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? Given that you're always going to switch? Well, the way that you would lose is you pick right, you pick correctly, and step 2, they're going to show one of the two empty or non-prized doors, and then step 3, you're going to switch into the other empty. But either way, you're definitely going to switch, so the only way to lose if you're always going to switch is to pick right the first time.