In 1800s America, something terrifying is feeding on the quiet town of Exeter. As members of George Brown’s family succumb one by one, the town considers drastic measures to protect the living from the dead. 

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Further Reading

Books

Food for the Dead: On the Trail of New England’s Vampires (2013) by Michael Bell.

Everything is Tuberculosis: The History and Persistence of Our Deadliest Infection (2025) by John Green.

Articles

“New England ‘Vampire’ Was Likely a Farmer Named John” by Jason Daley, Smithsonian Magazine (5th August 2019). Available here.

“Old cemetery revealing its secrets” by Jenn Heldt, The Bulletin (24th March 1990). Available here.

“Cemetery Holds Tales of Vampires” by Sam Libby, New York Times (16th February 1922). Available here.

“The Great New England Vampire Panic” by Abigail Tucker, Smithsonian (October 2012). Available here.

“The Man with a Fish on His Back” by Diane Wendy, Distillations Magazine (3rd April 2010). Available here.

“Exeter Hill”, Pautuxet Valley Gleaner (5th February 1887).

“Greene Valley”, Pautuxet Valley Gleaner (5th April 1889).

“Exeter Hill and the Vicinity”, Pautuxet Valley Gleaner (29th May 1891).

“Exeter Hill and Vicinity”, Pautuxet Valley Gleaner (27th November 1891).

“Exeter Hill and Vicnity”, Pawtuxet Valley Gleaner (22nd January 1892).

“Exeter Hill and Vicinity”, Pautuxet Valley Gleaner (26th February 1892).

“Exeter Hill and the Vicinity”, Pautuxet Valley Gleaner (25th October 1892).

“Exeter Hill”, Pautuxet Valley Gleaner (22nd June 1900).

“Exhumed the Bodies: Testing a Horrible Superstition in the Town of Exeter, The Providence Journal (19th March 1892).

“The Vampire Theory: That Search for the Spectral Ghoul in the Exeter Graves”, The Providence Journal (21st March 1892).

“Exeter”, Rhode Island Pendulum (31st July 1891).

“Exeter”, Rhode Island Pendulum (13th May 1892).

“Edwin A. Brown”, The Standard (20th May 1892).


Academic Articles and Historical Surveys

“Historical and Architectural Resources of South Kingstown, Rhode Island: A Preliminary Report”, Rhode Island Historical Preservation Commission (1984). Available here.

“DNA Testing Reveals the Putative Identity of JB55, a 19th Century Vampire Buried in Griswold, Connecticut” by Jennifer Daniels-Higginbotham et al., Genes (Basel), 22nd August 2019, 10(9), p. 636. Available here.

“Bioarcheological and Biocultural evidence for the New England vampire folk belief” by Paul Sledzik and Nicholas Bellantoni, The American Journal of Physical Anthropology, June 1994, 94(2), pp. 269-74. Available here.

“Late-life cardiac interventions and the treatment imperative” by Janet K Shim, Ann J Russ and Sharon R Kaufman, PLOS Medicine, 4 March 2008, 5(3). Available here.

“Death and the treatment imperative: Decision-making in late-stage cancer” by Alexandra Tate, Social Science & Medicine, August 2022, 306. Available here.

Blogs and Websites

“Tuberculosis: A Fashionable Disease?” by Imogen Clarke, Science Museum (24th March 2019). Available here.

“Tuberculosis Part Two: Treatments and Cures”, Science Museum (6th February 2024). Available here.

“Story of Us – T is for Tuberculosis”, Colorado Springs Pioneers Museum. Available here.

“Some Sweet Day, By and By”, Hymnary.org. Available here.

“Have Mercy…” by Jennifer L. Galpern, Rhode Island Historical Society (31st October 2016). Available here.

“Exeter History”, Town of Exeter Rhode Island. Available here.

“Tuberculosis”, Saint John’s Cancer Institute. Available here.

Tetlock’s response was to collect verifiable economic and political predictions from an increasingly wide range of experts, then wait patiently to see which predictions were correct. The result of this exercise was his 2005 book, Expert Political Judgment: How Good Is It? How Can We Know? The subject-matter specialists were barely more predictive than dart-throwing chimps.

