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Expected value is only as honest as the inputs
Expected value puts a single figure on an uncertain choice: weigh each possible outcome by how likely it is, and add them up. It is one of the most useful tools in decision making and one of the easiest to abuse, because the arithmetic looks equally confident whether the inputs were measured or made up.
An explanation of a decision method. Argumont is decision support, not investment advice.
Where the idea came from
The idea grew out of a gambling puzzle. In 1654 Blaise Pascal and Pierre de Fermat exchanged letters on how to divide the stakes of a game interrupted before it finished, and their answer weighed each player's remaining chances. That reasoning became a foundation of probability theory.
In 1738 Daniel Bernoulli added a correction that still matters: people do not value money in a straight line. Losing half your savings hurts far more than gaining the same amount pleases, so the highest expected value is not always the wise choice.
Working it through
List the outcomes that matter, give each a value and a likelihood, multiply, and add. A project with a 60 percent chance of earning $500,000 and a 40 percent chance of losing $200,000 has an expected value of $220,000. Nothing in that figure says you will earn $220,000, which is never one of the outcomes on offer.
The figure is a summary for comparing options with each other, not a forecast of what happens. Read it alongside the worst case, which is the number that decides whether you can afford to play at all.
Where the honest work hides
The likelihoods are where most expected value calculations go wrong. A 60 percent chance written by the project's sponsor is a hope with a decimal point. Before trusting the result, ask where each figure came from and how far it would have to move to change the ranking.
If shifting one likelihood by ten points reverses the choice, the calculation has told you something valuable: the decision turns on that estimate, and that estimate is the thing to go and test. A single expected value that hides this sensitivity is worse than no figure at all.
Expected value in a Decision Room
Argumont works the sums a question asks for exactly, from the figures you supply, so the arithmetic is never the weak point. The Inspector marks whether each likelihood rests on evidence or is unverified, and the Challenger presses on the estimate the ranking depends on. The Red Teamer runs the outcome that would hurt most, which keeps the worst case beside the average. The Human Decision is recorded separately from the Verdict and belongs to you.
A launch with one soft number
A manufacturer weighs a new product line costing $300,000. The sponsor estimates a 70 percent chance of $800,000 in profit over three years and a 30 percent chance of $100,000. Expected profit: $590,000, against $300,000 spent. Lower the good case to 40 percent, a figure the sales data could equally support, and expected profit falls to $380,000, barely above the cost. The calculation has not answered the question. It has shown that the whole choice rests on one estimate, and that estimate deserves a real test before the money moves.
Questions
- Should I always pick the option with the highest expected value?
- Only when you can survive the bad outcomes and the choice repeats often enough for averages to matter. For a single large bet, check the worst case first.
- What if I have no idea of the probabilities?
- Write a range rather than a point, say between 30 and 60 percent, and see whether the ranking holds across the range. If it does, the uncertainty matters little. If it flips, you know what to research.
- Is expected value only for financial choices?
- No. Any outcome you can value, such as hours saved or customers kept, can be weighed this way, provided the values sit on a common scale.
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