I am fascinated by the Monty Hall problem and its variants such as N-doors version here.
Now suppose expectations. How does the Monty Hall problem changes with expectations?
Contestant believes that prize is behind the door A with 0.01% probability, B with 10% probability and C with 89.99% probability.
Now the smart contestants pick up door A first because they know that host will show them B or C to be empty and they are planning to switch to C when B shown empty. Suppose host shows that the door C is empty -- all of a sudden, the contestants are skeptic about the prior probabilities
by prior probabilities, A is 100 times less probable than B in the original setting but how does the fact that C is empty changes the situation?
What kind of game strategy should be taken with prior probalities/expectations?
Suppose you are shown N-2 times to be wrong in all of your expectations with N doors, you make new expectation after each door opening. What is the optimal strategy?
Suppose you are shown N-2 times to be right in all of your expectations with N doors, you make new expectation after each door opening. What is the optimal strategy?