Assuming you understand the rule (that Monty will always open a door you didn't choose, and that door always has a donkey behind it), then one way to understand

Assuming you understand the rule (that Monty will always open a door you didn't choose, and that door always has a donkey behind it), then one way to understand the game is: You can choose to have: - The most valuable prize that's behind door A, or - The most valuable prize that's behind doors B or C When you look at it this way, it's obvious that you would rather have the most valuable prize from the 'other' doors, and the way to do that is to switch. Then you don't need to think about whether the probabilities change once Monty opens the door with the donkey. If you need convincing, here's a simple python script based on the above: https://gist.github.com/rahimnathwani/2b6ca328a74b37b952c75d14b6b34a93 https://gist.github.com/rahimnathwani/2b6ca328a74b37b952c75d... If you're still thinking about whether the probabilities change, consider whether 'Monty opens a door with a donkey behind it' is new information. It's not because he always does that. And the two doors you picked are fungible/identical except for physical position, as both are in the set of doors you didn't pick. So which one he opens is irrelevant.