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.

Smartness Part 2

The topic of this blog post came up at a party I was at last night.

What resulted was a pretty heated debate over whether or not you should switch doors.

I revealed the answer to the individuals who were there. Unfortunately it was not accepted with open arms, mainly because it required them to think "outside the box". In reality, they were not arguing against my opinion, but instead arguing against math. When math is right, it is very hard to prove him/her wrong. (Is math male or female? I'll let you decide).

It got so heated, we ran through the scenario a couple of times and created a small sample set using a bottle cap and three cups. Needless to say, the truth was revealed, to the chagrin of many.

Anyway, I want to encourage all my readers to post their thoughts on this topic before I post the answer. Take a risk. Hopefully you will all find this as fascinating as I do.

I'll post the answer tomorrow night at midnight.

Smartness

I wanted to test out the general smartness and IQ of my readers. Here is a question on probability that I read in the latest issue of The Week.

Here are the details. Your on a game show. You are presented with three doors. Behind one door is a car, and behind the other 2 doors is goats. You are asked to pick a door.

You pick a door, say number 1. The host, who knows whats behind the doors, opens another door, say door number 3, and reveals a goat, and then says to you, do you want to pick door number 2?

What do you do. Do you stay with your original guess of door number one, or do you switch to door number 2?

I want to see some answers down here in the comments section. I'll post the answer in a couple days. Take a risk and post. It'll be interesting to see everyone's response.