I think the difficulty in understanding have something to do with the way human interpret probability: it seems like frequentist is our default interpretation,

I think the difficulty in understanding have something to do with the way human interpret probability: it seems like frequentist is our default interpretation, and this problem is very much a Bayesian one. The host didn't pick the opened door randomly, it's conditioned on him not picking the door with a goat. If the door was opened truly random, then the chance of your door having the prize in all cases is 1/3, but then in 2/3 of all cases, the door being opened will have something behind it too (so the game then makes no sense!). The probability of the picked door doesn't change because the event following already conditioned on the door. If you still don't have an intuition after reading the 2 explanation in the article (especially the one with 100 doors), I'm not good enough right now to explain it any better. But the one way that works for me is to play around with more Bayesian statistics -- one day it just suddenly doesn't feel weird anymore! In Bayesian interpretation at least, knowledge does changes what the probability would be, as the number just correspond to your belief of an event happening. Just tangentially related, but this might have some interest to you: http://lesswrong.com/lw/oj/probability_is_in_the_mind/ http://lesswrong.com/lw/oj/probability_is_in_the_mind/