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
The key to the Monty Hall Problem is that the host knows where the goats are and where the car is.
Whether you’re dealing with 3 doors or 1000 doors, as other posters have suggested you think about it, your options become choosing 1 door (your original choice) or *every other door*.
If the host *didn’t* know where the goats and car are, and the game resets if Monty chooses to open the car door, then the odds at the end are truly 50/50.
That seemingly innocuous statement changes the game entirely.
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