Ergodicity and Insurance: Why 'Bad Bets' Make Sense

Insurance is a "bad bet" by expected value standards. On average, you pay more in premiums than you receive in claims: that's how insurance companies make money.

So why do rational people buy insurance? The answer is Ergodicity.

The expected value argument against insurance

Let's say your house has a 1% annual chance of burning down, causing $300,000 in losses. Insurance costs $4,000 per year.

Expected value of self-insuring:

0.99 × $0 + 0.01 × (-$300,000) = -$3,000 per year

Expected value of buying insurance:

-$4,000 per year (the premium)

By expected value logic, you should self-insure and save $1,000 per year. But almost everyone buys insurance anyway. Are they all irrational?

Why insurance makes sense: the ergodicity perspective

The expected value calculation assumes you can "average out" the outcomes over many parallel lives. But you only live one life.

Consider what happens if you self-insure and your house burns down:

• You lose $300,000
• If you don't have $300,000 in savings, you lose your home
• Losing your home may mean losing your job, etc.

The expected value calculation treats a $300,000 loss as 1/100th of a problem since it only happens 1% of the time. But if it happens to you, it's 100% of your problem, and it may be unrecoverable.

You can only use expected value considerations for decisions whose worst case you can easily absorb, not for decisions with a risk of game over.ShareCopy

The insurer has deeper pockets than you, and for them, a house burning is not an irreversible condition, so they can price the insurance premium near expected value (plus fees), while for you it's rational to buy at a bit more than that. This is well described in Ole Peters and Alexander Adamou's seminal paper, Ergodicity Economics.

Insurance as an ergodicity strategy

Insurance converts a non-ergodic situation (rare but catastrophic losses) into an ergodic one (small, predictable costs).ShareCopy

Without insurance:

• Most years: $0 cost
• Rare year: -$300,000 (possibly game over)

With insurance:

• Every year: -$4,000 (survivable)
• Rare year: -$4,000 (still survivable)

The insurance company can afford to take on your risk because they do experience ensemble averages: they have millions of policyholders, so their outcomes converge to the expected value. You don't have millions of lives to average across.

When insurance doesn't make sense

Ergodicity also tells us when to skip insurance:

Consider skipping insurance when:

• The loss is easily recoverable (extended warranties on cheap electronics)
• You have enough reserves to self-insure (wealthy individuals with diversified assets)
• The insurance is priced far above fair value

Buy insurance when:

• The loss would be catastrophic or irreversible
• You can't self-insure the full amount
• The premium is reasonably priced

The deeper principle

Insurance isn't about expected value; it's about staying in the game. Paying $4,000 per year is the price of ensuring that a rare event can't knock you out permanently, and that you can maintain a trajectory of growth in life and business.

This same logic applies beyond insurance:

• Emergency funds: "Dead money" earning low returns, but preventing catastrophic decisions during crises
• Diversification: Lower expected returns, but higher probability of surviving market crashes
• Conservative career choices: Lower expected earnings, but protection against career-ending risks

Learn more

• Ergodicity vs Expected Value - why maximizing expected value fails
• Ergodicity in Investing - applying the same logic to portfolios
• Ergodicity Economics - the academic foundations
• My book on Ergodicity - practical frameworks for any domain

The key insight: insurance buyers aren't "irrational;" they're correctly optimizing for time averages in a non-ergodic world. The small guaranteed loss of premiums is better than the small chance of an unrecoverable catastrophe.ShareCopy