Finally Figured Out Monty Hall!

Thanks to this explanation (coding it out in Ruby made it clearer to me, but it’s really the verbal explanation that worked).

At the outset you have doors A, B and C. Given the choice between A or B and C, obviously you would take the latter. That’s what you’re choosing here! B and C, which combined have a greater chance of being correct. It’s more likely that it was in the two you didn’t choose: specifically the one of them which isn’t wrong. But they still represent 2/3.

As a HN commenter put it, it’s easier to think of it when it’s 100 doors. To begin, you choose one. What’s the chance you’re correct? A measly 1%. You almost certainly got it wrong. Imagine if you could switch to select the other 99. Of course you’d do it! Now the host opens the 98 goat doors. The other 99 are 98 goats + 1 ?. Of course you should switch! You picked the minority, so the majority of times you are wrong. You’re being given a chance to switch to the majority. Of course, if no door is opened, you’re still picking one of 3 - you’re still a minority, so it makes no difference if you switch or stay.