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. Well, what's the probability of you picking right the first time? Well, that is only 1 3rd. So you see it here, and it's sometimes counterintuitive, but hopefully this makes sense as to why it isn't.