Another way to look at it is this: imagine you wake up after the bet, and don’t yet know whether you are going to quickly be killed or whether you are about to recieve a large cash prize. It turns out that your subjective credence for which branch you are in is given by the Born measure. Therefore, (assuming that not taking the bet maximises expected utility in the single-world case), you’re going to wish that you hadn’t taken the bet immediately after taking it, without learning anything new or changing your mind about anything. Thus, your preferences as stated either involve weird time inconsistencies, or care about whether there’s a tiny sliver of time between the worlds branching off and being killed. At any rate, in any practical situation, that tiny sliver of time is going to exist, so if you don’t want to immediately regret your decision, you should maximise expected utility with respect to the Born measure, and not discount worlds where you die.
Another way to look at it is this: imagine you wake up after the bet, and don’t yet know whether you are going to quickly be killed or whether you are about to recieve a large cash prize. It turns out that your subjective credence for which branch you are in is given by the Born measure. Therefore, (assuming that not taking the bet maximises expected utility in the single-world case), you’re going to wish that you hadn’t taken the bet immediately after taking it, without learning anything new or changing your mind about anything. Thus, your preferences as stated either involve weird time inconsistencies, or care about whether there’s a tiny sliver of time between the worlds branching off and being killed. At any rate, in any practical situation, that tiny sliver of time is going to exist, so if you don’t want to immediately regret your decision, you should maximise expected utility with respect to the Born measure, and not discount worlds where you die.