Insurance is a tax on fear

[JohnnyDoe]

Insurance only makes consistent sense for one party: the insurer. This is simple math. When you purchase coverage for minor to moderate risks, you're essentially handing your money to a professional gambler to place a bet you should be making yourself. The house always wins because the rules are engineered that way.

Why insurance doesn't make sense​

Let:

• p = probability of the loss
• L = size of the loss if it happens
• P = premium you pay
  

For an insurer to stay in business, your premium must cover more than the expected loss:

P = p·L + expenses + commissions + fraud leakage + reinsurance margin + profit + cost of capital

That extra amount on top of the pure risk is called the "load." Since load is always positive, your expected value (EV) on the bet is always negative:

Your EV = p·L − P = −load < 0

If you buy ten negative-EV bets a year, you don’t have peace of mind, but a slow leak in your wealth.

How to price uncertainty​

The theoretical argument for insurance is trading expected value for reduced volatility: you pay to avoid a nasty surprise. The rational way to price this is with expected utility theory. If we model your psychology as being roughly logarithmic with wealth, the maximum rational premium you'd pay above the expected loss is approximately:

Risk premium ≈ ½ · p · L² / W

where W is your current wealth. Translation: if a potential loss is a small fraction of your wealth, the amount you should rationally pay to offload the worry is practically negligible.

Example 1: medium loss​

• Wealth W = $1,000,000
• Loss L = $50,000
• Probability p = 1%

Expected loss = p·L = €500
Risk premium ≈ ½·0.01·(50,000²)/1,000,000 = $12.5
Fair premium to you = $512.5

Try to find a policy with a $512.5 premium on that risk. You won’t. You’ll see $700, $900, whatever. Negative EV to you, positive to them. Game over.

Example 2: truly catastrophic​

• W = $1,000,000
• L = $500,000
• p = 0.5%

Expected loss = $2,500
Risk premium ≈ ½·0.005·(500,000²)/1,000,000 = $625
Fair premium ≈ $3,125

Now if a real premium is near $3,100–$3,400, it may actually make sense. Big, rare, ruin-adjacent losses are the only place insurance earns its keep.

Why the house always wins​

1. The machinery is expensive. You're paying for skyscrapers, claims adjusters, sales commissions, and legal teams. It's a bulky business model.
2. Float belongs to them. You prepay premiums; they invest that cash pile (the "float"). Even if they break even on underwriting, the investment returns are pure profit for them, not you.
3. Adverse selection + moral hazard exist. Insurers price for the worst-case customer—the one who is accident-prone or outright fraudulent. Your honest habits subsidize their claims.
4. The fine lines. Deductibles, exclusions, sub-limits, waiting periods, “wear and tear,” “pre-existing,” “acts of [Insert Deity].” Your upside is capped; your downside is the premium, every year, forever.​

The industry sells fear. Humans are notoriously bad at judging small probabilities, instinctively overestimating the likelihood of vivid, rare events. Insurers package that cognitive bias into a product and sell it back to you with a bow on it.

Common traps with real numbers​

• Extended warranties
  Phone repair L = $200, p = 10% ⇒ EV $20. Warranty sold at $89. You’re burning ~$69 on average to avoid a $200 annoyance you could self-fund.
• Rental car CDW
  Five days at $20/day = $100. Suppose p = 1% to ding it badly, L = $1,000 ⇒ EV $10. You’re paying $90 for the privilege of feeling brave.
• Flight/luggage insurance
  Low-severity, high-friction claims with sub-limits. Same story: EV tiny, load large.
• Gadget theft insurance
  Deductibles and depreciation gut payouts. The check you imagine is not the check you get.
  

The Golden Rule (The Kelly Criterion)​

The optimal strategy is to only insure against losses that would be genuinely catastrophic: something that could wipe you out or force you to liquidate valuable assets at fire-sale prices. For everything else, self-insure. The Kelly principle, a foundational concept for rational bettors, is clear: avoid any recurring, negative-expectation bet that grinds down your long-term compounding power.

When insurance makes sense​

• Catastrophic tail risks relative to your wealth: medical catastrophe, liability that can destroy your net worth, your house burning down if replacing it would cripple you.
• Third-party liability where courts can assign ruinous damages.
• Legally mandated coverage. You don’t argue with cops on the roadside about expected utility.
• Subsidized group plans where load is unusually low or cross-subsidized. Rare, but they exist.
  

In all other cases, raise deductibles to the legal max and keep the premium savings.

How to decide​

Buy the policy only if:

P − p·L ≤ ½ · p · L² / W

If not, pass. For most small and medium risks, the right side is a rounding error and the left side is a fat load. Decline.

Examples​

• Self-insure the small stuff. Build a cash buffer and treat minor losses as operating expenses of life.
• Max out deductibles. Same coverage for catastrophe, less money lit on fire.
• Read sub-limits. If the $1,000 “limit per item” makes the policy irrelevant, don’t buy it.
• Don’t insure consumables. Phones, laptops, luggage, appliances. If you can replace it without selling a kidney, you don’t insure it.
• Insure liability intelligently. The thing that bankrupts you isn’t your cracked screen, it’s the lawsuit. Allocate premium there, not on trinkets.
  

Summing up, insurance, on average, is a negative-sum game for the buyer and a positive-sum business for the seller. Use it surgically for ruin-level risks and mandated liability. For the rest, keep your money.