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. You have a 1 3rd chance of winning if you stick to your guns and a 2 3rds chance of winning if you always switch. Another way to think about it is when you first make your initial pick, there's a 1 3rd chance that it's there, and there's a 2 3rds chance that it's in one of the other two doors, and they're going to empty out one of them, so when you switch, you essentially are capturing that 2 3rd probability, and we see that right there. I hope you enjoyed that.