Why people love buying Lotto and hate buying Insurance:

I am regularly reminded how people view value in our society when I see the manic behavior of those when purchasing Powerball tickets.   This phenomenon always has me asking the question, why people love buying lotto and hate buying insurance?  Both are purchases involving probablities and risk analysis but one has a higher expected value and higher utility value (Insurance) and one has a low expected value and low utility value (lottery). Most people don’t understand how to calculate expected value.

People are much more willing to trade a dollar with such a low expected value for lottery tickets in the hope that they win big vs. trade a dollar with a decent expected value for insurance protection.

The use of money for speculation or for a gain should be based on some expectation of a return or expect value of each investment/speculation.

The dislike or hate of insurance is truly misplaced by society.  This purchase provides more value than the lottery system but gets less credit.

Odds of Powerball:

Most people know the odds of winning the lottery are low, but they still buy a ticket for “fear of missing out”, “gotta be in it to win it”, “I like thinking about what I would do if I won”. and a variety of other qualitative reasons.

These are the odds of winning Powerball.

Numbers Matched Odds of Winning
5 + Powerball 1 in 292,201,338.00
5 1 in 11,688,053.52
4 + Powerball 1 in 913,129.18
4 1 in 36,525.17
3 + Powerball 1 in 14,494.11
3 1 in 579.76
2 + Powerball 1 in 701.33
1 + Powerball 1 in 91.98
Powerball only 1 in 38.32

Odds of needing Insurance:

Most people don’t like to think about or underestimate the probability of something bad happening.

This probability varies per product, person, location, asset, use, and a number of other factors, but do you think you have a higher probability than 1 in 38.32 years of needing auto insurance or filing an auto claim?  If so, how does it compare in value to you than Powerball?

  • How often have you been in auto accidents thus far (1 in x years)?  What’s the chance your house burns down or is robbed?
  • Each coverage or peril could be determined based upon the expected loss and a probability assigned to your specific risks/behaviors/assets?
  • Will the loss be more than you paid for insurance?
  • Can you calculate the Expected value of every insurance transaction?
  • Have you trained your mind to think in this way around risk?

Understanding utility value and Expected value (EV)

If you look at the expected value (EV) of a lottery ticket from the economist point of view the $1/$2 for the ticket is typically worth very little in expected value (EV) or return, it depends on the prize value but even the >$500m Powerball jackpots still have an EV less than $1.

The jackpot has to get upwards of $1B for the Expected value to get close to the $1/$2 you spent on the ticket.  Then contemplate the chance that you might have to split a jackpot with someone with the same winning ticket.  The EV is very low on Powerball.

Yes, the difference between Expected value and price of the ticket is partially the utility value or in this example the “Fun” associated with thoughts of winning or dreaming of what you would do with a large sum of money, how you would quit your job, etc…

But the piece remaining is the poor return/choice in economic value associated with buying a lottery ticket.

Why isn’t the Utility Value of Insurance recognizable?

I think people confuse or assume the utility value of insurance as the actual payment of a claim, however, the utility value of insurance is the promise to pay whether you have a claim or not.  The peace of mind provided by owning the insurance is the true utility value.  It lasts all year and has a much greater impact than the Powerball Utility value.

It is obviously less sexy or desirable to dream about being repaid for a loss as it is pulling a Jerry McGuire moment and quitting your job, but the utility value of being protected by insurance is and needs to be highlighted.


I hope to be there for my audience to help them better see and understand Expected value in every purchase, personal or business decision.  Also to help with identifying risk vs. Hazards which many people can confuse.   Having a probabilistic way of thinking when it comes to risk is the only way to be a true Shark.

Any future contributors whether brokers/agents/thought leaders are encouraged to include risk and expected value in their contributions so the audience can think about risk like an expert.

Related Articles:

About the author

Arnold Smith

Leave a Comment