Different levels of knowledge result in different probabilities… You have more information than she does. Your calculation computes the prior probability of you dying during one round. Her calculation computes the posterior probability of you dying during the whole game, given that you played and that the game has ended. The paradox only arises if one treats probability as an objective thing.
When you’ve just entered the room, what knowledge does one of you have that the other doesn’t; or why are you computing the probabilities of different events?
She has (will have) the knowledge that the game has ended, you don’t. If you could know that the game ends in this round, your probability of dying would be 100%.
She knows the game will end / will know the game has ended. She doesn’t know which round it will end / ended in. You also know the game will end, and not in which round; and you know what she will know upon waking up.
Looks like we are talking past each other, so the only way to continue is to show the calculation:
yours:
P(you die in this round| you play this round) = 1⁄36
your mom’s:
P(you die|game is over) = P(you play in the last ever round) = 9⁄10
You can express P2 by summing P1 over multiple rounds, weighted by the odds of the round being last and by the odds of you playing in it. But the important point that P1 and P2 are probabilities of different events.
Oh, I see. In that case, when you enter the room, why is her probability estimate different from yours? (Or if it’s not, why is yours >90%?)
Different levels of knowledge result in different probabilities… You have more information than she does. Your calculation computes the prior probability of you dying during one round. Her calculation computes the posterior probability of you dying during the whole game, given that you played and that the game has ended. The paradox only arises if one treats probability as an objective thing.
When you’ve just entered the room, what knowledge does one of you have that the other doesn’t; or why are you computing the probabilities of different events?
She has (will have) the knowledge that the game has ended, you don’t. If you could know that the game ends in this round, your probability of dying would be 100%.
She knows the game will end / will know the game has ended. She doesn’t know which round it will end / ended in. You also know the game will end, and not in which round; and you know what she will know upon waking up.
Looks like we are talking past each other, so the only way to continue is to show the calculation:
yours:
P(you die in this round| you play this round) = 1⁄36
your mom’s:
P(you die|game is over) = P(you play in the last ever round) = 9⁄10
You can express P2 by summing P1 over multiple rounds, weighted by the odds of the round being last and by the odds of you playing in it. But the important point that P1 and P2 are probabilities of different events.
And with that I am disengaging.