I agree it’s rare to have a global impact with a million dollars. But if you’re 50% confident the world will be destroyed tomorrow, that implies you have some sort of specific knowledge about the mechanism of destruction. The reason it’s hard to spend a million dollars to have a big impact is often because of a lack of such specific information.
But if you are adding the stipulation that there’s nothing Alice can do to affect the probability of doom, then I agree that your math checks out.
I agree it’s rare to have a global impact with a million dollars. But if you’re 50% confident the world will be destroyed tomorrow, that implies you have some sort of specific knowledge about the mechanism of destruction. The reason it’s hard to spend a million dollars to have a big impact is often because of a lack of such specific information.
But if you are adding the stipulation that there’s nothing Alice can do to affect the probability of doom, then I agree that your math checks out.