Tetlock’s book was a hammer blow to the fragile reputation of forecasters everywhere, but he didn’t give up on the possibility that better forecasts were possible. In Superforecasting (2015), he and his co-author, Dan Gardner, described a select group of genuinely skilled forecasters and highlighted some of the traits and habits that made them effective. With an uncharacteristic touch of hyperbole, Tetlock called these people “superforecasters”. One of the consequences of Tetlock’s work has been that lots of people are now publicly making testable predictions, including some certified “superforecasters”.

So the latest development is — forgive me — predictable. Why not compare some of these published, testable prophecies with those emerging from large language models (LLMs) and other AI systems? For example, do AI systems beat the market at forecasting interest rate decisions? (No, although they’re no worse.)

But asking computers to make these big-picture forecasts is not merely an attempt to test forecasting prowess. It is also, like Tetlock’s original research programme in the late 1980s, an attempt to cut through bullshit and test real skill. Experts and LLMs share a talent for plausible self-justification; a bad prediction, or a good one, sheds new light on those explanations. The title of Tetlock’s 2005 book, after all, was not about forecasting but about expert judgment. One way to evaluate the capability of an AI system is to ask it a question to which nobody — yet — knows the answer.

One effort at this evaluation comes from ForecastBench, a project of the Forecasting Research Institute (president, Philip Tetlock). ForecastBench reports that the results are already impressive, and improving. The typical superforecaster scores 68.9 on ForecastBench’s index of forecasting accuracy. At the time of writing, the best specialised AI forecasters are hitting 68.8. An ordinary human forecast averages 62.8, and regular LLMs with no special tuning are scoring over 61.

Before we ask how seriously to take any of these numbers, we should ask what they mean. One way to understand them is to imagine a forecaster who expresses perfect confidence with every prediction, assigning 100 per cent probability to some and 0 per cent to others, and is correct every time. This infallible oracle would score 100, the maximum score. A forecaster who shrugs and declares that every eventuality is a 50-50 call would hit the chimp benchmark: a score of 50.

The “superforecaster” score of 68.9 would also be achieved by a forecaster who happened to declare a list of events as 68.9 per cent likely to happen — and they all then did — and another set of events as just 31.1 per cent likely, and none of them occurred. Such a benchmark is a lot better than guesswork and a lot worse than omniscience.

Perhaps we should not be impressed that an ordinary LLM is barely worse than a human at predicting events such as “Will there be a presidential election in Ukraine before a ceasefire between it and Russia occurs?” Both the humans and the computers are much closer to the dart-throwing primates than to forecasting perfection.

The fact that specialised AI forecasters now seem indistinguishable from the much-vaunted superforecasters is far more impressive, but there is a long list of caveats. The first is that ForecastBench is not quite comparing like with like: the human superforecasters were answering one set of questions back in 2024, while the AI systems are answering a different set of questions today. This raises a question over the comparison, as clearly some questions are easier than others: “Will Scotland declare independence from the UK by the end of October?” is more straightforward to answer than “Will Vladimir Putin be president of Russia at the end of 2030?”

ForecastBench attempts to adjust for the difficulty of these questions, but admits that the comparison “relies on a statistical extrapolation that grows less reliable over time”. ForecastBench promises that more human forecasts are being gathered, so we may know more soon.

Predictions do not merely describe the future; they are often an attempt to shape it. The mere prospect of highly accurate computerised forecasts, based on systems controlled by the world’s most powerful companies, is not wholly reassuring. “The only way to know for sure where someone will be tomorrow is to make them be there,” says Carissa Véliz, author of Prophecy: Prediction, Power, and the Fight for the Future, from Ancient Oracles to AI.

But even if AI forecasting systems prove both innocent and accurate, there is something else missing. Forecasts are often valuable not just because of the outcome — a number describing the probability of a future event — but because of the process.

There is an analogy here with using an LLM to write an essay. Regardless of how excellent the result may be, the person who typed the prompt and pushed the button has missed out on the experience of thinking through the process of drafting and redrafting.

So, too, with forecasting. A good scenario-planning exercise is valuable not just because it might produce some thought-provoking descriptions of possible futures, but because it brings together experts and decision makers to ponder the imponderable in a structured manner.

Tetlock himself, with co-authors Barbara Mellers and Hal Arkes, has found that participating in forecasting tournaments tends to reduce political polarisation — presumably because good forecasts require an open mind, the ability to see the world as others see it and a willingness to admit error.

Good-faith forecasting is a practice that makes humans better humans. We should think twice before delegating the task to a machine.

Written for and first published in the Financial Times on 16 Sep 2026.

