Powerball is a Sucker’s Bet

Update. I have a more recent post calculating the expected value for the January 13, 2016 Powerball drawing.

Today, a lot of people are buying Powerball tickets for the first time. After all, the estimated jackpot is $550 million!1Cash value is actually “only” $360.2 million. But still — $550 million. That’s more than half a billion dollars!! But is their “investment” a smart bet?

After reviewing the Powerball odds and prizes page, it might seem so. Using the estimated jackpot, the expected value for a $2 ticket is $2.42.

Unfortunately, this calculation ignores the possibility of multiple winners having to split the jackpot.2The probability of multiple winners is not zero, especially when millions of tickets are being bought. You can improve your odds of avoiding duplication by going for the quick pick. These are more random than choosing “personal numbers,” which are likely to be limited to numbers 31 and lower. It also ignores taxes.3The odds of paying taxes on this are virtually 100%. Knowing how to avoid them is above my pay grade.

So buy a ticket if you want an infinitesimal chance at winning.4After all, if you want to get struck by lightning, you should be out standing in a field. But don’t waste your time buying two. After all, although the first ticket increases your odds an infinite percentage from zero, the second ticket merely doubles your odds.

Good luck! You’ll need it…

By Brent Logan

Engineer. Lawyer. WordPress geek. Longboarder. Blood donor. Photographer. More about Brent.


  1. For me, the biggest item that swing the value proposition away from Powerball is that comparing the two bucks you spend on the ticket is not equivalent to the potential millions if you do win. Studies have been done on the utility value of money in large and small amounts showing that the utility diminishes at a double exponential rate. So instead of a $2.42 value, you might be looking at more like a $.02 value for you $2 ticket.. or even less. This effect dwarfs taxes and odds.

  2. Art, the diminishing utility of money is an interesting concept. After some thought, it seems to make sense. Once you have spent enough on an object that it functions satisfactorily, spending additional money has diminishing returns. For example, a Honda Accord provides good transportation and maybe even better than that. Spending twice as much for another car is not likely to result in a car that is twice as good. Certainly, spending four times as much will not result in a car four times as good. Similarly, buying two cars instead of one car doesn’t double the value because I can only use one at a time.

    Even items that I can’t currently afford at any level of function (for example, a sailboat with a cabin) would offer limited utility assuming I have no additional time to enjoy them.

    And maybe that’s where the diminishing return issue breaks down: having sufficient money invested wisely could make it so I would not have to work another day in my life. It is hard to place value on gaining 40 extra hours of life each week. it would be interesting to try. ;-)

    Or, maybe removing the risk from life removes some of its enjoyment. What do you think?

  3. I love the idea of diminishing marginal utility but I find it really tricky to apply in any useful way, and I have to squint when I see it modeled. Right up there with the assumption that people tend to act in their own self-interest. Umm.. yeah, right. :-)

    When you buy a Honda Accord you aren’t really buying just the ability to travel from A to B. There are much cheaper ways to get places (bike, bus, get a friend with a car, walk, etc.). I think you’re buying convenience and time and status (or at least a social marker), at the very least. And if you add a capability dimension (do you need transportation for auto racing or getting groceries or attending a movie premiere or off-roading?) then you’re starting to get some context on what “utility” might mean to people. Yes, there is arguably un-diminished “utility” you can only get with 169+ cars (Jay Leno) that has very little to do with running errands.

    My favorite thing about lotteries — addressing your lovely “never have to work again” riff — is how quickly most of the winners go broke.. ha! Building the mental habits to grow or protect money is a lot of effort. It’s a skill that most people of average means don’t have.

    And even money “invested wisely” can disappear — do you really want any feelings of security in your life based on money? Good luck with that. I’ve met a few dragons who live on piles of money and I’m not sure there’s a very strong correlation between lots of money and security.

    Particularly lottery money!

  4. Yes, isn’t it fun contemplating winning this thing. A lot more fun than contemplating getting hit by lightning while drowning.

    I think the real value of the concept of diminishing marginal utility is know that it exists. Even without knowing the true extend of the diminishment, it does let you know that maybe you should discount the expected value downward somewhat.

    I heard a piece on NPR about a guy who tracked down lottery winners. Virtually all went broke in short order, yet most (as I remember it) said they didn’t regret the experience. It would be interesting to try to find that again.

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