Would you take £50,000 straight away, or flip a coin for a 50% chance of winning £1 million?

That was the question YouGov asked 4,598 adults in Great Britain.

The results were striking:

Source: YouGov, 22 July 2026.

Imagine you are offered the same choice:

Option A: Take £50,000 for certain.
Option B: Flip a fair coin. If it lands heads, you win £1 million. If it lands tails, you get nothing.

The coin is fair. The money is real.

Q1: Which option do you choose, and why?

Q2: Why might it be rational to take the guaranteed £50,000?

Q3: Why might it be irrational to take the guaranteed £50,000?

Q4: What factors might affect your answer? In other words, would everyone face this choice in the same way?

Q5: Economists often distinguish between money and utility.

Money is measured in pounds. Utility is the satisfaction, welfare or usefulness someone gets from those pounds.

Suppose utility from wealth is given by:

U(W) = √W

where W is your wealth after the choice, and you start with no other wealth.

Which option gives the higher expected utility? What does your answer suggest about the 73% who chose the £50,000?

Bonus: What is the smallest guaranteed amount someone with U(W) = √W would accept instead of the coin flip?

P.S roll up your sleeves and explore the question… once you’ve grappled with it for a while, if you are still stuck…Graduated hints below — but challenge yourself first! (Answer comes in the next edition! Subscribe to receive it directly to your inbox!)

4.5%

This issue’s marginal number is 4.5%.

That is what UK households now expect inflation to be over the next 12 months, according to the latest Citi/YouGov survey.

The number rose from 3.9% in August.

Source: Reuters, reporting on the Citi/YouGov survey, 28 September 2026.

Why does this matter?

Inflation expectations shape behaviour today. If households expect prices to rise, they may spend sooner or push harder for pay rises. If firms think customers expect higher prices, they may feel freer to raise theirs. And if workers and firms both build higher inflation into their decisions, inflation becomes harder to shift.

That is why the Bank of England watches what people think inflation will do next, as well as what it is doing now. A jump from 3.9% to 4.5% in a single month suggests those expectations may be starting to drift upwards, which adds to the pressure on the Bank as it weighs whether to raise interest rates.

The actual answer is about 17%, or exactly 1 in 6.

Here's why.

Don't start with the person who tested positive. Start with a crowd. Imagine 10,000 people.

How many have the condition? 1% of 10,000 = 100 people.
How many don't? 10,000 − 100 = 9,900 people.

There are two ways to get a positive result.

True positives: people who have the condition, and test positive.
99% of 100 = 99 people.

False positives: people who don't have the condition, but test positive anyway.
5% of 9,900 = 495 people.

Total positive results: 99 + 495 = 594 people.

Our person is one of the 594 who tested positive. Only 99 of them actually have the condition.

Five out of every six positive results are false alarms.

Because the condition is rare, and the healthy group is enormous.

The test is good at spotting the condition. But a 5% false-positive rate applied to 9,900 healthy people produces 495 false alarms. That swamps the 99 genuine cases.

The mistake in the "99%" instinct is mixing up two different questions:

"If you have the condition, how likely is a positive test?" That is 99%.
"If you have a positive test, how likely is it that you have the condition?" That is about 17%.

They sound similar, but they're very different. Confusing them is called base rate neglect: ignoring how common something was to begin with.

Bayes' theorem does the counting in one line:

P(C) = 0.01: the base rate, how common the condition is.
P(+ | C) = 0.99: the chance of a positive test if you have it.
P(+): the chance of a positive test overall, from both routes:

So:

It's the same calculation as the 10,000 people, written with probabilities instead of people. If the formula ever feels abstract, go back to counting people.

Suppose the condition affected 10% of the population instead of 1%, with the same test.

Out of 10,000 people: 990 true positives and 450 false positives.

Same test, very different answer. How believable a positive result is depends as much on the base rate as on the test itself.

Suppose the person takes a second, independent test and it's positive again.

Their starting probability is now 1/6, not 1%. The first result updated it. Using the same method:

This is Bayesian updating: each new piece of evidence moves your belief, starting from wherever the last piece left it. It's why doctors often confirm a positive screening result with a second test before acting.

Economists face this constantly, whenever evidence is imperfect and what's being tested for is rare:

In each case, the question is not "how good is the test?" but "how good is the test, given how rare the thing is?"

Answering 99%. That's the probability of a positive test given the condition, not the other way round.
Forgetting the false positives. Both routes to a positive result have to be counted.
Ignoring the base rate. A 1% starting point changes everything.

Extension reading:

Watch first: Bayes' theorem, the geometry of changing beliefs (3Blue1Brown, YouTube, about 15 minutes). The best short introduction anywhere. It uses the same "imagine a crowd of people" method as our solution. Prefer to read? The written version is on the 3Blue1Brown website.

How experts get it wrong: Natural frequency trees improve diagnostic efficiency in Bayesian reasoning (free research article). A real study of the breast screening version of our problem. Skim the introduction for a striking finding about how doctors answered.

For the ambitious: What Can Education Learn from Real-World Communication of Risk and Uncertainty? by Sir David Spiegelhalter and Jenny Gage (University of Cambridge, PDF). Why counting people (expected frequencies) beats formulas, from Cambridge's leading expert on risk.

Books:
The Art of Statistics by David Spiegelhalter (2019). A brilliant, readable guide to thinking with data.
Reckoning with Risk by Gerd Gigerenzer (2002). The classic book on why people misread test results, and how natural frequencies fix it.

P.S: Bonus marginal thinking:
Is the test "99% accurate"?

No, and it's a good question to ask. The 99% describes only one thing the test does. To judge a test properly, you need to look at all four possible outcomes.

Using our 10,000 people:

From this one table, you can calculate four different "accuracy" numbers, each answering a different question:

1. Of the people who have the condition, how many does it catch?
99 ÷ 100 = 99%. This is called sensitivity, and it's the "99%" in the question.

2. Of the people who don't have it, how many does it correctly clear?
9,405 ÷ 9,900 = 95%. This is called specificity.

3. Of all 10,000 results, how many are correct?
(99 + 9,405) ÷ 10,000 = 95%. This is overall accuracy.

4. If you test positive, how likely is it that you have the condition?
99 ÷ 594 = 17%. This is the positive predictive value, and it's the number the patient actually cares about.

The same test is 99%, 95%, 95% or 17% "accurate", depending on the question you ask. That's why a single accuracy figure can be so misleading.

Imagine a "test" that simply tells everyone they're negative, without testing anyone at all.

It would be right for all 9,900 healthy people, and wrong for the 100 who have the condition:

A test that does nothing is "99% accurate", yet it never catches a single case. When a condition is rare, overall accuracy mostly measures how good a test is at saying "no" to healthy people. That's why doctors and statisticians talk about sensitivity and specificity instead.

Whenever someone quotes a test's "accuracy", ask: accurate at what? Catching cases? Clearing healthy people? Or telling you what a positive result means? They're different numbers, and the last one depends heavily on how common the condition is.

This applies well beyond medicine: fraud detection, AI classifiers and exam grading all face the same trap. An AI model that flags "no fraud" on every transaction would also score over 99% accuracy, and be completely useless.

Marginal gains… Answer for today’s question is out in two days… Come back then or subscribe to get it direct to your inbox!

P.P.S.

Feel free to share this resource with a friend!