It’s also helpful (but not essential) to realize that the choice of which door to open has two parts, a rule and a decision. If the participant is doing a switc

It’s also helpful (but not essential) to realize that the choice of which door to open has two parts, a rule and a decision. If the participant is doing a switch or a stay strategy, the decision aspect has no impact on winning. The rule part is Monty can’t reveal the car. The decision comes up if the participant chooses the car first. Monty will have two doors to choose from to open. But if you have a stay strategy you’ll win for either choice, and if you have a switch strategy you’ll lose no matter what. So his decision doesn’t matter. This makes it very easy to simulate. It also might lead to people to understanding the solution. If you pick wrong first, you’ll see staying always loses and switching always wins. The probability of picking right first is 1/3, of picking wrong first 2/3. Since switch always works when you pick wrong and you pick wrong 2/3 times, go with that.