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?
This is the bimonthly 'What are you working On?' thread. Previous threads are here. So here's the question:
What are you working on?
Here are some guidelines: