Fact of the Day .CA

Okay everyone, it’s Scratch Your Head Because of Math Time!

Back in the mid-1960s, a game show called Let’s Make a Deal, hosted by Monty Hall, began airing. It involved a lot of odd little deal games, with players risking guaranteed money and prizes for potentially greater prizes, or possibly duds like goats and dog food.

For this particular problem, we refer to a ‘What’s Behind Door Number…’ game. Contestants were presented with three doors, one of which had a wonderful prize, the other two… less desirable rewards. So a contestant selects a door (say, #2). Monty Hall then reveals what was behind one of the doors they did not select (say, #3) – it thus being that Monty Hall knew which door the prize was behind. The contestant was then given The Deal: would you like to switch doors? The question is, would you switch? Does it matter?

Intuition (for those of us who aren’t mathematicians) would suggest that it wouldn’t matter, since the choice is 50/50 – two doors, right? Wrong. It is actually advantageous to switch to the other door. This is kind of a weird idea to get your brain around. To try to simplify it, your original odds of selecting the prize door are 1/3. When Monty reveals one of the incorrect doors (which had a 2/3 chance), the odds of the door you selected remain the same (1/3), which the OTHER door still has a 2/3 chance with it. Trust me, it works. The key is that Monty knows what is behind each door. If he did not, then there would be no advantage to switching, and he could even reveal the door with the prize.

If you would like to try it yourself, here is a link to a simulation with Monty Knows and Monty Doesn’t Know options. Have fun, and don’t give yourself a headache.