Sound advice for winning on a game show

Paul Michael — Mon, 25 Feb 2008 18:23:03 +0000

I've been a closet fan of game shows for years; most likely because I love the idea of getting something for nothing (hey, this is a frugal writer after all). I recently stumbled across something called "The Monty Hall Paradox" and it's opened my eyes to the laws of probability in the seemingly innocent world of game shows. And armed with this knowledge, you've got a much better chance of winning something.

Monty Hall was the host of a show called "Let's Make A Deal," which was very popular in the 60's and 70's. One of the cunning and cruel games he liked to play was the "3 doors dilemma." It worked like this: You would be presented with 3 doors. Behind one door is a fabulous prize, like a car or vacation. Behind each of the other two doors is a dud, like a goat or toilet paper.

Monty would ask you to choose a door. Then, before you opened it he would open one of the two remaining doors to reveal one of the dud prizes. Now he asks you a simple question..."Would you like to stick with your original choice, or switch to the other door?"

At this point you're rubbing your head, like I was, and you come up with the only logical solution; it doesn't matter. There are now two doors, one has the star prize, one doesn't, so it's 50/50, right?

Not so. Not so at all, as I found out when I delved deeper into the paradox and discovered that dozens of very smart mathematicians have been trying to explain this one for eons.

I have posted several videos and links below so that these boffins can explain it for you, much better than I could here. But, in a nutshell, here's the solution; you should ALWAYS switch doors.

The reason is simple...at the start of the show you have a 33% chance of picking the star prize, and a 66% chance of picking the dud prize. So, the odds are you will pick a door with a dud prize. That means that when Monty Hall reveals a dud prize behind one of the other doors, the remaining door is much more likely to be the star prize. See? Well, I had to watch the videos to be convinced, so give at least the first one your attention.

But if you ever do make it onto a game show, maybe like The Price Is Right, or someone tries the same trick using 3 cups and a ball, you now know just what to do to put the odds firmly back in your favor.

Video 1 - The 5-minute explanation

Video 2 - The TV show explanation

Video 3 - The math boffin 20-minute exploration