To
Anyone with a decision to make
From
Daniel Okafor-Reyes
Re
Agenda item 1
Date
2026-11-09

Expected Value for Everyday Decisions

Weight each outcome by how likely it is, add them up, and you have the average result of a choice repeated many times. It is the first question a good executive asks.

Executives make many decisions under uncertainty, and the good ones share a habit: before asking "what will happen?", they ask "what happens on average, and how bad is the bad case?" The first half of that question has a precise name. In probability, the expected value of a random quantity is, loosely, the average outcome you would get if you could repeat the situation many times, found by multiplying each possible outcome by its probability and adding the results.

The calculation in three steps

  1. List the outcomes that matter. Keep it short: three or four is usually enough.
  2. Give each a probability. They must add up to one. Rough estimates are fine as long as you write them down.
  3. Multiply each outcome's value by its probability and add the products.

Take a simple, made-up illustration. A choice gives you a gain of 100 with probability one half and a loss of 40 with probability one half. The expected value is 0.5 × 100 + 0.5 × (−40) = 30. Repeated many times, you would expect to come out ahead by about 30 per go. The numbers are invented for the arithmetic; the method is what matters.

What expected value does well

  • It forces you to name the outcomes instead of reacting to the most vivid one.
  • It makes you commit to probabilities, which can then be checked against what happens.
  • It lets you compare options on one scale.

What it does not tell you

An average hides the spread. A choice with a positive expected value can still ruin you if one outcome is a loss you cannot survive. That is why expected value is the first question, not the only one. The second is about risk: how much could I lose, and can I absorb it? That leads to the idea of a risk budget, covered in the next memo.

It also assumes you can repeat the situation. For a one-off decision, such as accepting a job, the average over many imaginary repetitions is still a useful guide, but your tolerance for the bad case should weigh more.

Include the hidden costs

When listing outcomes, include what you give up. Opportunity cost is the value of the best alternative you forgo by choosing one option. Time spent on a project with a modest expected gain is time not spent on something better. A complete expected-value sketch includes "what else could I do with this money and time?"

Games of chance as a teaching case

Casino games and lotteries are the cleanest examples of expected value because their rules fix the probabilities. They are designed so that, for the player, the expected value of each bet is negative; the difference is how the operator is paid. That makes them useful for understanding the concept, and a reminder that a game can be enjoyable while still being, on average, a cost.

On gambling. Games of chance are priced so that the operator comes out ahead over time. If you play, fix a loss limit in advance and treat it as the cost of entertainment, not as an investment. If it stops being fun or starts costing more than you planned, in the US you can call 1-800-MY-RESET.

Practise it

Pick one decision this week, write down three outcomes and their probabilities, and calculate. You will rarely follow the number blindly, but you will notice when your instinct and the arithmetic disagree, and that is exactly the moment to think harder.

Name the outcomes, put numbers on them, and look at the worst case before the average.

Filed 2026-11-09