Expected value: translating intuition into numbers

Suppose someone offers you a bet: roll a fair die. Roll a 6 and they pay you $800. Anything else, you pay $100. Take it?

Intuition says: 6:1 payout, looks good. Compute expected value:

EV = (1/6 × +800) + (5/6 × −100)
   = 133 − 83
   = +50

You average +$50 per roll. Take it.

What if a 6 pays $500 instead?

EV = (1/6 × +500) + (5/6 × −100)
   = 83 − 83
   = 0

Break-even. Intuition still feels positive — but you'd be wasting time.

The discipline of EV

Expected value isn't about turning into a calculator. It's about translating intuition into checkable numbers. Most of the time you'll find:

• Choices that look "worth a shot" have negative EV
• Choices that feel "too risky" have great EV (but irreversible loss may still rule them out)
• Two options you thought were "about the same" differ by multiples in EV

EV doesn't tell you whether to act (single-shot decisions still need to consider irreversible loss), but it tells you where intuition is lying.

A life example

Decide whether to spend $90 on flight delay insurance:

• Probability: this route's history shows ~8% chance of >3 hour delay
• Payoff: $450 reimbursement on delay

EV = (0.08 × 450) + (0.92 × −90)
   = 36 − 82.8
   = −46.8

You lose $46.80 on average per flight. Long-run, don't buy.

But what if today's flight connects to a make-or-break meeting where missing it carries massive cost? Then it's not a pure EV decision — you layer on irreversible-loss thinking, where Margin of Safety takes over.

When to use it

• Quantifiable, repeatable choices
• Investing, insurance, pricing, wagers
• Most effective when probabilities and payoffs can be reasonably estimated

When not to use it

One-shot, non-repeatable life decisions (marriage, kids) don't fit pure EV — emotion and meaning resist quantification. Extreme tail risk needs Margin of Safety on top.

Full questioning lives on Hone's framework page.