Decision Frameworks: Expected Value, Reversibility, Opportunity Cost

Good decisions and good outcomes are not the same thing

Here's the idea that reorganises how you think about choices: a decision can be good and still turn out badly, and bad and still turn out well. You can make a smart bet with the odds in your favour and lose; you can do something reckless and get lucky. Judging a decision purely by how it turned out ("it worked, so it was right") is resulting — confusing the outcome with the process — and it teaches you the wrong lessons every time.

So you can't control outcomes, but you can control the quality of your decisions, and that's a skill with actual tools. This lesson gives you three that cover most real choices: expected value (how to weigh uncertain outcomes), reversibility (how much a wrong choice will cost you), and opportunity cost (what you're really giving up). They're the frameworks the rest of the curriculum keeps pointing back to — from exam guessing (LN-03) to job offers (CR-08) to which path after school (CR-10).

What you'll have at the end

• Expected value: a number for decisions under uncertainty (and where it misleads)
• The one-way vs two-way door test that tells you how careful to be
• Opportunity cost: the hidden price tag on every yes

Expected value: weighing uncertain outcomes

When a choice has uncertain results, don't just picture the best or worst case — weigh each outcome by how likely it is. Expected value (EV) = each outcome × its probability, summed.

A game: 50% chance to win £100, 50% chance to lose £40.
EV = 0.5 × (+100) + 0.5 × (−40) = 50 − 20 = +£30
Positive EV → over many plays, you come out ahead.

This is the engine behind a lot of good decisions: take positive-EV bets, avoid negative-EV ones. It's why you never leave an exam answer blank when there's no penalty (LN-03) — a guess is positive EV. It's how insurers, investors and poker players think.

But EV has two big caveats:

• One-shot vs repeated. EV describes what happens on average over many tries. For a decision you make once, the average may never materialise — you get one draw. A positive-EV bet you make a thousand times is a good idea; the same bet once, where losing wipes you out, may not be.
• Ruin overrides EV. If a "loss" outcome is catastrophic and unrecoverable — you lose everything and can't play again — a positive expected value doesn't save you, because you won't be around for the average to arrive. Never take a bet where the downside is ruin, however good the EV. Protect the downside first, optimise second.

So: use EV to compare options, but check the shape of the downside before you trust the average.

Reversibility: one-way vs two-way doors

The second question is: if this turns out wrong, how expensive is it to undo?

• Two-way doors (reversible). You can walk back through easily — try the elective, take the job for a year, start the project. Wrong? Reverse it at low cost. Decide these fast and cheaply. Agonising over an easily-undone choice wastes the thing you're trying to protect (time), and you'll learn more by trying than by deliberating.
• One-way doors (irreversible or costly to undo). Hard or impossible to walk back — large debt, a tattoo, dropping out of something you can't re-enter, a decision that closes other doors. These deserve real deliberation, more information, more caution.

The classic error is treating them backwards: paralysed over a reversible choice, casual about an irreversible one. Match your care to the reversibility. And a strategic move: when uncertain, look for the reversible version of a big choice — a trial, a pilot, a smaller first step — so you can learn before you commit (this is why CR-10 says prefer reversible paths when you don't know your goal).

Opportunity cost: the price of every yes

Every choice has a hidden cost: the value of the best thing you didn't do instead. Saying yes to one thing is saying no to whatever else that time, money or attention could have gone to — and that forgone alternative is the true cost, not the zero it feels like.

• "Free" is rarely free. A "free" three hours doing X costs you the best other use of those three hours. Spending on A is not spending on B.
• It reframes decisions. "Should I do this?" is the wrong question; "is this the best use of this time/money, versus my alternatives?" is the right one. A decent option can be a bad choice if a much better one was available for the same cost.
• It exposes sunk cost's twin. DT-07's sunk-cost fallacy says ignore what's already spent; opportunity cost says do account for what you're giving up going forward. Together: decide by the future alternatives, not the past spending.

Putting them together

For a real decision, run all three:

THE DECISION: .................................................
EXPECTED VALUE — outcomes × probabilities; and is any downside
   catastrophic/unrecoverable? ................................
REVERSIBILITY — two-way (decide fast) or one-way (deliberate)? .
OPPORTUNITY COST — what's the best thing I'd give up? Is this
   the best use of the resource? ..............................
→ DECISION (and why it's defensible regardless of how it lands):

Notice the output is a defensible decision, not a guaranteed-good outcome — because those are different things, which is where we started. And a final humility check: know when to stop analysing. For small or reversible choices, "good enough" fast beats "perfect" slow (satisfice, don't maximise); reserve the deep analysis for the one-way doors.

What this means for you

• Judge decisions by process, not outcome — good decisions can lose; don't learn from luck (resulting).
• Expected value weighs outcomes by probability — but beware one-shot bets, and never risk ruin however good the EV.
• Match care to reversibility: decide two-way doors fast, deliberate on one-way doors — and seek the reversible version when unsure.
• Opportunity cost: every yes is a no to the best alternative. Ask "best use of this resource?", not "should I?"
• Satisfice small/reversible choices; reserve deep analysis for the irreversible ones.

Exercise (35 min, verifiable output)

1. Take one real decision you're facing (or recently made).
2. Expected value: list the outcomes and rough probabilities; compute or reason the EV — and check whether any downside is unrecoverable.
3. Reversibility: is it a one-way or two-way door? Does your level of agonising match?
4. Opportunity cost: name the best alternative use of the same time/money — is this genuinely better?
5. Decide, and write one sentence on why the decision is sound regardless of how it turns out.

✅ Finish check: one real decision run through EV (with the downside checked), reversibility, and opportunity cost, ending in a choice you can defend on process, not outcome.

Summary card

• Decision quality ≠ outcome. Judge the process; don't learn from luck (resulting).
• Expected value = Σ(outcome × probability). Great for repeated bets; watch one-shot draws; never risk ruin whatever the EV.
• Reversibility: two-way doors → decide fast; one-way doors → deliberate. Seek the reversible version when unsure.
• Opportunity cost: every yes = a no to the best alternative; ask "best use of this?", not "should I?"
• Satisfice the small/reversible; deep-analyse only the irreversible.

Sources

1. Duke, A. — Thinking in Bets, 2018
2. Kahneman, D. — Thinking, Fast and Slow, 2011
3. Bezos, J. — One-Way vs Two-Way Doors (shareholder letters)

Next lesson: DT-11 — Fermi Estimation: Producing a Number When You Have No Data (L3) Related: DT-07 Ten Cognitive Biases · CR-10 University, Trade, or Building · CR-08 Evaluating a Job Offer · LN-03 Exam Strategy Path: related — the how-to-decide toolkit