subjective utility function). Either or both of these changes may be appropriate to deal with your own subjective views of objective reality, but that’s what they are—personal transformations. However, enough people subscribe to such transformations that EU (expected utility, or see cumulative prospect theory) makes sense more widely than just for you. We indeed perceive probabilities differently from their objective meanings and we indeed value payoffs differently from their mere dollar value.
Now, if you just want a number that best represents the payoff structure, we have candidate central tendencies—mean is a good one (that’s just EV). But since the payoff distribution is highly skewed, maybe you’d prefer the median. Or the mode. It’s a classic problem, but it’s finding what represents the objective distribution rather than what summarizes your possible subjective returns.