I ran the Oxford Half Marathon in support of a very good cause and in memory of my mother. If you felt able to contribute something, I’d be extremely grateful.

This episode is available exclusively to Pushkin+ subscribers and members of the Cautionary Club.

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Further Reading

On the Zenith Foundation experiments

Goodfellow, L. D. (1938, reprinted 1992). A psychological interpretation of the results of the Zenith Radio experiments in telepathy. Journal of Experimental Psychology: General, 121(2), 130–144. https://doi.org/10.1037/0096-3445.121.2.130

William Poundstone Rock Breaks Scissors (in the UK, How to Predict the Unpredictable)

Stacy Horn “ESP Games and Academic Politics”

Royal Gazette and Colonist Daily, Thursday October 7 1937

On Louisa and JB Rhine, and ESP Cards

Seymour Mauskopf and Michael McVaugh The Elusive Science (1980)

Feather, S. R. and Ensrud, B. (2018). Joseph Banks Rhine. Psi Encyclopedia. Last updated: 30 April 2026.

Linda Rodriguez McRobbie “How One Man Used a Deck of Cards to Make Parapsychology a Science” Atlas Obscura 27 December 2016

Rhine, J. B. & Rhine, L. E. (1927). One evening’s observation on the Margery mediumship. The Journal of Abnormal and Social Psychology, 21 (4), 401-421

“Doyle Declares Margery Genuine” New York Times 5 March 1927

Massimo Polidoro “A Telepathy Investigation” Skeptical Inquirer Sep/Oct 2018

“Tomorrow, I will be going across channels with zero views, going into their chat, and pumping people up.” But it might not end up quite how you expect… Amygdala, a short film by Joe Edmundson Foot and Stella Harford.

Interested in tabletop roleplaying? The Dice Exploder podcast is my absolute favourite, offering endlessly original, stimulating and creative discussions of different game mechanics.

Caspar Henderson, author of The Book of Barely Imagined Beings, has a substack, The Kinetikon – all about movement, with Caspar’s customary grace and wisdom.

Africa Harford also offers a substack, Elementary, My Dear, exploring the theory and the history of chemistry.

The Runnign Channel have produced a moving documentary about Jess Furness’s attempt to run 42 marathons in a year, in honour of what would have been her late brother’s 42nd birthday. Simple, affecting and inspiring. (Even if I think they have slightly glossed over how hard a single marathon is…)

In 1980s Southern England, intricate crop circles are appearing overnight, and people are desperate for an explanation. Could humans really create something so complex without anyone spotting them? The truth is out there! Actually, the truth is right here. The problem is getting people to believe it.

Members of the Cautionary Club have access to all episodes ad-free, monthly bonus episodes, monthly behind-the-scenes video conversations, and our newsletter.

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Further Reading

This script relied on Rupert Sheldrake’s account of The Crop Circle Making Competition, alongside an article by the Wessex Sceptics and personal correspondence from Matt Ridley; contemporary reporting in outlets such as Time magazine; and four books – Round in Circles: Physicists, Poltergeists, Pranksters And the Secret History of the Cropwatchers, by Jim Schnabel; Circular Evidence: A detailed investigation of the flattened swirled crops phenomenon, by Colin Andrews and Pat Delgado; Crop Circles: Signs of Contact, by Colin Andrews; and Crop Circles: Conclusive Evidence? by Pat Delgado.

Craig Anderson, Mark R. Lepper and Lee Ross describe their research on risk-taking firefighters in Perseverance of Social Theories: The Role of Explanation in the Persistence of Discredited Information, published in the Journal of Personality and Social Psychology. Anderson’s reflections on vaccine hesitancy are found in Psychological processes underlying denial of science-based medical practices, co authored with Sara Prot. 

It’s fair to ask, though, how much pluralism does the modern economy really give us? A foolish question, in some ways. In his modern classic The Origin of Wealth (2006) the economist and complexity theorist Eric Beinhocker estimated that at least 10 billion distinct products and services were available in a major urban economy such as New York City, compared with a few hundred available to a traditional hunter-gatherer society. The variety is staggering. Some would say it is overwhelming.

And yet, isn’t it a familiar complaint that everywhere seems to look the same? Walk down a shopping street in Manchester or London, Munich or Copenhagen, and the similarities are as striking as the differences. Big brands are everywhere, and not just the classics such as McDonald’s and Starbucks. Newer chains such as Five Guys and Blank Street seem to spread with remarkable speed.

