I have read through around 10 articles and webpages on this problem, and still don’t understand. I’ve run simulations and yes, switching does get you better odds, but why?
In: Mathematics
Okay, so you do understand that Monty Hall knows where the car is and doesn’t open a losing door ever. So look at the game from his point of view.
If the contestant picks the car the first time around, Monty Hall has his choice of which door to open. But only if the contestant chose the car the first time around before anything else happened, which makes it a 1 in 3 chance for this situation. Staying makes the contestant win.
If the contestant picks a losing door the first time around, Monty Hall is **forced** to open the other losing door. The rules force him to. This is a 2 in 3 chance. Switching makes the contestant win.
Since your odds of winning based on your first door pick alone were not very good, and the fact that Monty Hall knows where the car is, when he opens a door you should be asking yourself, “why *didn’t* he open the other door?”
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