Smartness Part 3: The Answer

The Answer......... A rational player would SWITCH!

Now I don't mean to offend anyone if you said you wouldn't switch. It certainly doesn't mean you are irrational.

What I presented here to you was the Monty Hall Problem, named after the host of Lets Make A Deal.

Here is the explanation of the answer:

The overall probability of winning by switching is determined by the location of the car. Assuming the problem statement in my original blog post and that the player initially picks Door 1:

• The player originally picked the door hiding the car. The game host must open one of the two remaining doors randomly.
• The car is behind Door 2 and the host must open Door 3.
• The car is behind Door 3 and the host must open Door 2.

Players who choose to switch win if the car is behind either of the two unchosen doors. In two cases with 1/3 probability switching wins, so the overall probability of winning by switching is 2/3.

For those of you who are visual learners, this picture should help clarify for you.


If you still don't get it, set up an experiment like we did at a party I was at the other night.

Have someone be the game show host, and someone be the contestant. Take three cups (doors) and a bottle cap (a car) and run through the scenario 100 times (or 10). If you follow the switching strategy, you should win a car about 66 (or 66.66%) times, and win a goat about 33 (or 33.33%) times.

So for those of you who got it right, congratulations. You are probably far smarter than I will ever be.

For those of you who got it wrong, don't make the same mistake twice. The odds are in your favor in the future to win a car, or whatever is behind those doors.

Whatever you do, don't hate me, hate math. It was math who proved you wrong.