Expected Value
When is a bet you will probably lose still the right bet?
The idea
Expected value combines possible outcomes with their probabilities.
In the real world
A small experiment can be worthwhile despite likely failure.
Going deeper
Expected value combines the size of each outcome with its probability, which means a decision can be correct even when the most likely single result is failure. A 10% chance at £500,000 for a £20,000 cost is worth taking, and will usually lose.
Two conditions matter. The bet must be repeatable, or part of a portfolio of similar bets, for the average to be realised — a single favourable gamble can still ruin you. And the downside must be survivable, because expected value arithmetic assumes you are still there for the next one. Both are why the framework applies well to experiments and badly to existential risks.
Where it stops applying
Probabilities in real decisions are estimates, often bad ones, and a confident number can make a guess look like analysis. The framework is most useful for structuring the comparison, less so for producing a precise figure.
Why it matters
It lets you judge a decision by its full range of outcomes rather than the most likely one.
Try this today
Estimate outcomes, probabilities, and costs.
Test yourself
An experiment has a 10% chance of unlocking £500,000 and costs £20,000. It will probably fail. Should that stop you?
Show the answer
No. Weighting the outcomes by their probabilities gives £50,000 against a £20,000 cost. The most likely single result is failure, and the decision is still favourable, because size and likelihood have to be considered together.
Learn this in the feed Answering from memory, then again days later, is what makes it stick.