What are the odds?

$1.3 billion!  That’s quite a hefty jackpot for the next Powerball drawing, even if the number is deliberately inflated to raise the hype.  Still, the lump sum payout is estimated to be $806 million; not a bad day at the office.

The odds are posted around the web, but how are they determined?

The updated version of Powerball started in October; five numbers are drawn from a set of 69 white balls and one number from the set of 26 Power balls.  To win the jackpot, your five numbers and one Powerball number have to match up with the drawn numbers.  Your chance of one of your five numbers matching the first ball pulled is 5 out of 69 (7.25% probability).  Once a ball is pulled, it is not replaced, hence the chance of one of your four remaining numbers matching is 4 out of 68 (5.88%).  This continues until the five white balls are chosen (3 out of 67, 2 out of 66, and 1 out of 65) and then the Powerball at 1 out of 26.  When all is said and done, out of the 35,064,160,560 ways the six total numbers could be pulled, you could win 120 different ways, since the order that the numbers are pulled doesn’t matter (permutations vs. combinations anyone?).

odds
Odds are 292,201,338 to 1

When does it makes sense to play?  Well, Walter Hickey has made a name for himself looking at this sort of thing.  His 2013 article says it only makes sense if you take the annuity and if the jackpot is greater than $345 to $380 million.  Mind you, this was when Powerball was way easier to win (odds were a paltry 175,223,516 to 1 back then!)  With the tougher odds, breakeven, assuming just one winner, looks like this:

expected value

Once the jackpot hits $491 million, you can statistically justify purchasing a ticket, since the expected value is above $0.  Of course, that is **AFTER TAXES**.  With a top federal tax bracket of 39.6% and state taxes ranging from 0% to 8.8% and some cities adding their own levies as well.  That means it only works with jackpots from $813 million to $1.029 billion!  Assuming multiple winners, which is more and more likely with more tickets purchased, that minimum number keeps going up.  This is getting ugly…

Long story slightly longer, the odds are such that it is nearly impossible to statistically justify purchasing a ticket.  Am I playing?  Uh… yes, I am.  Why?  Consider it a cheap insurance policy.  Should the office pool hit, I’ll have options.  Besides, it’s entertaining to share in the thrill of anticipation, even if it will undoubtedly end with a tiny payback.

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