A playground for ideas

Why games are so useful for refining scientific and statistical methods

Earlier this week, I chatted to BBC Radio 4 and The Times about the quality of decision-making in The Traitors TV show. The interviews came about because I’d responded on Twitter to an interesting question posed by Tom Whipple: does the group voting on The Traitors do any better than simply making random choices? Because there are often different numbers of traitors and contestants in each round, it gets quite fiddly.

A few respondents on Twitter put forward – then withdrew – suggestions for common statistical tests. So I thought I’d try get a rough idea by treating performance-relative-to-guessing as an unknown value, then trying to estimate it (with accompanying uncertainty). If you’re interested in the results, you can listen to the interview on today’s episode of More or Less or read the analysis in today’s Times.

But here I want to talk about the question presenter Tim Harford asked me at the end of the Radio 4 programme. Towards the end, he was gently sceptical on behalf of potential listeners, basically asking me ‘isn’t it a bit of a waste of your time to be analysing a TV show?’

He’s written a lot about games and puzzles, so I knew the question was a bit light-hearted. But it raised an important point: what it is about seemingly shallow games that draws in so many people interested in deeper science and statistics?

The answer is that games of chance can reveal much about how the world works, and the tools we need to analyse it. They’re why Alan Turing spent time analysing the game theory of poker strategies, Henri Poincaré used roulette to inspire his early work on chaos theory, and Karl Pearson studied roulette spins while developing the concept of a p-value and hypothesis test. And they’re why, a few years ago, I wrote a whole book about these ideas and innovations.

As scientists, we spend much of our time trying to distinguish signal from noise, dealing with incomplete information, complex processes, and random outcomes. From rock-paper-scissors to poker, games are a microcosm for many of these things; a structured way to refine the tools we need to study chance, data, risk, and decision-making.

On the face of it, analysing data from the Traitors is just a quick evening distraction. But it’s also a way to think about what we can extract from experiments where the datasets are small, the numbers change over time, and our measurements are often the result of complex human dynamics. And how, with appropriate uncertainty, we can still converge on a reasonably faithful approximation of the truth.