MTM22: The Cryptography Workbook (part 1)

You butchered the Monty Hall problem. The setup is 3 doors. 2 goats 1 prize. You select a door. Before opening your door the host reveals a door from the remaining two that contains a goat and asks you if you want to switch your selection to the other unopened door. The hosts action is not random, they always show a goat and never reveal the prize. If you write out the sample space, you will see that switching your choice increases your probability of selecting the prize from an initial value of 1/3 to 2/3. Imagine instead if the host offered you to open both of the other doors or stay with opening a single door. Since the host's actions are deterministic, that is essentially the same thing.