Three doors, one prize: which one to choose? Here is the Monty Hall paradox

You chose door 2 and then they tell you the prize is not in door 3. Would you switch to door number 1? Here’s what you should do.

The popular game show television Let’s Make a Deal In the 1970s, it presented a probability dilemma to competitors, marveling at the possibility of winning a dream car that seemed too tangible in front of three simple doors.

The grand prize was hidden behind one of the doors; the other two each had a goat. The game was simple: the competitor had to guess the door (1, 2 or 3) the vehicle was in.

However, in response to the first guess, Monty Hall, the presenter — who knew very well where the car was — only opened a door where the car was not, that is, one of the doors where there was a goat.

Now with the chances of finding the car reduced to two doors, the player was faced with a dilemma: he had the opportunity to change doors. The game would give rise to a much-discussed paradox: Is it worth changing doors or not?

What you should always do (and why)

At first glance, our brain tends to assume this question is irrelevant. After all, the car didn’t move, nor did it change doors: the chance of hitting the car door increased, from 33.3% to 50%. But let me tell you that our brains are very tricky.

In fact, there is a very straightforward answer and strategy that you should always follow in this scenario, and that is always change doors. We will explain everything below.

It is important to remember that the presenter does not open a door randomly. You can only open a door with a goat. And that’s where the dilemma resolves itself — the competitor is often the one who doesn’t notice. Why eliminating an option by chance is very different from eliminating an option with inside information.

Practical example

Let’s now put the reader in the role of competitor:

Imagine the three doors. Let’s assume you chose door number 1. There are three possible scenarios: the car is in door 1, door 2 or door 3, all with probability of 1/3.

If the prize is in door 2, the presenter is forced to open door 3 (goat) and must offer to exchange it for door 2. If he exchanges it, he wins; if the prize is in door 3, the presenter is forced to open door 2 (goat) and offer to exchange it for door 3. If you exchange it, you also win; Only in the case where the prize was already in your initial choice (door 1) will you lose.

In other words, after opening the first door, changing doors increases (from 1/3 to 2/3) the probability of winning the car. Trading only loses if your first guess is correct.

But always remember: Changing does not guarantee a car. It just considerably increases your chances of driving more stylishly.

But… why do some people insist that it is 50-50?

One of the most common errors in human reasoning is desire for equiprobabilityexplains . When we see two options, we tend to assume they are equally likely. And this informal rule is often useful in everyday life, but it is curiously misleading here. The process that led to two doors remaining confuses us.

But there is also a emotional factor to take into account, explains Walter Herbranson, a comparative psychologist at Whitman University, to the magazine. THE repentance It weighs heavily on people’s minds, who tend to “stick” with their first choice because they can’t deal with the possibility that, if they change and lose, they will always know that it was their fault for not having a better car.