I didn't believe the result. So, I had to sit down and decide to write the source code to simulate it, and as I'm typing the code my internal monologue is sayi

I didn't believe the result. So, I had to sit down and decide to write the source code to simulate it, and as I'm typing the code my internal monologue is saying "if you stay, 2/3 of the time you lose, but if you change, 2/3 of the time you win," and I was like, "CRAP!" It was like - my fingers knew how to type the correct solution, and once my brain saw my fingers type it, my brain finally caught up.