A Powerball ticket costs $2 and has 1 in 292,201,338 chance of winning. The price and the odds are the same every week. What changes is the jackpot amount. For Wednesday’s drawing it’s $1.5 billion.
Do the math: The expected winning is $1.5 billion divided by 292,201,338, or $5.13. That's than the $2 the ticket costs!
There is a catch. You might have to share the jackpot with someone else. Last week about 400 million bought Powerball tickets. Notice that’s more than the 292 million possible numbers. As it happened, no one picked the right combination. If we assume a similar number of tickets will be sold this week, then each set of numbers is selected by 1.37 ticket buyers on average. In other words, if choose a random set of numbers, there’s a good chance you’ll be the only one picking that set. And even if there’s one other person with that set of numbers, that would cut your expectation in half, from $5.13 to about $2.57—which, you’ll notice, is still greater than the cost of ticket.
I haven’t even factored in the smaller prizes. They further increase a player’s expectation. In short it appears that, even with all the media hype and the hundreds of millions of other players, a Powerball ticket is currently a positive-expectation wager. That’s a rare thing, though it’s the not the first time it’s happened, either.
Should you buy a ticket then? Let me first say that there is a simple strategy that increases your chances considerably. You pick unpopular numbers.
The fact is that some numbers are far more frequently chosen than others. For instance “lucky” 7 is a poplar number. Should you include 7, you increase the chance that, should you win, you’ll be sharing a jackpot. Consequently smart players avoid 7.
You might think that “unlucky” 13 would be a savvy contrarian pick. Nope. Thirteen is a moderately popular choice, it turns out.
You’ll notice that the Powerball jackpot has gone uncollected for many weeks, despite the fact that there are currently more ticket buyers than available numbers. And there’s a good chance that, when the jackpot is won, it will be split by several people. This reflects the psychology of choosing numbers. Choices cluster on popular numbers.
There has been considerable research on which numbers are least popular (and thus best to pick). I’ll give a chart adapted from my book Rock Paper Scissors.
These are unpopular numbers—those relatively unlikely to lead to a shared jackpot. All you do is select your six numbers from this set at random. A low-tech way to do that is to write the numbers on index cards, shuffle them, and draw numbers.
Note that the “Powerball” pick has to be between 1 and 26. There are only three candidate numbers for that: 10, 20, and 29. Make sure to choose that at random too.
Now here’s why you shouldn’t quit your day job. Those who have read my book Fortune’s Formula will know about something called the Kelly criterion. By Kelly standards, Powerball remains a sucker’s bet—positive expectation or not.
Remember, the chance of winning at Powerball is 1 in 292,201,338. Nothing in the above system changes that.
With two drawings a week, you would have to play a ticket in every single drawing for about 2.8 million years, on average, to win your first jackpot. The policy of buying lottery tickets is a certain financial drain that almost certainly never pays off while you’re drawing breath.