[Rebel_Ace]

Clearest explanation I have seen regarding this scenario. It can confuse quite a few people. Most people FORGET to account for the CONSTRAINTS of the game as to which door Monty can open. They "naturally" compute the odds as if the door Monty opens was selected at RANDOM (which it CANNOT be 2/3 of the time).

Well done.

[An.American.Expatriate]

They "naturally" compute the odds as if the door Monty opens was selected at RANDOM (which it CANNOT be 2/3 of the time).

That makes more sense to me that than the authors explanation!

However,

Given A = prize
Pick A - Open either B or C
Pick B - Open C
Pick C - Open B

What is not clear is why switch.

After having Picked A - I can not know whether Monty was forced to open either B or C, or whether he had a choice.

So, if B is eliminated after the first round - I have two choices (Stay / Switch) and two arguments, Monty:

1. Was forced to open B as C contains the prize, or
2. had a choice to open either B or C as A contains the prize.

I'm likely missing something - but I still don't see the reason for switching.