What’s the Monty Hall Problem?

Fifty years ago there used to be a TV game show called “Let’s Make A Deal” hosted by Monty Hall. It was an audience participation show where Monty would pick out a member of the audience to play a game.

One of the games involved Monty showing three curtains on the stage. Behind one curtain a big prize was hidden. Behind the other two curtains were joke gifts.

The audience member would then get the chance to pick a curtain. After the curtain was picked, Monty would reveal what was behind one of the other two curtains. Monty always revealed a joke gift.

Then, Monty would ask: “Would you like to stick with your original choice or switch to the other curtain?”

Stick or Switch? This is a great statistics question! Many professors of statistics have gotten this question wrong. Using statistics you can arrive at an answer that maximizes the chances of winning. Of course, when you don’t know what the future holds you can still lose, even when making the “optimal” choice. However, if you apply statistics to the problem you will end up winning more often!

Try a few rounds of the game above and see how it goes. Then you can also click on Run 10,000 which will run the game 10,000 times and show you how the percentages break down over large numbers.

So what’s the right choice: stick or switch? Why? Doing the math can help you navigate through problems you’ll encounter and doing your homework will result in better outcomes over time.