So what is the probability of winning if you always switch? Well, it's going to be the probability that you initially picked wrong. Well, what's the probability that you initially picked wrong? Well, there's two out of the three ways to initially pick wrong. So you actually have a 2 3rds chance of winning. There's a 2 3rds chance you're going to pick wrong and then switch into the right one. Likewise, what's your probability of losing?