The independent offerings are a bit samey, too: hipster cafés increasingly seem assembled from the same flat-pack kit. Even the cornucopia of digital content is filtered through a few platforms: Audible for audiobooks, Spotify for music, YouTube for video and Kindle for ebooks.

Maybe we shouldn’t be complaining about this. Andy Warhol celebrated it: “You know that the President drinks Coca-Cola, Liz Taylor drinks Coca-Cola, and just think, you can drink Coca-Cola, too . . . All the Cokes are the same and all the Cokes are good.”

Still, “all the Cokes are the same” is hardly a manifestation of the glorious pluralism I celebrated last week. Does this apparent monoculture reflect a corporate conspiracy, or a flattening of our own tastes, or is there some more subtle process at work?

One answer comes from data scientist Lauren Leek, who was recently flat-hunting in The Hague. “Every flat I scrolled, in a city I barely know, I already recognised: the same refinished parquet, matte-black taps, rewilded pot plant on the same windowsill,” she wrote. “Same with the café near every place I’ve lived, flat white and exposed brick and oat milk assumed.”

It was as though “everywhere is converging on the same few templates, and I’m exactly who those templates were optimised for”. One possibility is that Leek is in her own perfectly crafted filter bubble, shown exactly what she wants to rent, to buy, to drink, and happy enough with the results, even if they are a little unsettling. If she stepped away from what her phone was recommending, she’d see plenty of very different offerings.

But perhaps the personalisation filter is not just shaping what Leek sees, but shaping the world? Leek has in mind a simple algorithm: “predict what people want, show them more of it, watch what they pick, update”. That could describe YouTube or Spotify, but the physical world, too: if Gail’s or Pret A Manger runs an algorithm to decide where to locate, and the algorithm spits out a range of streets that look like they should have a Gail’s or Pret on them, then it’s easy to see how everywhere starts to seem the same.

This process can produce a kind of converging feedback loop: algorithmic predictions smooth out the world. This then makes it easier for the algorithm to predict what people will do. And the better the algorithm’s prediction, the more similar everything becomes.

The simplest form of this model failure would be a YouTube autoplay that directs you to a slightly more popular cousin of the video you’ve just watched. After that, in turn, a slightly more popular choice again. Leave the loop running and eventually every autoplay is an endlessly looping Baby Shark, the cultural black hole from whose gravitational pull nothing can escape.

(YouTube, of course, tries to avoid this. There is a countervailing risk, in which every recommendation becomes edgier and more extreme. These are tough technical problems; it is not always easy to be an algorithmic overlord.)

Ultimately, though, we should not reflexively blame the algorithm. Algorithms can be changed if they are not producing the desired results. The deeper trade-off here is an ancient one: should businesses stick with a proven formula for success, at the risk of missing out on something even better? Or explore the unknown?

It is not just entrepreneurs and managers who need to wrestle with this “explore-exploit” trade-off. We all do. Pop into a McDonald’s or a Blank Street, buy a ticket for yet another Marvel movie, and you’re almost guaranteed a certain minimum quality.

But take a risk — an independent bistro, an art-house movie, the local wine — and you might get something that is better than good. Or worse. The less willing we are to take a risk, the more safe options we are likely to be offered.

The trade-off depends on individual taste, of course, but it also depends on some well-understood variables. The time-horizon matters. If you’re visiting somewhere new for three days and you find a great restaurant, it might be a good idea to stick with it. If you’re in town for months — or years — then it’s worth casting the net more widely, even though you’ll likely chew through some grim menus.

The cost of experimentation matters, too. Aspiring writers can try all sorts of things out on Substack without asking publishers, readers or themselves to take the risk involved in a full-fledged book. The Dan Browns and Sarah J Maases of the world might prefer to stick with writing, printing and selling in a form that readers demonstrably want to buy.

If the variety of the modern economy really has diminished, that would be because the trade-off between exploring new options and exploiting old recipes has changed, either for businesses or for us as consumers. Why might that be?

Surely not because experimentation is more expensive. And not because time-horizons are short, given that real interest rates even now remain lower than they were in the 1980s and 1990s.

Maybe the question is based on a false premise, then. Maybe the modern economy is more varied than ever.

