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Tag: expected value

  • Powerball isn’t a sucker bet?!

    Powerball isn’t a sucker bet?!

    Shocking! A colossal expected Powerball payout means more people are buying tickets. More tickets being sold means the expected payout is getting even more humongous. So much more gargantuan that it’s worth redoing the expected value calculations I did a few days ago.1Because I didn’t repeat myself in this post, you might want to go read the earlier post to see what I had to say.

    Well, that’s interesting! Looks like the expected value now matches the “investment.”

    Of course, there are a couple more factors to consider when determining the true value of such a large winning:

    1. According to the law of diminishing marginal utility, we might need to discount the expected value by some unknown amount to get a “true” expected value; and
    2. Any substantial winning can free up time that would otherwise be spent working. In effect, such a large winning would “buy time.”

    There’s more on both of these topics in the comments section of a post I wrote about an earlier Powerball drawing.

    Just remember, you’re more likely to be struck while lightning, while drowning than to win Powerball.

    I’m off to buy my ticket…2IMHO, there’s no reason to buy more than one. The first ticket makes winning (barely) possible and increases your odds of winning by an infinite factor (though increasing it by a nearly zero offset). The second ticket only doubles your chances. You’ll have to decide for yourself whether the entertainment value of entering is increased by buying more tickets — if you do, don’t forget the law of diminishing marginal utility. ;-)

    • 1
      Because I didn’t repeat myself in this post, you might want to go read the earlier post to see what I had to say.
    • 2
      IMHO, there’s no reason to buy more than one. The first ticket makes winning (barely) possible and increases your odds of winning by an infinite factor (though increasing it by a nearly zero offset). The second ticket only doubles your chances. You’ll have to decide for yourself whether the entertainment value of entering is increased by buying more tickets — if you do, don’t forget the law of diminishing marginal utility.

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  • Powerball is *still* a sucker bet

    Powerball is *still* a sucker bet

    Update. I have another post on tonight’s Powerball drawing with updated calculations. It just might surprise you.

    With the next Powerball estimated jackpot at 1.3 billion dollars, I decided to figure out whether it was worth buying a ticket. I did this calculation a few years back, but since then Powerball has changed the odds1That’s right — they made it harder to win. in an attempt to get bigger jackpots. Looks like it’s worked.

    Some notes:

    1. The jackpot is not $1.3 billion unless you choose to get the payout of 30 payments over 29 years. Otherwise, the estimated immediate cash payout is “only” $806 million.
    2. If you don’t consider taxes, it’s a good bet to buy a Powerball ticket for this drawing. After all, an expected value of $3.08 is greater than the $2.00 “investment.”2It’s hard for me to call a lottery purchase an investment. So, scare quotes. ;-)
    3. Taxes are not insignificant. The top federal tax bracket is 39.6%.3Should you be lucky enough to win, it will be important to note that the lottery will withhold only 25% for your federal taxes. I guess the IRS expects you to be smart enough to not spend the other 14.6% before the taxes are due. Don’t make them wrong. The top Oregon bracket is 9.9%.4Unless you’re also in Oregon, your state income taxes are likely lower.
    4. I oversimplified the tax calculations, applying the top appropriate bracket over the entire amount for each line, instead of doing multiple calculations. I think this could only possibly be significant for the second line, maybe resulting in an error in the expected value of a penny or two. So, not significant.
    5. I don’t attempt to account for multiple winners. I don’t have enough data.5I guess one benefit of the lottery making it harder to win is that it has also decreased the odds of simultaneous winners. There is something you can do to decrease the odds of sharing a winning ticket with someone else — stop using your favorite numbers, especially if they are based on calendar dates. You’re only using a subset of the available numbers and so is everyone else doing what you’re doing. Let the computer choose random numbers for you with a quick pick.

    So, is “sucker bet” fair? Wikipedia defines a sucker bet as “A sucker bet is a gambling wager in which the expected return is significantly lower than the wager(s).” I guess it’s up to you whether $1.77 is significantly less than $2.00.

    See you in the Powerball line. ;-)

    • 1
      That’s right — they made it harder to win.
    • 2
      It’s hard for me to call a lottery purchase an investment. So, scare quotes. ;-)
    • 3
      Should you be lucky enough to win, it will be important to note that the lottery will withhold only 25% for your federal taxes. I guess the IRS expects you to be smart enough to not spend the other 14.6% before the taxes are due. Don’t make them wrong.
    • 4
      Unless you’re also in Oregon, your state income taxes are likely lower.
    • 5
      I guess one benefit of the lottery making it harder to win is that it has also decreased the odds of simultaneous winners. There is something you can do to decrease the odds of sharing a winning ticket with someone else — stop using your favorite numbers, especially if they are based on calendar dates. You’re only using a subset of the available numbers and so is everyone else doing what you’re doing. Let the computer choose random numbers for you with a quick pick.

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  • 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…

    • 1
      Cash value is actually “only” $360.2 million. But still — $550 million. That’s more than half a billion dollars!!
    • 2
      The 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.
    • 3
      The odds of paying taxes on this are virtually 100%. Knowing how to avoid them is above my pay grade.
    • 4
      After all, if you want to get struck by lightning, you should be out standing in a field.

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