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April 02, 2012 9:01 AM Why a Mega Millions Ticket is a Good Investment

By Joshua Tucker

Having already been critiqued for my economics acumen by Andrew Gelman earlier, I figured I might as well wander even deeper into the lion’s den by trying my hand at probability theory. Someone correct me if I’m wrong, but despite the flurry of articles about how buying a lottery ticket is inherently irrational, at this point isn’t a lottery ticket a good investment?*

As I understand it, the expected payoff from a lottery ticket is simply the probability that you win times the value of jackpot. According to CNN, the chances of winning the lottery are 1 in 175 million, and the jackpot is $640 million. Let’s even posit that you lose half of the present value of the jackpot to taxes and the fact that you probably don’t actually get all of the money now, we’re still looking at a 1 in 175 million chance of winning $320 million dollars. By my calculation, that means the expected value of a lottery ticket is $1.83. Since a lottery ticket only costs $1, that would suggest that on this particular day, a Mega Millions lottery ticket is a good investment.

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* Note that I’m assuming that you only care about the financial payout from the lottery ticket. Apparently winning the lottery can also ruin your life. Or not.

[Photo credit: ABC News]

[Cross-posted at The Monkey Cage]

Joshua Tucker is a Professor of Politics at New York University.
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Comments

  • Don Hosek on April 02, 2012 3:45 PM:

    The problem here is that as the prize gets higher, the probability of multiple winners also increases, giving you a lower expected value of a lottery ticket. It would only take two winners splitting the pot to bring your expected value in the above scenario below a buck (as it turned out there were three).

  • horn on April 02, 2012 4:52 PM:

    Any number of intelligent people have run the numbers, your odds of winning solo are slightly less than 20%, so it being 'a good bet' is not remotely correct.