Sunday, January 10, 2016

No Powerball Winners, Jackpot Grows to Estimated $1.3 Billion; Does It Makes Sense to Play?

By Robert Wenzel

There were no winners in Saturday night's record $949.8 million Powerball drawing, the next jackpot could reach an estimated $1.3 billion, lottery officials say.

Powerball is played in 44 States, Washington D.C., Puerto Rico, and the US Virgin Islands.




Alex Tabarrok did the math when the Powerball Jackpot was estimated to be$800 million:
Today’s Powerball lottery offers a prize of $800 million. Is the prize high enough to make it worth playing for an economist? In other words, is the prize high enough to be a net gain in expected value terms? Almost!

The odds of winning are 1 in 292.2 million. So the expected value of a ticket is $800*1/292.2=$2.73. A ticket only costs $2 so that’s a positive expected value purchase! We do have to make a few adjustments, however. The $800 million is paid out over 30 years while the $2 is paid out today. The instant payout is about $496 million so that makes the expected value 496*1/292.2=$1.70. We also have to adjust for the possibility that more than one person wins the prize. If you play variants of your birthday or “lucky” numbers that’s a strong possibility. If you let the computer choose your chances are better but with so many people playing it wouldn’t be surprising if two people had the same number–I give it at least 25%. So that knocks your winnings down to $372 million in expectation.

Finally the government will take at least 40% of your winnings, leaving you with $223 million in expectation. At a net $223 million the expected value of a $2 ticket is about 75 cents. Thus, a Powerball ticket doesn’t have positive net expected value but the net price of $1.25 is significantly less than the sticker price of $2. $1.25 is not much but to get your money’s worth buy early to extend the pleasure of anticipation.

At $1.3 billion, here are the new numbers, if there is only one winner:

The expected value is  $4.54

The instant payout is: $2.83

Adjusting for the possibility of two winners and taxes the payout is: $2.08

So we now have an expected net positive value outcome.

That said, the odds are so slim, it doesn't make sense to put any serious money into Powerball lottery tickets because you won't be able to "ride out the string". That is, it would take 292.2 million in bets ($584.4 million) to assure winning.

So if you lay out the next 10 years of your income, say $1 million, your odds of winning, with that bet are only 1 in 584.4.. The risk/reward ratio doesn't make sense for most, to risk the $1 million, since most wouldn't have significant additional assets and the likely loss would be financially devastating.

On the other hand, even if the expected net value was somewhat negative (as it was at $800 million), it would make sense for most to play and buy a $2.00 ticket because  the almost assured loss of $2.00 would be no big deal relative to the potential reward of $800 million (less taxes).

It is when you start betting serious dollars, and thus upping the cost of your near assured loss, that it makes no sense to bet. But spending $2.00 to potentially win $1.3 billion? Yeah go for it.

For most economists, they fail to understand why the bet makes sense, even when it is a net negative outcome, because they fail to take into account that the marginal value of the $2.00 loss of a single bet. For most of us, the $2.00 loss is nothing. Thus, the bet makes sense. This might not be the case for all. For a homeless man with $7.00 in his pocket that he will need to survive through Thursday, a loss of the $2.00 might be too significant for him to make the long odds bet to get him off the street---way off the street.

On the other end of the scale, it might make sense for someone with $100 million in cash to consider betting $1 million since the million (and the likely loss) may not be important to him relative to the possibility of gaining the net from $1.3 billion.

Robert Wenzel is Editor & Publisher at EconomicPolicyJournal.com and at Target Liberty. He is also author of The Fed Flunks: My Speech at the New York Federal Reserve Bank. Follow him on twitter:@wenzeleconomics

13 comments:

  1. Neat analysis. However, worth noting it is immoral to play. Participation in the lottery at all is voluntarily contributing to a program that raises funds used for aggression.

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  2. I get a kick that if one takes the cash payout, minus taxes one ends up with ~483 mil (out of the projected 1.3 bil annuity)which is close to a third of the advertised jackpot. Since the govt lottery does it, A-OK; if a private company did that? Standby for the state or fed AG's lawsuit. None of this diminishes the fun of wondering what you would do so that you don't come back in the next life as a North Sea barnacle (doubling the funding of the Mises Institute??)

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  3. Penn Gillette had a very interesting question on his December 27th podcast. He asked would you have a better chance at collecting a payout playing the lottery or taking a life insurance policy out on a stranger, celebrity or relative? I am sure the odds are much better to take the policy than to play the lottery. This however is based on a $1 million policy vs. $1 million lottery, but it could be a $1 billion lottery, but I am sure you couldn't get a $1 billion policy, but I don't know.

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  4. It makes for great daydreaming as to what I would do with the winnings. The odds are far to low to ever tempt me to participate, despite the interesting math.

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  5. I always tell people who tell me about playing the lottery, "At least I can't loose if I don't play".

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  6. I'm surprised Tabarrok fails to highlight the non-monetary rewards, which Matt Murphy touches on.

    Here's a great article by David Ramsay Steele highlighting these: “Yes, Gambling Is Productive and Rational”, Liberty (1997) (Reprinted in A Rhetoric of Argument by Jeanne Fahnestock & Marie Secor.)

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  7. I already won last weekend by not playing. I will win again but not playing Wednesday.

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    1. What are you going to do with your $2.00 in "winnings"?

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  8. At issue, from a Misesian standpoint, is the use of class probability when the issue at hand falls under case probability.

    Payout nonsense only begins to works when the player is going to play an infinite number of plays or if all players pool their tickets in a collective effort.

    Otherwise, keep your money in your wallet unless your enjoyment of a chance to win exceeds that of your money.

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  9. Cool analysis. It does however give you a real world example of what such astronomical odds really mean in real life. For so many millions of players and still nobody wins is a sobering demonstration.

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  10. I hope that the Powerball-driven cash fever will die out tomorrow. The media is going crazy about it, thelotter review. Still I think it won't be a great loss buying one ticket just for fun even despite the above reasoning.

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  11. no reason to play, no reason to believe

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  12. We have to choose a game with better chance of winning, like Australian lotteries! We have one chance in 45 millions to predict Oz Lotto results ! It's much better that in PowerBall !

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