[not_kurt_godel]

I feel similarly about Monty Hall. I literally just made a spreadsheet of all the possible outcomes, and sure enough, switching leads to winning 2/3 of the time. Even though I can see the indisputable data in front of my eyes, my brain just won't fully accept it. Looking at it, I realized an interesting little wrinkle that I think might have to do with the problem's psychological quirkiness in some way I can't fully articulate: When you stay you win 1/3 of the time. When you switch, you win 2/3 of the time. BUT if you randomly pick between staying and switching, you win 50% of the time because (1/2)(1/3) + (1/2)(2/3) = 1/6 + 2/6 = 3/6. There is a correct-ish-ness to the intuitive answer of 50%...it's just not...actually correct.