The Monty Hall problem (mathematical problem)

The Monty Hall problem is a probability puzzle based on a game show. You're presented with three doors: behind one is a prize, behind the others, empty. You pick one door. The host, who knows what's behind each door, opens another door revealing no prize. You're then offered the choice to stick with your original door or switch to the remaining unopened door. Mathematically, switching doors gives you a 2/3 chance of winning, versus 1/3 if you stay. Switching improves your odds because the host's reveal provides additional information, shifting the probability in your favor.