I always found that one makes things more complicated. I like this explanation better: You win by switching as long as you were wrong in the initial guess. Y

I always found that one makes things more complicated. I like this explanation better: You win by switching as long as you were wrong in the initial guess. You have a 2/3 chance of being wrong in the initial guess. Therefore you will win by switching 2 times out of 3. Can also phrase it in reverse: You lose by switching if you were right in the initial guess. You have a 1/3 chance of being right in the initial guess. Therefore you lose by switching 1 time out of 3.