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Lottery gone wild... 600M$ in tonight's Powerball

powerball 600m May 18 2013
Craziness all around... this evening someone might win more than 600M$ in one of US' biggest lottery games... The Powerball. With odds of 1 out of 175 million to win, and $2 per ticket, this becomes an interesting math game...

So... how do the odds stack up ? To win the Powerball game you need to correctly pick 5 numbers out of 59 - and one out of 35. If you have Excel handy, you can easily figure out the odds using the handy function COMBIN... your odds are

COMBIN(59,5) * COMBIN(35,1) = 5,006,386 * 35 = 175,223,510. One out of 175 million.

If you do not want to use Excel, but want to manually calculate these odds you will have to dig up your statistics books...

Now... the funny things is that if you would play every combination, it would cost you $350M in tickets. And that is about what the winner will get paid - if he or she is the only winner who has the 5+1 numbers correct. The lump sum amount the Powerball pays is indeed different than the overall amount to be won : if the jackpot is 600M$ this amount would be paid over 30 years - or the winner can choose to get all the winnings upfront in which case they are being discounted, and the winner receives 376.9M$ (also called the cash value of the Powerball Jackpot).

To make things a bit more complex... if you would play all 175M combinations, you would obviously also win many more other prices... adding to your price money. Next to the winning jackpot combination, there are 8 more ways to win "some" money. And these prices are fixed (i.e. they are independent of the size of the jackpot and the number of tickets sold).

Powerball Odds and Winnings for May 18th 2013

powerball odds winnings #wins total winnings
5 X 175,223,510.00 $376,900,000 1 $376,900,000
5 5,006,386.00 $1,000,000 35 $35,000,000
4 X 15,929,410.00 $10,000 11 $110,000
4 455,126.00 $100 385 $38,500
3 X 1,137,815.00 $100 154 $15,400
3 32,509.00 $7 5,390 $37,730
2 X 59,885.00 $7 2,926 $20,482
2 1,711.00 $4 102,410 $409,640
1 X 2,065.00 $4 84,854 $339,416
Cost of tickets covering all combinations: $350,447,020 (at $2.00 per ticket) Cash Winnings $412,871,168
Column A: Correct number of picks (out of 5 picks)

Column B: Powerball pick correct (X=yes)

Column C: Odds (1 out of...) In Excel: COMBIN(59,A)*(COMBIN(35,B)

Column D: Winnings for this combination (per the Powerball rules)

Column E: Number of wins if you would buy all 175,223,510 combinations

Column F: Total winnings (D * E)

This table assumes you correctly play all 175 million combinations and you are the only jackpot winner... in case there are multiple winners, this table changes in a big way - in fact, only the winnings for 5+X change... but that does turn the winnings bottom up !

And yes... I did buy a few tickets for this evening's Powerball lottery... so I have a one in 175M chance to win... I typically do not buy lottery tickets - given the statistics behind them they should really be considered a voluntary tax for stupid people. But sometimes dreaming just feels good - especially if the jackpot is 600M$ !

Back to the setup of the Powerball... Most of the States (and the US Virgin Islands) participate - making this an almost nation wide lottery. And people living in States in which no tickets are being sold, frequently will drive to a neighboring State to buy some lucky chances...

map powerball us states

Read more at the Powerball home page:

Another great website (mathematical background) : Durango Bill's Powerball Odds

Jullie miste de orkaan dat is

Jullie miste de orkaan dat is ook een serieuse jackpot

Jürgen's picture

No - I didn't win. But yes,

No - I didn't win. But yes, somebody won the jackpot of more than 600 million dollars yesterday evening (someone in Florida according to the news reports). So... no record setting jackpot for next Wednesday (if nobody had won this weekend, then the new accumulated Powerball Jackpot would have been more than 1 billion dollars !!!)...