Make the game last at most an hour with exponentially decreasing round lengths.
Assuming you mean that the game is guaranteed to be completed within one hour, it is equivalent to a potentially infinitely long game with fixed round length, and we are back to my point.
When she wakes up, she knows the game has ended. Before she goes to sleep, she knows she will know this when she wakes up. So how can her probability estimate change between the two 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: