There’s a game I often play with people – whether they’re engineers, students or even hedge fund managers. The challenge: Pick the ace.
I lay three cards facedown on the table and tell them to pick one, without turning it over. Mathematically, they have a one-in-three chance of being right. Then, I turn over a card they didn’t choose that’s not the ace. I give them a choice: Stay with your card or switch to the other unknown card.
Ninety-nine times out of 100, they stick with their original pick.
Then I’ll up the stakes by using 10 cards instead of three. Now they only have a one in 10 chance of picking the ace. I then turn over eight cards, none of which are the ace of course. Again I give them a choice: Stick with your card or switch to the other unknown card.
Ninety-eight times out of 100, they stick with their original pick.
However, I know they should switch. Why? Conditional probability.
This game is a take on the Monty Hall problem, a concept that academics have debated for 80 years, and it’s still a powerful teaching tool. When you pick one card out of 10, you have only a 10% chance of being right, and a 90% chance of being wrong.
Those probabilities don’t change when I start to reveal the cards they didn’t choose. There is still only a one in 10 chance they picked the right card to begin with.