Let’s Make a Deal — And Never Trust your Gut Decision (or Monty Hall)

 

Who didn’t love Lets Make a Deal? Monty Hall, despite being creepy, can tell us a lot about how to make decisions and how we value information given to us. Thus, we have The Monty Hall problem: Assume a room is equipped with 3 doors. Behind 2 are goats, and behind the third is a new car. You are asked to pick a door, and will win whatever is behind it. Let’s say you pick door 1. Before the door is opened, however Monty opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). Of course, you think, I will stick with my gut decision. But that is wrong. Never trust your gut in this situation. You have been given more information and you should factor this in. (watch now and see how it works)

The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat. But after Monty has eliminated one of the doors for you, you obviously do not improve your chances of winning to better than 1/3 by sticking with your original choice. If you now switch doors, however, there is a 2/3 chance you will win the car (counterintuitive though it seems). So don’t always trust your gut. Sometimes you may have unwittingly been given more information…take it and run:

d_1 d_2 winning probability
pick stick 1/3
pick switch 2/3

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