Generalized Monty Hall choice: 1. You pick a door. 2. One of the doors you didn't pick is opened. 3. You are given the option of keeping your original door, or switching to ALL of the other doors.

When there are only two doors, the problem breaks down because you will be able to figure out 100% what's behind each door at step two, so it's no longer a matter of playing probabilities, you can simply choose the door that has the prize. >>4 # If there's a condition that the door that's opened at Step 2 has to contain a goat, then the Monty Hall choice cannot be presented in the 50% of games where the contestant's first choice is incorrect, as opening the door the contestant didn't pick necessarily reveals the prize.

1. You pick a door.

2. One of the doors you didn't pick is opened.

3. You are given the option of keeping your original door, or switching to ALL of the other doors.

When there are only two doors, the problem breaks down because you will be able to figure out 100% what's behind each door at step two, so it's no longer a matter of playing probabilities, you can simply choose the door that has the prize.

>>4 #

If there's a condition that the door that's opened at Step 2 has to contain a goat, then the Monty Hall choice cannot be presented in the 50% of games where the contestant's first choice is incorrect, as opening the door the contestant didn't pick necessarily reveals the prize.