On the long running television game show, Let’s Make a Deal, contestants are presented with a dilemma. The host begins by unveiling three numbered doors. He then explains that behind one of the doors is a brand new car, while the other two each contain a goat. The way the game works is, the contestant begins by selecting a door with the understanding that whatever is behind that door, the contestant gets to keep. After the initial selection is made, the host must then open a one of the remaining doors to reveal one of the goats. At that point, the contestant is given the opportunity to change their selection.
The question is, should the contestant switch to the other unopened door?
Although most people intuitively and confidently answer, it doesn't make a difference, the only rational answer is, YES!
Here is why:
Scenario 1: You initially selected the door with Goat 1. The host would then reveal Goat 2. If you stick with your door, you win a Goat. If you switch, you win the Car.
Scenario 2: You initially selected the door with Goat 2. The host would then reveal Goat 1. If you stick with your door, you win a Goat. If you switch, you win the Car.
Scenario 3: You initially selected the door with the Car. The host would then either...
Reveal Goat 1. If you stick with your door, you win the Car. If you switch, you win Goat 2 - or -
Reveal Goat 2. If you stick with your door, you win the Car. If you switch, you win Goat 1.
In 2 out of 3 scenarios, you win the car when you switch. In 1 out of 3, you win a goat by switching. Therefore, if you prefer a brand new car over a goat, you should switch when given the option
Intuition often leads to irrational decisions. At Bija Advisors, we use cognitive science to help the world's most experienced and successful investment managers make better decisions. Learn more.