There are several problems. You’re really looking to take free money from expected utility maximizers, not “expected value maximizers”, and the equation from an expected utility maximizer’s point of view is:
Expected change in utility given that I have N dollars = [U(N-1) P(no pay|X) + U(N+X+5-1) P(pay|X)] - U(N)
Key points here are the transformation of dollar winnings to utility (diminishing marginal utility of money), the fact that the expected value looks more like 5/X (not 5) dollars, and the fact that the expected utility maximizer cares about P(pay|X), not P(win the bet|X) - its estimation of your ability to pay cannot be swept under the rug, so p quickly becomes much smaller than 1/X when X is 10^100.
There are several problems. You’re really looking to take free money from expected utility maximizers, not “expected value maximizers”, and the equation from an expected utility maximizer’s point of view is:
Expected change in utility given that I have N dollars = [U(N-1) P(no pay|X) + U(N+X+5-1) P(pay|X)] - U(N)
Key points here are the transformation of dollar winnings to utility (diminishing marginal utility of money), the fact that the expected value looks more like 5/X (not 5) dollars, and the fact that the expected utility maximizer cares about P(pay|X), not P(win the bet|X) - its estimation of your ability to pay cannot be swept under the rug, so p quickly becomes much smaller than 1/X when X is 10^100.