Another way to think about it: Your initital guess (which was 1/3 probability) would have had to have been right, to make it not correct (or not the right choi

Another way to think about it: Your initital guess (which was 1/3 probability) would have had to have been right, to make it not correct (or not the right choice) to move over to the other door. So moving to the other side (essentially you are just moving over to the 2/3 "probability block"; you were originally on the 1/3 "probability block"), inherently moves your odds over to 2/3. Staying only makes sense if you think you guessed correctly initially, and what are those odds, well those odds are 33%! And what are the odds of anything other than that initial guess (eg moving over) ? Well those odds would be 2/3! This is the only way that I was able to wrap my brain around it. We actually did it by just doing an A B C guess three times in a row. My wife picked a letter. Then I picked a letter. It worked three times in a row, because I never initially picked the letter she did. So three times in a row, me moving over to the remaining letter (after the letter that neither of us picked had been eliminated; obviously we kind of got lucky in me not picking her letter in three tries), ended up of course as being the letter she had picked. Moving over doesn't work only when you actually choose correctly initially, which would only be 1/3 of the time. So again, moving over makes your odds 2/3. It's brillantly simple really, yet extremely difficult to get to a method of actually understanding it, and this is the best way I've found.