The Lottery-Insurance Paradox

Why would a rational person purchase insurance yet also play the lottery?

It’s a question that has puzzled Economists (and fake Economists, like 2/3 of the staff at DQYDJ) for a long time.  Think about it, a lottery is the exact opposite of insurance.  When it comes to insurance, a person purchases coverage to hedge against risks.  In a lottery, sums are spent for a long-shot chance at the ‘risk’ of a payoff.  People are risk-seeking when it comes to playing the lottery yet risk-averse when it comes to purchasing insurance.  What gives?

A Primer on Insurance

1995 Saab 900s

My Old Saab 900s... Only Had Cheap Insurance on It!

There are all sorts of types of insurance – auto, home, life, health, death, even body-part insurance (among a universe of many more).  In exchange for a recurring or one-time fee, the holder of a policy hedges against some event occurring – say, in the case of body-part insurance, damage to a limb.  If that event occurs, the issuer of the insurance policy will pay out according to the details of the policy – perhaps a lump sum in the case of life insurance, or the cost to repair damage to a vehicle in car insurance.  In the insurer – insured relationship, the insured reduces risk by buying the policy while the insurer spreads risk by issuing many policies, collecting premiums or lump sum payments in excess of the cost of a negative event, and investing any money collected in the meantime before events demanding payout occur.

To explain why a risk-seeking person might acquire insurance, it’s best to keep a few things in mind.  First, some forms of insurance are provided with a job, commonly health and life insurance.  Other forms of insurance are required – for example, home insurance is mandated when a bank issues a mortgage, and car insurance is mandated when a person chooses to purchase (well, and operate…) a car.

All of that doesn’t quite get to the heart of the issue – take car insurance, for example.  Car insurance laws come with mandated minimums which a policy has to meet to be considered allowable.  In many cases, one can just purchase cheap car insurance and set coverages to the lowest allowable.  In some states, a person could even self-insure with sufficient reserves.  However, in many cases even people with risk-seeking personalities will get more insurance than is mandated.

Winning the Lottery

The lottery (and gambling in general) is the opposite.  The ‘risk’ event is actually a benefit to the holder of a fractional claim on the prize.

In a lottery, a claim holder pays an agreed upon amount for a fractional share of a prize.  The lottery itself generally has some defined payout which goes to a certain number of people at the end of the lottery.  The gambler purchases a ticket or some other claim, and the lottery makes money by setting the total payout of the lottery to less than is collected in claims and administrative and advertising costs.  It’s a big business – in many cases governments will actually run lotteries.

An Economic Conundrum!

See the problem?  Lottery playing and gambling is inherently risk seeking.  The games guarantee that you pay something into the system, while placing risk on the holder of the lottery and transferring risk to you.  On the other side of the coin, insurance guarantees you pay some amount for a policy but it will transfer your risk to the policy writer.  How can we rectify a rational actor both participating in a lottery and buying insurance?

Here’s the funny thing – I was hoping you readers would toss out some ideas.  Our friend (the Nobel Prize Winning) Daniel Kahneman and his colleague Amos Tversky even developed Prospect Theory in part because of the conundrum.  Recent studies point to a genetic connection, which even suggests that one gene can make folks tend towards more lottery playing (and less insurance buying) or the opposite.

If it’s enough to get the Nobel committee to toss out Nobels, it’s enough for us to discuss here!  Here are some questions for you to think about:

  • Why do gamblers buy insurance?
  • Do you think that people are, in general, over or under insured?
  • How do you think moral hazard affects the behavior of insurance purchasers, especially the risk-seeking variety?


        • says

          Well, considering the cost of replacement in that car was pretty cheap, I knew the risk that I was getting into. On the other hand, perhaps there was a bit of moral hazard involved? Would have I gotten into a stupid accident if I didn’t have the insurance coverage I did?

          I probably would have driven it for another year, at least, haha.

  1. Anonymous says

    I don’t consider myself a gambler, but I do play the lottery every once in a while.  Generally when we play it’s in lieu of going to the movies or something else that would cost more than $1-2.  We find a few hours of entertainment in daydreaming about what we would do if we won, and I’m generally more satisfied with that than a movie. 

    I’m probably over insured.  I haven’t revisited the idea of how much coverage I should have in a couple of years, but when I was shopping around before renewing my policy recently I found that if I went with any other company I would have no way of being able to afford it.  I’ll probably have to look into what my car is worth and what deductibles I can afford the next time my policy comes up for renewal.

