An expected value (EV) is the probability-weighted average of a decision's outcomes: EV = Σ (probability of outcome i × value of outcome i). It's the most important calculation in decision-making under risk. It makes you stop thinking in single scenarios, like "if the thesis works, I make 3×," and start thinking in the whole distribution of what could happen, each outcome weighted by how likely it is. As a probabilistic thinker, you stop asking "will this work?", a yes-or-no question the future refuses to answer in advance. You ask "what are the possible outcomes, how likely is each, and what is each worth?"
Worked example: a pharma stock ahead of a regulatory decision
A worked EV table with an asymmetric payoff. A US specialty-pharma stock trades at $40 ahead of a binary regulatory decision. You estimate three outcomes:
| Outcome | Probability | Price if it happens | Contribution (prob × price) |
|---|---|---|---|
| Approval (blockbuster) | 20% | $120 | $24.0 |
| Partial / delayed approval | 30% | $55 | $16.5 |
| Rejection | 50% | $25 | $12.5 |
| Expected value | $53.0 |
The EV is $53 against a $40 price, a +32.5% expected return, so on the numbers it's an attractive bet. But look at its shape. The most likely outcome, at 50%, is a −37.5% loss, and only a 20% tail delivers the +200% that carries the EV. This is an asymmetric payoff, Pabrai's Dhandho in EV clothing. The upside is far larger than the downside, so a probability-weighted edge exists even though you'll lose money more often than not. Two lessons fall out straight away. First, you can't judge the bet by its most likely outcome. You have to weigh the whole distribution. Second, and this is the spine of everything here, you must not judge the decision by its outcome.
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What is resulting, and why does it matter?
Suppose you take the bet and the drug is rejected. You lose 37.5%. Was it a bad decision? No. If your probabilities were well-founded, it was a good decision with a bad outcome, and you should make that same bet every time it's offered, because across many such bets the +EV compounds in your favour. The poker champion and decision scientist Annie Duke has a name for judging a decision by its result instead of its process. She calls it "resulting," and it's the most corrosive error in all of investing. Resulting teaches you the wrong lessons. It praises the reckless bet that got lucky and punishes the sound bet that got unlucky, so an investor who learns from outcomes learns to be reckless. Your only defence is to separate decision quality from outcome quality, and to grade, reward and journal the process: whether the probabilities were estimated in good faith, whether the EV was positive, and whether the position was sized so a bad outcome couldn't ruin you.
It's the reason your mastery gates score reasoning, and the reason your decision journal records the thesis and the odds before the outcome is known. It's also why the app's leaderboards rank process and calibration and never portfolio P&L (working agreement #8, competency C9). In a game this thick with luck, process is the only thing you control, so it's the only fair thing to score. A good decision can lose money, and a bad one can make money. Over a career, only the quality of your decisions compounds, and the luck averages out.
Is a positive expected value enough?
One caution before we size anything. A positive EV is necessary, but it isn't sufficient. The pharma bet above has a great EV. But put your whole portfolio into it and a 50% chance of −37.5% becomes a 50% chance of a portfolio-wrecking loss you may not recover from. EV tells you whether to bet. It doesn't tell you how much. For that we need Kelly, and then we need to see why even Kelly has to be reined in. That last part is the deepest idea here.