The Monty Hall Problem is a probability puzzle that has been mulled over for decades. While the premise and response seem simple, it can be difficult to grasp how it actually works.

Origins of the Monty Hall Problem

The puzzle is so named because it is based on one of the premises in the game show Let's Make a Deal, created and originally hosted by Monty Hall. The question is posed as follows:

You have three doors to choose from. Behind one door is a new car, and behind the other two are goats. You choose door number one. The host, who knows what is behind all three doors, tells you that behind door number two there is a goat. In order to maximize your likelihood of winning the car, do you stay with your original choice or switch to door number three?

This question was originally asked in 1975, sent in by a reader to the magazine American Statistician. In 1990, Marilyn vos Savant published the question in her "Ask Marilyn" column in Parade magazine, making it even more wide-spread.

Should You Switch Doors?

The solution to this problem is that yes, you should switch your choice. While this seems counter-intuitive, it has been proven statistically that you stand a better chance if you switch.

In layman's terms, when you make your original choice, you have a one-in-three (1/3) chance of choosing the correct door, and a two-in-three (2/3) chance of having chosen a goat. Therefore, if you switch your choice, you have a 2/3 chance of winning the car.

While this solution seems fairly straight-forward, the Monty Hall Problem continues to be debated amongst mathematicians and math enthusiasts, mostly because it can be difficult to grasp when looked at from a different angle. For example, if you take each door separately, each has a 1/3 chance of having the car behind it.

Therefore, switching would seem to make no difference.

Having the host reveal one of the doors is the key to solving the puzzle. Think of it this way: once you choose your door, you have 1/3 chance of being right, while the house has 2/3 of a chance. If you switch your pick, you then move into the 2/3 chance group, which doubles your chance of winning the car once the host removes the option of the door with the goat behind it.

Still Not Convinced?

Perhaps the best explanation of how The Monty Hall Problem works comes from Numberphile on YouTube. In this video, adjunct professor Lisa Goldberg, from the Department of Statistics at the University of California, Berkeley, gives graphic examples to illustrate how swapping your choice is actually the way to go.

To make her point even more clear, she expands the problem to include 100 doors. In this way you can clearly see how it is advantageous to change your pick.

Not a Guarantee

While you definitely have a better chance at winning that new car (or a vacation or a houseboat or a nice bag of cash) by swapping your choice of doors, the solution to the Monty Hall Problem is by no means a guarantee that you will win. Instead, changing your pick will improve your odds of winning the big prize.

There's always a chance that you could end up with a zonk, because statistics are never a sure thing. But if you want to have the best chance at winning the big prize, switch your pick when Wayne Brady gives you the opportunity - but only if he's already revealed one of the doors that holds a zonk. (Not to go off on a tangent here, but if none of the doors are revealed, then all of them have the same chance at hiding a car behind them.)