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
I think the thing that helped me understand better is this:
if you picked the RIGHT door originally, and then switch, you will end up with a bad door; that’s clear: you have the right door, thus by switching you are for sure going to a bad one. So if you chose right and switch, you end up with a bad door.
If you picked the WRONG door, and then switch, you will end up with the RIGHT door. You have a bad one, Monty eliminates the other bad one, this the only one left is the right one and if you switch, you will get it. So if you chose wrong and switch, you end up with the good door.
Now, originally there were 2 bad doors and one good door. So you had 2 or 3 odds of picking a bad door and 1 of 3 of picking the good one. Since switching will always take you to the opposite result (see above), then in 2 out of 3 cases switching results in winning and in 1 or 3 cases switching results in losing.
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