Suppose that at 12:00PM I roll a hundred-sided die. If the die shows a number greater than 34, the game terminates. Otherwise, at 12:05PM I consult a switch with two settings, A and B. If the setting is A, I pay you $24,000. If the setting is B, I roll a 34-sided die and pay you $27,000 unless the die shows “34”, in which case I pay you nothing.
Let’s say you prefer 1A over 1B, and 2B over 2A, and you would pay a single penny to indulge each preference. The switch starts in state A. Before 12:00PM, you pay me a penny to throw the switch to B. The die comes up 12. After 12:00PM and before 12:05PM, you pay me a penny to throw the switch to A.
But you’d know that you’d switch back to A, so you’d never really get B. You’d keep B, as it’s not a choice between A and B; it’s a choice between A + 2 cents and A.
But you’d know that you’d switch back to A, so you’d never really get B. You’d keep B, as it’s not a choice between A and B; it’s a choice between A + 2 cents and A.