Powerball Lottery Tickets // Lotteries

Powerball Lottery Tickets

Powerball probabilitiesThe Powerball lottery jackpot has hit a whopping $400 million, and the question on everyone's mind is "At what point should I actually start caring about the Powerball Lottery"?

Answering this question is not so simple, because in addition to calculating the odds of winning a potential jackpot, you also have to figure out the odds that you will have to split the potential jackpot. And the odds of a split change all the time, because the bigger the jackpot, the more people buy tickets. So we've decided to really drill down into the math to combine all the factors, including jackpot size, and the odds you will have to split the pot if you do win.

Powerball is interesting in the sense that there are a number of stagnant cash prizes that you can win, as well as an ever-increasing jackpot.

The expected value of spending $2 on a Powerball ticket is actually -$1.58 when you ignore the jackpot. That's right, the expected value of playing when you ignore the jackpot is negative.

powerball wins losses players dollarsAnd while the probability that you in fact win the jackpot is outstandingly small — 1 in 175, 223, 516 to be precise — the jackpots can grow outstandingly big, which makes it so that at some point, you can actually get a positive expected value.

For instance, when we last looked at Powerball the jackpot had reached a whopping $600 million. If you look at it in the most rudimentary form, your expected value for playing Powerball was not only positive, but also pretty attractive. Because of the ludicrously high jackpot, people could expect to gain about a $1.78 after playing.

Walter Hickey / BI

One complicating factor, however, is the fact that when you factor in the probabilities of split jackpots, you will decrease that expected value.

The probability that the winner will have to split the jackpot is also really significant.

Powerball winner probabilitySo, the expected value for the Powerball lottery is actually a function of the number of players.

And clearly, the higher the Powerball Jackpot, the more people who will participate.

So is there a way we can analyze the Powerball lottery to try to figure out how many people will play the lottery at a given given Jackpot? Does that relationship actually exist?

As it turns out, it absolutely does. Let's check it out.

We looked at over one thousand Powerball lotteries — 1117 to be precise — that have taken place since 2003 in order to get a sense of how many people play the game.

LottoReport.com keeps an outstanding record of how much each Powerball lottery has taken in over the past two decades. It's remarkable. For pre-January 18, 2012 Powerball lotteries, the amount of money collected is the amount of tickets sold, as they cost only $1 prior to that switch. After January 18, 2012, we merely have to divide the take by two to ascertain the number of tickets bought.

LottoReport also lists the jackpot, in millions, for each lottery.

Combining this dataset with information from Powerball that shows when a lottery was a winner — and how many winners there were – we're able to make this nice plot of lottery participation as a function of Jackpot value. Red dots are lotteries that had a winner:

Walter Hickey / BI Cool, right?

So we can notice a very, very clear upwards trend. The higher the jackpot, the higher the participation.

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