What Is The Monty Hall Problem?
The Monty Hall Problem is a mathematical brain-teaser loosely based on a game show. Let me explain the game at the heart of the problem:
You begin with three doors. Hidden behind the doors are two goats and a car. Monty (our game host) asks you to select a door: you will win what is behind the door. Once you have chosen, Monty will open a door different from the one you selected to reveal one of the goats. Monty then asks you a question: "Do you want to stick with your original choice or do you want to switch your selection to the remaining upopened door? Now's your chance to change your mind."
You end up with two doors to choose from; one contains the car and the other contains a goat. What are the odds of picking the winning door? Are you better off sticking with your original choice or switching to the other door?
Are your chances of winning 50/50?
Many people, including respected mathematicians understand that there are two doors to choose from: it's essentially heads-or-tails whether you will win a car or a goat. In other words, it appears to be 50/50. However, it's not that simple. The first part of the game plays an important roll in your chances of winning the game.
Let me explain. At the beginning of the game you have three doors. The odds of finding the car at this point is 1 out of 3. You decide to pick door number one. Monty opens up door number three to show you a goat. The odds of a car being behind door number one, the one you picked, is still 1 out of 3. It doesn't change.
"Wait, those aren't good odds! I need that car so I can drive my goats to the vet! What should I do?!" I hear you say.
Should you SWITCH to increase your chances of winning?
What you need to do to have a better chance of winning is simple: switch doors. If you stick with your first choice you will only have a 1 in 3 chance of winning that car, the same as you did at the beginning. Odds are it is more likely that the door you picked hid a goat: a 2 in 3 probability. As the other goat has been taken out of the equation there is a 2 in 3 chance the car is behind the other door.
Still not convinced? You're not alone. That's why I created a simulation of this game. You can play it and see for yourself or read more about The Monty Hall Problem.