Something weird happened in March of 2005: 110 people in 26 states correctly picked five out of six Powerball numbers, good enough for second-places prizes of between $100,000 and $500,000 each. Lottery officials were mystified and initially suspected fraud on a massive scale. But in the end, the explanation was far less sinister: those numbers happened to be the "lucky numbers" printed on the fortunes of a popular brand of fortune cookie.
This illustrates an overlooked fact about lottery drawings: the numbers that win lotteries are 100 percent random. But the numbers that people pick are not.
Many lotto players play the exact same numbers each week -- establishing ownership over a set of "my numbers" is part of the fun, after all. These numbers are often tied to important dates -- anniversaries, birthdays, etc.
Here's the funny thing about dates, though: there are only up to 31 days in a month, and 12 months in a year. So imagine a hypothetical lottery where there's only one number and you could choose anything between 1 and 100. And say you decided to pick an important date -- birthday, anniversary, whatever. That self-imposed restriction narrows your selection down to 1 to 31, and excludes 69 other digits from consideration.
This has no bearing on your overall chance of winning -- the numbers 1 through 31 are just as likely to be drawn as the numbers from 32 to 100. But there's an awfully good chance that anybody else playing our hypothetical lottery might have been picking dates and constricting themselves to the same range too. In the event that the winning number is between 1 and 31 and you happen to guess it, there's a much higher chance that you'll have to share your winnings with someone than there would be if you'd picked the less obvious numbers from 32 through 100.
Academics have studied this phenomenon. A 1999 paper in the Journal of Risk and Uncertainty noted that the most popular numbers played in the U.K. national lottery were typically 7, 14, 21, 28, 35 and 42 -- the multiples of lucky number 7. The combination is played tens of thousands of times each week. And in a testament to some British lotto players' laziness, the combination 1, 2, 3, 4, 5 and 6 is also played thousands of times each week.
While lotteries almost always publish records of their winning numbers, databases of the numbers people play are a lot harder to come by. This is partly because it would be helpful to players to know these numbers. If you knew what numbers other people were playing, you could pick less popular numbers to maximize your chance of not having to share your winnings should you hit it big.
Still, some limited data is out there. That 1999 paper analyzed 69 million U.K. lottery tickets from a single drawing. The lotto didn't hand over the actual numbers played, but they did share the distribution of number combinations. The paper found that among the players' lottery tickets, there were far more number combinations that appeared multiple times -- dozens, hundreds, thousands of times -- than you'd expect from random chance alone. Conversely, there were also many many combinations that didn't show up in player tickets at all.
So this suggests that people aren't choosing numbers at random -- but what numbers are they choosing? To get a sense of that, a group of math and stats professors at Dartmouth and other U.S. universities obtained a complete set of player-chosen Powerball numbers in one state for the May 3, 1996 drawing. There were 17,000 tickets where players chose their own numbers (from 1 to 45 back then), rather than letting a computer do it for them.
Here's what the distribution of the over 100,000 numbers on those 17,000 tickets looked like:
For starters, that heavy line across the middle is the expected number of picks for each number based on purely random chance -- the professors got this by looking at the distribution of a similar number of the computer's picks for that same game.
As you can see, the smaller numbers on the left-hand side of the chart were chosen way more often than the larger numbers on the right. Number 7 was the most popular -- people picked it over 5,000 times, or 19 standard deviations above the mean.
Numbers 3 and 5 were also popular, perhaps because the drawing was held on the 3rd day of the 5th month. The numbers 1 through 12 -- months -- were more popular than the numbers that come after. And after 31, the last day of most months, numbers are typically picked less often than you'd expect from random chance.
Keep in mind this is a highly limited dataset. It represents one drawing in one state 20 years ago. Certain numbers may have become more popular since then (the numbers from Lost, for instance), others less so.
Still, the human predilection to choose numbers that are familiar to us doesn't seem likely to go away. You can't predict which numbers will win tomorrow's big drawing. But you can safely assume that many people will be picking numbers based on dates, or perceived luckiness, or popular TV shows, or other factors that are known to us all.
So if you don't want to share that $1.5 billion jackpot, steer away from those numbers. Better yet -- let the computer pick your numbers for you.