Known odds and unknown odds

Two people are about to lose money.

The first is playing a dice game. Six faces, one die, and a payout table pinned to the wall. Before a single throw, everything worth knowing is known: the list of outcomes, and the chance of each one.

The second has opened a bakery on a street with no bakery. Everything worth knowing is unknown, and most of it is unknowable. Not because nobody has measured it — because there is nothing to measure yet.

Both are taking a chance. They are not taking the same kind of chance, and almost every bad argument about risk starts by treating them as though they were.

Why the difference bites

Every technique for handling risk assumes the distribution. Expected value assumes it. Insurance pricing assumes it. Any calculation that multiplies an outcome by its probability assumes somebody knows the probability.

Under uncertainty, that number is a guess wearing a decimal point.

The dangerous move is not the guess. It is that once a guess has been written down and multiplied by something, it stops looking like a guess. A model inherits the confidence of its arithmetic, and the arithmetic is flawless whatever you fed it.

Predict

Someone builds a careful model of a new business: sizes the market, estimates a conversion rate, projects three years of revenue. Every calculation is correct. What is the most likely reason the result is still misleading?

Choose one answer

The arithmetic will contain an error somewhereThe inputs are estimates of quantities that do not yet exist, and the output looks exactly as confident as if they were measurementsThree years is too short a horizonThe model should have used a range instead of a single number

Lock in answer

The two live side by side

Most real situations are a mixture, and the useful skill is separating the parts rather than labelling the whole thing.

A shop knows roughly what fraction of stock it loses to breakage each year — that part is risk, and it can be budgeted for like a cost. The shop does not know whether a larger competitor will open across the road — that part is uncertainty, and no budget line covers it.

The same split runs through a career, a portfolio and a marriage.

Not the same thing

Risk

The outcomes are known and so are their probabilities, or a large enough history exists to estimate them.

Measured in

A probability distribution — percentages that add to one hundred

For example

The chance that a house in a large pool of similar houses burns down this year.

Chase it alone and

Treating an estimated distribution as a measured one, then sizing a position as if the tails had been observed rather than assumed.

Uncertainty

The list of outcomes is incomplete, the probabilities are unavailable, and there is no comparable history to borrow from.

Measured in

Nothing numeric. At best, a list of what you would have to believe

For example

Whether a business idea nobody has tried will find customers at a price that works.

Chase it alone and

Refusing to act until the numbers arrive, when the numbers are never going to arrive, and the only way to learn is to take a small survivable step.

Which is which? Put each one on a side.

• The chance a fair coin lands heads eleven times in a row

  RiskUncertainty

• Whether the skill you spent six years learning is still valued in fifteen

  RiskUncertainty

• The share of borrowers in a large, long-running loan book who miss a payment next month

  RiskUncertainty

• Whether a country you have never worked in will suit you

  RiskUncertainty

What to do differently in each

Under risk, the work is arithmetic and pooling. Compute the expectation, check the spread, and if the risk is poolable, get it into a pool.

Under uncertainty, arithmetic is theatre. The work is different:

Make the step small enough to survive being wrong. Not because you expect to be wrong, but because you have no way of knowing how wrong you could be.

Buy information before buying commitment. A month of doing the thing badly on a small scale tells you more than a quarter of modelling it.

Prefer reversible moves. Under uncertainty, the option to change your mind is worth paying for, and it is usually cheaper before you commit than after.

Write down what would change your mind. In advance. Afterwards, everything you learn will feel like confirmation.

Check

Someone says: the odds of this business working are about thirty percent. What is the most useful response?

Choose one answer

Ask where the number came from, and treat it as a statement about their confidence rather than about the worldAccept it and compute the expected valuePoint out that nobody can know that, and drop the subjectAsk for a wider range instead of a point estimate

Check answer

›Why this distinction keeps getting flattenedOptional

Both words map onto the same feeling — the feeling of not knowing — and language follows feelings rather than structures.

There is also a professional incentive. A number can be put in a document, defended in a meeting, and pointed at afterwards. A sentence saying the distribution is unavailable cannot be any of those things, and the person who writes it looks less competent than the person who writes 30%, right up until the moment the outcome arrives.

That asymmetry is not a moral failing of analysts. It is what happens when the reward for looking rigorous arrives years before the reward for being right.

Worth remembering

• Risk is a situation where the outcomes and their odds are known; uncertainty is one where they are not, and often cannot be.
• Every technique that multiplies an outcome by a probability assumes somebody knows the probability.
• A guessed input passed through correct arithmetic comes out formatted like a measurement, and gets argued about as one.
• Most real situations are a mixture, and the useful skill is separating the poolable part from the unknowable part.
• Under uncertainty the tools are small survivable steps, cheap information, reversible moves, and writing down in advance what would change your mind.