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
It’s not 2 doors, 50-50. It’s 2 doors, 33-67 (67 being 66.6666… rounded up). How is this possible?
Think of the three doors as two groups. Group #1 is the door you picked. Group #2 are the two doors you did not pick. Group #1 and Group #2 are NOT 50-50 because group 1 has one door and group 2 has two doors. So it’s 33-67.
When one of group #2’s doors is eliminated, and group #2 now only has one door, the odds DO NOT CHANGE. Group #1 is STILL 33% and Group #2 (despite having only one door remaining now) is STILL 67%.
So of course you wouldn’t stick with the door in group #1, it only has a 33% chance of winning. You’d switch to the door in group #2, which has a 67% chance of winning.
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