if you just set up the lottery equivalences they simplify to U(life - $X) = U(life - $Y) pretty much implying that whatever the correct choices of X and Y happen to be, they’re equal.
the setup is very dependent on the exact probabilities: if you change the cases to 10-shooters where you can remove one from five bullets or where you can remove two from two bullets, there’s not a proof that the amounts you should pay are equal.
if you just set up the lottery equivalences they simplify to U(life - $X) = U(life - $Y) pretty much implying that whatever the correct choices of X and Y happen to be, they’re equal.
the setup is very dependent on the exact probabilities: if you change the cases to 10-shooters where you can remove one from five bullets or where you can remove two from two bullets, there’s not a proof that the amounts you should pay are equal.