Economics of Insurance, Part 3

To wrap this all up, think about this gamble.

Flip a coin. If it's heads, you win $10, if it's tails, you lose $10.

You may only play once, and you must either play the game or pay someone $1 and they will play the game for you, taking your winnings and eating your losses.

Mathematically, your expected return is better if you play. You have a 50% chance of gaining $10, and a 50% chance of losing $10. It's break-even.

If you opt to pay the dollar, overall you have a 50% chance of winning $9, and a 50% chance of losing $11. Now it's no longer break-even; you're at a $1 disadvantage.

Only a fool would pay that dollar, right?

Let's keep the same game but scale the numbers a bit. If you win, you make $1,000,000. If you lose, you lose $1,000,000. Or, you can pay $100 to get out of playing. You are not a rich person and losing $1,000,000 would ensure you'd be poor for the rest of your life.

Now, your expected return is still break-even if you play, so what do you do?

I think in this case more people would opt-out of the game, because the potential for a life-ruining outcome is now 50% instead of none. Most people probably would not take that gamble.

Let's examine the company that takes the $100. Let's assume that a large number of people play this game. On average, the company makes $100 per game. Since the game is fair, they pay out in losses just as much as they win in winnings, so they break even there, since they are able to play the game many times. The more they play, the less risky the game is for them, and they still make a $100 profit each time.

This illustrates the value that insurance companies create. Even in a completely fair, break-even situation, the stakes might be so high that a reasonable person would like to bow out completely, and would even pay money to do so.

And that's why you would want to buy insurance.