“Every time you draw a card with a star, I’ll double your utility for the rest of your life. If you draw a card with a skull, I’ll kill you.”
Sorry if this question has already been answered (I’ve read the comments but probably didn’t catch all of it), but...
I have a problem with “double your utility for the rest of your life”. Are we talking about utilons per second? Or do you mean “double the utility of your life”, or just “double your utility”? How does dying a couple of minutes later affect your utility? Do you get the entire (now doubled) utility for those few minutes? Do you get pro rata utility for those few minutes divided by your expected lifespan?
Related to this is the question of the utility penalty of dying. If your utility function includes benefits for other people, then your best bet is to draw cards until you die, because the benefits to the rest of the universe will massively outweigh the inevitability of your death.
If, on the other hand, death sets your utility to zero (presumably because your utility function is strictly only a function of your own experiences), then… yeah. If Omega really can double your utility every time you win, then I guess you keep drawing until you die. It’s an absurd (but mathematically plausible) situation, so the absurd (but mathematically plausible) answer is correct. I guess.
Sorry if this question has already been answered (I’ve read the comments but probably didn’t catch all of it), but...
I have a problem with “double your utility for the rest of your life”. Are we talking about utilons per second? Or do you mean “double the utility of your life”, or just “double your utility”? How does dying a couple of minutes later affect your utility? Do you get the entire (now doubled) utility for those few minutes? Do you get pro rata utility for those few minutes divided by your expected lifespan?
Related to this is the question of the utility penalty of dying. If your utility function includes benefits for other people, then your best bet is to draw cards until you die, because the benefits to the rest of the universe will massively outweigh the inevitability of your death.
If, on the other hand, death sets your utility to zero (presumably because your utility function is strictly only a function of your own experiences), then… yeah. If Omega really can double your utility every time you win, then I guess you keep drawing until you die. It’s an absurd (but mathematically plausible) situation, so the absurd (but mathematically plausible) answer is correct. I guess.