I hope so. Because if not, the most plausible explanation for being surrounded by familiar brand names and cookie-cutter stylings is simply that we are being given exactly what we want. Maybe we, like Warhol, are delighted that all the Cokes are the same, and all the Cokes are good.

Written for and first published in the Financial Times on 9 September 2026.

I’m running the Oxford Half Marathon in October in support of a very good cause and in memory of my mother. If you felt able to contribute something, I’d be extremely grateful.

One hundred years ago, on 16th February 1923, the Tomb of the Pharaoh Tutenkhamun was officially opened. Disturbing the remains of the Egyptian pharaohs is known to incur a deadly curse, so why did a team of archeologists still risk inciting the wrath of King Tutankhamun by entering his burial chamber? And how many of them met a premature end for their impudence?

This classic episode was first released in November 2021.

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Further reading and listening

Roger Luckhurst’s book, The Mummy’s Curse , is the perfect guide to every angle of the tale. Nigel Blundell’s The World’s Greatest Mistakes gives a vivid tabloid-style version, and Snopes described and then fact-checked the tale of the Unlucky Mummy. Skeptoid covers and debunks various explanations for the curse.

The Mesmeromania incident is covered in detail by Christopher Turner for Cabinet Magazine. Shankar Vedantam and Bill Mesler set it in wider context in their fascinating book Useful Delusions.

Charle’s Duhigg’s story about Target and the pregnant teenager is in the New York Times Magazine.

Academic studies on placebos, nocebos, and the BMJ article about the mummy’s curse:

Howick, J. Unethical informed consent caused by overlooking poorly measured nocebo effects. Journal of Medical Ethics. https://ora.ox.ac.uk/objects/uuid:07126ead-92c8-4b82-87b2-7e677aaf98b5

Colloca L, Miller FG. The nocebo effect and its relevance for clinical practice. Psychosom Med. 2011;73(7):598-603. doi:10.1097/PSY.0b013e3182294a50

Nelson MR. The mummy’s curse: historical cohort study. BMJ. 2002 Dec 21;325(7378):1482-4. doi: 10.1136/bmj.325.7378.1482. PMID: 12493675; PMCID: PMC139048.

It was not the colour scheme that worried me, nor even the narrow-seeming niche, but the fact that Oxford is blessed with so many bookshops already. On the 15-minute stroll from Bad Girl Books to the Oxford institution Blackwell’s, the bibliophile risks being distracted by The Last Bookshop, an Oxfam second-hand shop, The Last Bookshop (another one — surely they can’t both be the last one?), and the Blackwell’s science-fiction, manga and games branch, heaving with its own lavish selection of romantasy titles.

Attempting to avoid all that will only lead you into a capacious Waterstones, another Oxfam bookshop and the independent bookshop-café Gulp Fiction. Flee to Oxford’s northern district of Summertown and you may fall into the gravity well of a generously proportioned branch of Daunt Books. And all that is before we mention the elephantine online competitor, Amazon.

I note all this not to prompt tears of rage and envy if you are reading this in a book desert, but to point out that Bad Girl Books was clearly doomed from the start to be a vanity project that would drain the life savings of the naive proprietor Starlin Marot.

On opening day, however, customers were literally queuing down the street. On day two, customers were still queuing down the street. I left town for a couple of weeks, and when I returned, things were different: the queue management system had improved, and the line now stretched down a side street.

It turns out that authors of books such as Death’s New Pet, Heavensent & Hellbent, Web of Vows and Vengeance and A Kiss of Hammer and Flame have been showing up each summer weekend to participate in a Mini Summer Romantasy Festival. Despite the heat, customers couldn’t get enough. Bad Girl Books was off to a flying start.

I am pleased to have been proved wrong. It is a delight to discover how many different enthusiasms exist in the world. I am not buying what Bad Girl Books is selling, but that is not the point: others are purring with satisfaction, and that’s good enough for me. (Also: like me, romantasy readers are nerds. It is great to see nerds well served.)

But there is a broader point here, too. If Oxford had a committee in charge of approving new bookshops, I would be overqualified to serve on it, being an author, book enthusiast and professional economist. And if I had been on that committee, I would have patiently, patronisingly explained that there was no business case for Bad Girl Books and the business plan should be rejected.

Thankfully there is no such committee, leaving the proprietor free to make her foolish decision — or to demonstrate that the decision was not so foolish after all. A thriving economy allows people to take their own risks, follow their own dreams and make their own mistakes.

