Expected Value Explained: The Most Important Concept in Decision-Making

Expected value (EV) is the weighted average of all possible outcomes of a decision, where each outcome is weighted by its probability of occurring. It tells you what you'd get on average if you could repeat a decision infinitely many times.

The formula is straightforward:

EV = Σ (Probability of Outcome × Value of Outcome)

Or in plain English: multiply each possible result by how likely it is, then add them all up.

This deceptively simple concept is the foundation of rational decision-making under uncertainty. It's how insurance companies price policies, how venture capitalists evaluate startups, and how poker professionals decide whether to call a bet. Once you internalise expected value thinking, you'll never look at decisions the same way again.

Suppose someone offers you this game: flip a fair coin. Heads, you win £200. Tails, you lose £100. Should you play?

Let's calculate the expected value:

• Probability of heads: 0.5 × £200 = £100
• Probability of tails: 0.5 × (-£100) = -£50
• EV = £100 + (-£50) = +£50

The expected value is positive — £50 per flip on average. You should play this game every single time it's offered to you. Not because you'll win every flip (you won't), but because mathematics guarantees that over many repetitions, you'll average £50 profit per game.

This is the key insight: a positive expected value decision is correct even when the individual outcome is uncertain. You're not predicting what will happen; you're identifying which choice has the mathematical edge.

The insurance example reveals something crucial: expected value alone doesn't always determine the right decision. Insurance has negative EV for the buyer (that's how insurers make money), but it's still rational to buy because it eliminates the small probability of a catastrophic loss.

This is where utility theory enters the picture. A £45,000 loss hurts far more than a £45,000 gain helps. When stakes are large relative to your wealth, you should be willing to pay a premium to reduce variance — even at the cost of negative EV.

The rule of thumb: maximise EV when you can absorb the variance; buy insurance (accept negative EV) when a bad outcome could ruin you.

Consider two investment options:

Option A: Savings account — guaranteed 4% annual return, no variance.

Option B: Global equity index fund — expected return of ~8% per year, but with annual volatility of roughly ±15%.

In any given year, the index fund might return +25% or -10%. But the expected value is clear: 8% beats 4%. Over 30 years, the difference is staggering.

• £10,000 at 4% for 30 years = £32,434
• £10,000 at 8% for 30 years = £100,627

The positive-EV choice (equities) triples your outcome over three decades. The key requirement is that you can tolerate the short-term variance without being forced to sell at the bottom. This is why emergency funds exist — they let you stay in positive-EV investments during temporary downturns.

Interesting — in this hypothetical, the current job actually has slightly higher expected value. But the analysis doesn't end there. Several factors might tip the scales:

1. Option value: startup experience opens doors that a corporate role doesn't
2. Learning rate: you might gain 3 years of skill development in 1 year at a startup
3. Asymmetric information: if you know the startup's team is exceptional, your P(success) might be higher than the base rate
4. Age and risk tolerance: at 25 with no dependants, the downside is easily absorbed

The EV framework doesn't give you a mechanical answer to every life decision. What it does is force you to be explicit about your assumptions — the probabilities, the payoffs, and what you're optimising for. That clarity alone is worth the exercise.

1. Ignoring the probability side of the equation

People fixate on the size of outcomes and neglect their likelihood. A lottery jackpot of £50 million sounds life-changing, but at odds of 1 in 45 million, the EV of a £2 ticket is approximately -£0.89. The big number is irrelevant if the probability is vanishingly small.

2. Treating one-shot decisions as if they're repeated games

EV is most powerful in repeated decisions. For true one-off events (selling your house, choosing a university), you need to supplement EV with considerations about variance and irreversibility.

3. Using wrong probability estimates

Garbage in, garbage out. If you estimate a 90% chance of your business succeeding when the base rate for new businesses is 20%, your EV calculation will be wildly optimistic. Always start with base rates and adjust from there.

4. Forgetting about hidden costs and externalities

The true cost of a decision includes time, stress, opportunity cost, and impact on other areas of your life. A positive-EV side project that destroys your sleep and relationships might have negative total value.

You don't need a spreadsheet for every decision. Here's how to integrate EV thinking into everyday life:

Ask: "What are the possible outcomes, and how likely is each?" — Just framing a decision this way forces you out of gut-reaction mode and into analytical thinking.

Look for positive-EV bets you're avoiding due to loss aversion. — Many people avoid investments, career moves, or conversations because the downside feels scary, even when the expected value is clearly positive.

Seek repeatable positive-EV situations. — The power of EV is strongest in repeated games. If you can find situations where you have an edge and can play many times (networking, content creation, investing), the law of large numbers works in your favour.

Update your probabilities when new information arrives. — EV calculations are only as good as your inputs. Be willing to revise estimates as reality provides feedback.