The Statistics Behind Striking It Rich — or Not — with Powerball

At 1 in 292 million, the odds of winning the largest lottery prize in U.S. history — this week’s estimated $1.5 billion Powerball lottery — are stacked against you.

How difficult will it be to win? Well, the $2 investment into a lottery ticket may be better spent elsewhere, according to Cal Poly Statistics Professor Kevin Ross.

Ross, who specializes in probability, explains that the odds of picking the right combination of numbers is like every person in the U.S. writing his or her name on a slip of paper, putting those slips of paper into a giant hat, shaking it, and then pulling out a slip with his or her name on it.

“It’s not very likely,” Ross said.

However, there is a distinction to be made: The probability of someone winning is often pretty high. But the probability that that someone is you is miniscule.

“If 400 million tickets are sold, then you would expect at least one ticket somewhere to win,” Ross said.

So, can you increase your chances of winning the astronomically large Powerball jackpot? The answer is yes and no.

Buying multiple tickets is a viable solution, but a person would need to buy roughly 15 million tickets just to have a 5 percent chance of winning. Additionally, letting the computer generate your numbers or picking them yourself yields the exact same outcome.

“In terms of your chances of winning, it doesn't make any difference,” Ross said. “People tend to confuse particular outcomes with the more general events they represent."

So, someone who chooses the numbers 1, 2, 3, 4, 5 and 6 has the same chances of winning as someone with the random, computer-generated numbers 6, 12, 20, 38, 43 and 48.

Picking your own numbers, however, has one distinct advantage.

“It might be better to pick a sequence like 1, 2, 3, 4, 5 and 6, which many other people probably would not pick because they erroneously think such a combination is less likely than others or to pick higher numbers because a lot of people pick birthdays,” Ross said. The advantage here is not that you’re more likely to win — you’re just less likely to split the jackpot.