You are right, to make this easier to understand, imagine replacing Monty Hall with a street peddler. You are playing a game with a street peddler. There are 3

You are right, to make this easier to understand, imagine replacing Monty Hall with a street peddler. You are playing a game with a street peddler. There are 3 cards, two are duds and one is the prize. He lets you pick one card. When you picked a card he flips one of the other two revealing it as a dud, and gives you the option to switch. Do you switch? A person who have heard the naive explanation to the Monty Hall problem would say yes. A smart person would say no. Why? Because it is not in the street peddlers interest to let you win, he has mouths to feed and need the money! So the only reason he reveals another card and asks you to switch is because you picked the right one from the beginning, so staying in this case means 100% chance of winning, and switching is 100% chance of losing. For the naive Monty Hall interpretation to be correct we need two things to be true: Monty Hall always opens a door and the thing behind the door is always a goat. If any of those two are not true then the popular explanation is wrong, and if you look around most explanations of the problem leaves those facts out. For example, in this article they forgot to say that the game host always opens a door and when he opens it it is always a goat. This shows that the author of the article (and almost everyone here at HN) doesn't understand Monty Hall. Instead they talk like non mathematicians like "Why would the game not open a door sometimes?" or "Why would he open a door with not a goat? It said he opened a door with a goat this one time!" etc. The problem with those things is that the explanation only says what happened this one time, so you can't possible write down the event tree without making a lot of extra assumptions about the game.