On Finding Traitors: Hannah Fry’s Method Fails

Celebrity mathematician, Hannah Fry, arrived at UK Celebrity Traitors with spreadsheets and a war story. For those unfamiliar with The Traitors, the game is simple. Most contestants are secretly designated "Faithful," while a small number are secretly chosen as "Traitors." The Traitors know who each other are and secretly "murder" one Faithful contestant each night, removing that person from the game. During the day, everyone discusses who might be a Traitor and votes at the Round Table to banish a suspect. The Faithful win by identifying and eliminating all the Traitors; the Traitors win by surviving the suspicions, votes and banishments long enough to control the endgame.

Before the 2026 series, the Cambridge mathematician told the BBC that she had studied previous games looking for patterns in how Traitors behave. She even said she was using "the same bit of maths that Alan Turing used to crack the Enigma machine."

One pattern caught her attention. Early in the game, a Traitor will sometimes vote for somebody nobody else has named. Instead of joining the crowd, the Traitor throws away a vote on an unlikely target. Cat Burns, a Traitor on the previous celebrity series, was Fry's example.

The idea makes sense. Look at enough previous games and perhaps certain patterns will emerge. Do Traitors vote differently from Faithful players? Do they defend other Traitors? Do they accuse people in unusual ways? Feed all this into a spreadsheet and perhaps mathematics can tell you who is most likely to be lying.

But Fry also admitted something important: the Faithful are so unpredictable that it is difficult to separate a genuine pattern from ordinary human chaos. She was not even sure whether her mathematics would help. That is where the real problem begins.

The comparison with Alan Turing is clever, but there is a huge difference between cracking Enigma and catching a Traitor.

At Bletchley Park, Turing and the other codebreakers were dealing with a machine. Enigma followed rules. However complicated those rules were, the machine did not know that British mathematicians were studying it. It could not discover Turing's methods and deliberately change its behaviour to fool him.

A Traitor can. Suppose Fry discovers that Traitors often cast strange individual votes early in the game. The discovery is useful only while Traitors keep doing it. Once players know that people are looking for this behaviour, they can stop doing it. Better still, a clever Traitor can deliberately behave in whatever way everyone currently thinks a Faithful player should behave.

The reverse problem is just as bad. A genuinely Faithful player might cast an odd vote simply because he is confused, suspicious or trying not to follow the crowd. His behaviour then resembles the supposed Traitor pattern even though he is innocent.

That makes the mathematics much less powerful than it first appears. Previous series also provide only a small amount of evidence. Worse still, each new group of contestants has watched previous series. They learn from earlier players and change their behaviour. The game is therefore constantly changing.

There is a deeper problem. Human beings are not machines following fixed rules. They think about what other people think about them. That is especially important in a game built around deception. A Traitor is not simply hiding a secret. The Traitor is performing the role of an innocent person. That means speaking, voting, making alliances and reacting to accusations in ways designed to look Faithful.

The better the Traitor, the more useless simple behavioural rules become. If everyone decides that Traitors are quiet, a clever Traitor becomes talkative. If everyone decides that Traitors talk too much, the Traitor becomes quiet. If mathematicians announce that Traitors make unusual early votes, the Traitor follows the crowd.

The same difficulty affects almost every supposedly scientific method of finding the guilty player. Someone watches facial expressions. Someone else studies alliances. Another player remembers exactly who voted for whom. The game theorist calculates what a rational player should do.

All these methods can provide clues. None provides a reliable test, because the person being tested can change his behaviour after learning what everyone is looking for.

That is what separates Hannah Fry's spreadsheets from Alan Turing's attack on Enigma. Turing was studying a machine that could not study him back. Fry is studying intelligent human beings who are watching one another, lying to one another and changing their behaviour as the game develops.

The mathematics is real. The patterns may be real. The spreadsheets may even give Fry a small advantage. But Enigma could not hear Turing thinking. The Traitors can.

However, if one had a game Traitors, Parliament Australia, apart from One nation, some independents, and a couple of Liberals, the odds of picking a traitor are overwhelming. It would not be entertainment, yielding maybe negative ratings!

https://www.youtube.com/watch?v=twDvxNooI_4