Marot is not the first Oxford entrepreneur to be underestimated by an Oxford economist. William Morris began his business career running a bicycle-repair shop on High Street, before moving into the manufacture of automobiles. As ever-larger manufacturing plants were built in Cowley, east Oxford, the economic historian Edwin Cannan — who taught at the London School of Economics but lived in Oxford — was opining in 1927 that he could not imagine where the demand would come from.

I stumbled upon Cannan’s concerns in John Kay’s The Truth About Markets (2003), which suggests that a key feature of the market economy is missing from most economics textbooks. Those textbooks tend to describe an allocation mechanism where prices ensure that supply equals demand, and competitive pressure pushes those prices down to the point where they equal the cost of production. That description is not wholly wrong, but it leaves out a lot. For Kay, much of what a market economy does well can be described with the phrase “disciplined pluralism”.

By pluralism, he means that many different ideas can flourish. Pluralism is vital in a world where the right way forward is never obvious. There is no committee of experts to decide whether Marot should be able to launch yet another bookshop, or whether a bicycle-repair boy will ever find enough customers for his newfangled motor cars.

More precisely, no committee of experts has veto power. A new start-up, whether the product is romantasy books or bicycles, will probably have to convince somebody — a family member, a bank manager, a group of enthusiastic backers on Kickstarter — to risk some cash. But a well-functioning economy will offer many such options to many budding entrepreneurs, even if it does not offer limitless funding to everyone.

This is no mere theoretical idea. IBM turned down the chance to fund Chester Carlson’s brainchild — the photocopier. No matter. In the end, Carlson found somebody willing to take a risk and the result was the Xerox Corporation. Many other projects, from Google to The Beatles, were rejected before finding a backer who mattered.

Pluralism sounds fun, but Kay also emphasises the importance of discipline. Pluralism means trying many ideas; discipline means closing down the ideas that do not work before they consume too many resources. Evolution by natural selection achieves pluralism through the mixing and mutation of genes, and discipline through the brutal process of survival of the fittest.

A market economy achieves pluralism through rules and laws that do not forbid new businesses, along with a financial system that funds a variety of them. It achieves discipline through competition and, sometimes, the bankruptcy courts. No matter how much your financial backers like your business idea, it will not last long if it does not also appeal to some customers. An investment bubble can loosen the discipline and postpone the reckoning, but not for ever.

At a time when the performance of the British economy leaves a lot to be desired, policymakers should keep the idea of disciplined pluralism in mind. In a healthy economy, there must be ways for new business ideas to be born — and for failing ideas to die.

Written for and first published in the Financial Times on 2 Sep 2026.

I’m running the Oxford Half Marathon in October in support of a very good cause and in memory of my mother. If you felt able to contribute something, I’d be extremely grateful.

Before he became Muhammad Ali, Cassius Clay was known as the “Louisville Loud-mouth”, as famous for his sharp taunts and poetic put-downs as he was for his skills in the ring. In 1963, Clay arrived in England to take down beloved British Heavyweight, Henry Cooper. Clay is the clear favourite, but the showdown will be remembered as one of boxing history’s most shocking battles, changing both men forever and showing what it really means to win. 

This episode was originally released to members of the Cautionary Club, and Pushkin+ subscribers.

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Further Reading

Ali. A Life Jonathan Eig. 2017

Henry Cooper: A Hero For All Time Norman Giller. 2012 

Ali in Britain Michael Tanner 1995

Time “Prizefighting: Murder on the BBC.” Friday, June 28, 1963

Guardian “Observer picture archive: Cassius Clay in London, 30 May 1963” Sat, 1 June, 2019

The Long Win: The search for a better way to succeed. Catherine Bishop. 2020.

The legend related in William Poundstone’s book How to Predict the Unpredictable (2014) (in the US, Rock Breaks Scissors) is that nobody ever beat the machine over an extended run, with one exception: Shannon himself. As the machine’s algorithm was simple and elegant, he was able to mentally emulate it and play the opposite of whatever he knew the machine would predict.

How did the machines work? The logic was simple: both took notes of how their opponent behaved. For example, if you’d won a couple of times in a row, did you usually ride your luck by sticking with the same choice or did you tend to switch? The presumption was that no human plays randomly. We all have certain habits or instincts. No supercomputing was required: Shannon’s machine had just 16 bits of memory. We humans are not hard to read.

