I think this solution can be very counter intuitive or natural depending how you picture the problem in your head. If you are thinking about you playing the ga

I think this solution can be very counter intuitive or natural depending how you picture the problem in your head. If you are thinking about you playing the game then of course it is very counter intuitive, because you are playing the game and you have only one chance. Doesn't matter that by switching your chances rise to 2/3 because you play the game only once, and in the end you either win or lose. On the other hand if you think about it from a statistic/probabilistic point of view then it's all natural that the chance is 2/3 but there is the notable exception that you don't play in this case and you neither win or lose.