Article

Teodora Miscov
Teodora Miscov 13 December 2017

The surprising truth of Christmas freakonomics

We all make hundreds, if not thousands, of decisions every day. Our decisions are influenced by cognitive and behavioural biases that don’t always result in outcomes we expect. The psychological pain of losing something is roughly twice as powerful as the pleasure of gaining something.

Last year, we produced the Deal or No Deal Dilemma because we all make hundreds, if not thousands, of decisions every day. Our decisions are influenced by cognitive and behavioural biases that don’t always result in outcomes we expect.

To show exactly how much we are influenced by cognitive biases, we teamed up with content production agency Amoveo and went out on the streets of London to do an experiment.

So why didn’t people switch?

We know the psychological pain of losing something is roughly twice as powerful as the pleasure of gaining something. So, when holding a box in your hands that may contain money, the thought of losing that by switching causes you to be more likely to stick with it.

People also tend to assume when you have the choice of keeping the box you selected or switching, it’s a 50-50 chance of winning the money either way. But this isn’t the case.

The Logic

There is a 1/3 chance of the money being in the box you initially chose, and a 2/3 chance that the money isn’t in the box you initially chose. After removing one of the other boxes to reveal sweets, there’s still a 1/3 chance that the money is in the box you’ve chosen and a 2/3 chance that the money isn’t in the box you’ve chosen.

This means that there is a 2/3 chance that the money isn’t in the box you’ve chosen, and that it’s a 2/3 chance that the money is the box left on the tray.

Another way of looking at it…

Imagine that instead of 3 boxes, there are 100 boxes. All of them have sweets inside of them - except one, which has the money. You choose a box, say, box number 53. At this point, all of the other boxes except one are opened - all containing sweets. You are given the offer to switch to the other box. Would you switch?

You might think “Why would I? Maybe I actually picked the correct box on my first guess.” But what’s the probability that that happened? 1/100 or 1%. In other words: there is a 99% chance that the money isn’t in the box you initially chose.

If it’s not in the box you chose, it must be in the other box left for you. By removing all the other boxes containing sweets, you have been given the opportunity to choose a box that has a 99% chance of having the money in it. This is because your box and the box left must add up to 100% in total probability. Therefore if you switch, you would have a 99% chance of winning.

It’s up to you which option you find most attractive, a 99% chance of not getting the money or a 99% of getting the money. We know what we would go for…

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