An even simpler exploit is the double-tailed coin. Any scoundrel with such a coin can decide any disagreement by offering to toss it, then calling “tails”. But even if he offers his mark the opportunity to call the toss, he will probably win, because people will call “heads” more often than not.

One of the first academics to figure this out was Louis Goodfellow, who in the late 1930s recruited volunteers to write down a series that reflected an imagined set of coin tosses. Seventy-eight per cent of his participants began their sequence with “heads”.

In a larger dataset — originally gathered in an effort to study telepathy (a story for another day) — Goodfellow found that more than 20 per cent of participants either chose the sequence HHTHT or HHTTH. Other random-seeming sequences beginning with heads were also popular, such as HTTHH and HTHHT. Few people favoured anything beginning with tails, and the least popular sequence was TTTTT, chosen by about one person in 600. Any mathematician can tell you, however, that there are 32 possible outcomes of tossing a coin five times, and each of the 32 is equally likely.

Fifteen years later, Alphonse Chapanis, a pioneer of ergonomics, asked volunteers to take an hour or so to fill a large grid with thousands of random digits. Analysing the results produced some striking observations. The 10 least popular adjacent combinations of digits, in order, were: 66 99 00 11 33 44 88 22 77 55. And the 10 most popular? 32 43 21 76 65 10 31 87 86 54 — something about the human brain likes descending couplets, it seems. In a truly random sequence, 66 is just as likely to appear as 32, but what seems random as we scribble it down is anything but. Such regularities can be exploited by an outguessing machine, a conman, even a password guesser.

They can also be exploited by lazy students. Author William Poundstone offers a few tips to brute-force your way through multiple-choice tests. If you have no idea what the answer is on a true-false question, guess “true”. And if you know what the answer to the previous question was, guess that this time it will change. Offered four options, go for “B”. Always choose “all of the above” or “none of the above”, if available — they are disproportionately likely to be the correct answer. None of these methods guarantees success, but they do improve your odds because most setters of multiple-choice questions are more predictable than they realise.

If you really need a random sequence, then don’t ask a human. One alternative is to ask a machine to generate the randomness — but be careful. In 1980, the Pennsylvania “Pick 3” lottery was rigged by staff at the TV studio where the draw was televised. Every number except the 4 and 6 balls was weighted with a judicious addition of latex paint, meaning that when the fan was switched on to blow the lightweight balls around, all the 4 and 6 balls floated to the top. Alas for the conspirators, the heavy bets on 4-6 combinations coupled with the portentous winning number 666 were enough to raise suspicions.

Almost the same story played out in the digital realm more recently, when an IT expert at the Multi-State Lottery Association admitted introducing a backdoor to the software that generated lottery numbers: while it was usually random, on certain dates it would produce random-seeming numbers that he could predict.

Computer cryptography relies on having a large number that cannot be guessed, and the best way to have an unguessable number is to make it random. Unfortunately, this is harder to do than one might imagine, and several computer systems — most notoriously Sony’s PlayStation 3 — have been hacked because the attackers figured out how the “random” number was being produced.

If lottery machines — physical or digital — can be rigged, and humans are incapable of inventing truly random sequences of numbers, it is tempting to resort to the good old-fashioned coin toss. Not so fast. Persi Diaconis, celebrated both as a mathematician and magician, has found that a coin toss is, in general, a 51/49 proposition in favour of finishing the same way up that it started. To illustrate the idea further, Diaconis built a coin-tossing machine. Insert a coin heads-up and the machine will flip it nicely in the air — to land heads-up every time.

This is no mere theoretical problem. At the International Congress of Mathematicians this summer, maths author and YouTuber Matt Parker and friends ran a stall in which maths-curious members of the public could try tossing a coin. Parker promised to give $1,000 to anyone who managed to toss 10 heads in a row — a fun challenge to prompt people to explore what an unlikely outcome really felt like.

Alas, it wasn’t as unlikely as he had imagined: having been forced to hand over the $1,000 prize twice on the first day, Parker looked at the accumulating data and realised that the entire distribution of coin flips was unexpectedly biased towards strings of tails or strings of heads. The effect was stronger than Diaconis had predicted, perhaps because many of Parker’s coin tossers were rather young and unable to reliably flip coins high enough to rotate much. Parker’s solution: on the second day of the conference, he switched to dice. The pattern of results reverted to something much closer to pure randomness . . . whatever that is.

Written for and first published in the Financial Times on 28 August 2026.

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