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