    • says

      I play a decent amount of lottery tickets around the holiday time… they make pretty good gifts because even if they’re cheap you’re “giving the fantasy”, like you said. Even though the odds are low anyone will hit anything noteworthy, at least it’s a gift you know will be used!

      There’s another car insurance mandate – some (most?) loans will mandate certain coverages with collision and comprehensive, with something like a $1,000 maximum deductible. If you own your car outright you can do whatever you want, but it is a good idea to check on the value of your car.

  2. says

    Where I am the government runs the casinos,so it works out: Pensioners come in and play, the government collects, pays out the pensions again, and all are happy. 😉

    • says

      Yeah, and it always makes me feel a bit dirty to see the government run lotteries – so the government runs commercials to entice people to buy claims on a prize which are less than the fraction they pay into the prize, ostensibly to put back into the community.

      I don’t know, it just feels wrong, haha. I suppose people do know that they aren’t getting out exactly what they put in, so it’s not blind, but it still seems shady to me.

  3. Andy Hough says

    When you play the lottery you control how much money you put at risk and can keep the amount really small.  When you buy insurance you are also controlling how much money you have at risk.  That’s my theory for how a person can participate in both behaviors.

    • says

      True – to a certain degree, you can control the cost of your insurance. I’m thinking of car insurance: play with your limits, play with your deductible and coverage, even switch to a separate company. Still, just buying insurance in some cases seems to go against the risk-seeking behavior.

  4. says

    Gambling is a indirect tax on the stupid (or irrational).

    That governments are involved in one way or another, either through direct sponsorship or the scam that is school funding, makes gambling that much more repulsive.

    I’m not against it, mind you.  Adults can do what they wish with their money, including pissing it way.  Just quit it with the hypocritical it’s-for-the-children angle.

    Hmmm, how to approach this from a libertarian/paternalistic emperor-for-a-month perspective? I’m going to have to think on it.

    • says

      Maybe you could have people pay a tax based upon IQ in your emperor fantasy? Easier than the lottery… but the natives might get restless. At least the promise of a prize means most people won’t complain!

  5. says

    I am really curious as to the one-third that is not a fake economist…lol

    Seriously, though I am not sure why the connection isn’t there for you – I am putting $X at risk with $Y premium and on the flip slide I am putting $x at risk for the small possible $Y lottery payment 

    • says

      Haha, Cameron hasn’t written anything since complaining about paying off student loans too early back in October. You’ve been stuck with Bryan and me since then. I’ll see what I can do about him; he claimed he had a few drafts ready but I have nothing in my inbox now.

      Maybe you’re right – but I do love analyzing ridiculously minute details to death and perhaps a little beyond… plus, I figured if a Psychologist could win an Economics Nobel for it, a Computer Engineer could muse about it publicly, heh. Here’s the original article if you’re interested.

  6. says

    Lottery playing is genetic?!  That makes sense, as the apple doesn’t fall far from the tree.  Think about it, who do you see buying lottery tickets most often at the convenience store?  It’s the poor people.  Generally, poor people breed poor people and rich people breed rich people.  Poor people risk more than they can afford with the hope of hitting the jackpot.  Rich people divert risk by purchasing insurance.

    • says

      Haha, nature versus nurture and nature wins on the scratch tickets?

      On the ‘rich vs. poor’ aspect, I’d prefer not to enter the fray but I’ll give you an example of the rich playing the lottery. Of course, perhaps it wasn’t ‘playing’, so much as dumb luck on a whim.

  7. says

    I feel that the majority of people are under-insured as opposed to over insured. Even at the wealth management firm that I work at, we only deal with high net worth clients ($2m+) and many of them are under-insured.

    I’d like to see a break down of how many of those with minimum insurance coverage play the lottery regularly. I think that the numbers are skewed because many states require insurance coverage for auto’s. Without the requirement, I venture that many more people would not have insurance (and those are the same ones that play the lottery.)

    • says

      You know, I will try to pull that one off. It’ll be almost impossible to give an exact participation rate, but we can figure out which income bracket gambles the most by looking at tax returns (which will show winnings over a certain amount.) Thanks to the IRS it’s doable…

      Give me a little while to put it together; thanks for the idea!

    • says

      Jon, looked into it a bit and I think you were right. There isn’t much hard data on insurance and gambling, and I couldn’t find a good way to do it with the CPS data on IPUMS-CPS. However, I found some good articles which seem to imply that gamblers are under-insured:

      California Research Bureau
      Adjunctive Desk Reference @

      I know – interesting, but it doesn’t seem real until someone puts data to it. This site doesn’t have the budget to commission a survey, heh… so we’re probably out of luck on this one!