Decision points — expected value, and the decisions it quietly gets wrong

For each option, list what could happen, how likely each outcome is, and what each is worth. Multiply and add:

That's a weighted average of the outcomes — "what this choice is worth on average". For decisions you make over and over — stocking rules, triage rules, inspection policies — it's exactly right, because over many repeats you really do experience something close to the average.

• Decisions you only make once. A 10% chance of winning £1m has an expected value of £100,000. But you will never receive £100,000 — you'll get the million or, far more likely, nothing. For one-shot choices, the average is a number you never experience. Look at the actual outcomes instead.
• Bets you can't survive losing. An attractive-on-average gamble that includes a company-ending outcome is a bad gamble, whatever the average says — because the average is calculated over futures where you no longer exist to enjoy it. Ask "what's the worst case, and can we live with it?" before asking about the average.
• Made-up probabilities. The formula is only as honest as its inputs, and workshop probabilities are often theatre — confident-sounding numbers with nothing behind them. Simple stress test: nudge each probability a little. If the best option flips, the analysis has actually told you something valuable — go find out more before deciding. There's even a formal number for how much resolving the uncertainty is worth before you commit, and it's frequently the most useful figure in the room.

Use expected value to structure the conversation — it forces the options, chances, and stakes into the open. Then decide with three extra things in view: the actual spread of outcomes, the worst case, and how reversible the choice is. The maths of averages is kindest to people who can afford to be wrong.