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'Wie is de Mol?' through the eyes of a statistician

There are many ways to predict the mole. Mole spotters often talk about body language, intrigue, granted screen time or social behaviour. Nice, vague and exciting, of course, and good for a heated discussion but could it be more exact? What about mathematics, can it help us here too?

Photo of UT Stories Editorial Team
UT Stories Editorial Team

Statistician Jasper de Jong has been studying 'mole hunting' for years. As a game fanatic, mathematician and fan of Wie is de Mol?, he has applied some insights from probability to the popular TV programme.

Jasper can calculate the probability of someone being the mole in various game situations. Unlike the more social solution methods, this calculation gives a precise number. Moreover, this method is less impressionable by the show's creators, who, of course, do everything in their power to lead viewers and the various mole prophets astray. The equation Jasper uses is called Bayes' theorem. This mathematical theorem gives the probability of an event, provided another event occurs.

Take the game situation where two candidates are eliminated from the game and two players cannot be eliminated because they have something called a 'vrijstelling'. So the remaining four do, of which only two candidates make it through to the next episode. Before the verdict, all six candidates have a certain chance of being the mole, and these chances obviously change when two candidates are eliminated. Sometimes this feels logical but sometimes it goes against intuition.

Bayes' theorem looks like this:

Patrick and Ron drop out, we see that in the episode and so is the given situation B. What then is the probability that Peggy is the mole (situation A | given situation B)? You can use Bayes' theorem to calculate this by assuming the reverse (what is the probability that Patrick and Ron drop out if Peggy is the mole) and the probabilities P(A) and P(B).

Jasper calculates that the probability of Peggy being the mole has increased from 1 in 6 to 1 in 3. So the chance becomes twice as big! And a bigger chance than the expected 1 in 4 as there are still four candidates left.

Watch the video for more precise calculations and even more situations. For example, what is the probability that Tygo is the mole?

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