If you’ve been noticing recent patterns in the Pick 3 lottery game, you’re not alone.
Last week, a reader called the News-Democrat to say he was seeing more Pick 3 sets with a repeating number — 181, 992, or 633, for example.
The reader, who wished to remain anonymous because of how playing a lottery game would affect his image at work, has been playing Pick 3 for years — the same seven numbers, seven tickets a day, seven days a week — and remembered when Pick 3 used to be a live drawing with numbered plastic balls drawn from a hopper.
Today, numbers are randomly generated from a computer and animated on screen, which, in an era of computer hacking, would raise anyone’s eyebrow. In fact, on Sept. 15, the number 186 was chosen at both the midday and evening draw.
But Pick 3 players have nothing to worry about, explained Dr. Andy Neath, a statistician at Southern Illinois University at Edwardsville. The repeats bear out in the long run, which we can see with a little math.
Let’s start by finding the total number of possible Pick 3 sets. Dusting off the cobwebs from our memories of Statistics 101, we can find this by multiplying 10 three times, once for every number in a set, from 0 to 9. That comes to 1,000.
Now let’s take the chances that every number in a set is unique, or, in other words, not repeating. We can find this by multiplying 10 by 9 by 8 — once a particular number is selected, say ‘2’, then there are only nine other numbers for the second position, and eight for the third position. That number comes to 720.
Now take the chances of a triple. “This can occur in 10 different ways, one for each of the possible digits,” Neath wrote in an email.
So, the chances of a just one repeating number in a set, then, is 1,000 minus 720 minus 10. That equals 270, or 27 percent of the time.
The results, please
Jason Schaumburg, the Illinois Lottery spokesman, said the Lottery occasionally receives calls from concerned players about peculiar numbers, but, he said, the games would be hard to fix.
He pointed to a list of answers to frequently asked questions about the digital draw system, which the Lottery started using in October 2015. It cited operating costs, old equipment and the proliferation of games as a few logistical reasons it moved away from live draws. In addition, the Lottery thought digitization would make the games more “secure, reliable and efficient.”
Perhaps most importantly, the Lottery stated, “the system cannot be changed without direction from the Department of the Lottery, the manufacturer, and the independent certifier.”
Still, it’s easy to see why the reader who called in had a hunch that something was wrong.
First, he doesn’t play repeating numbers, and seeing them crop up would frustrate anyone.
Second, he was, in fact, onto something.
For the past couple of months, there has been a slight uptick in the number of Pick 3 sets with repeating numbers.
Indeed, of the 62 drawings from Aug. 16 to Sept. 15, 37 percent have contained a repeating number. That’s more than the 27 percent it should be.
But Neath threw ice on that observation.
“Patterns also arise under randomness, so streaks and clusters are not always indicative of an underlying effect,” Neath wrote. “It is common to believe that randomness implies the sequence will be devoid of patterns. That is not the case.”
Taking into account the remaining Pick 3 drawings since Jan. 1, the recent sequence of repeating numbers isn’t increasing the overall average. There were 518 drawings between Jan. 1 and Sept. 15. So how many of those sets have had repeating number?
Just 27 percent.
What about all the 0s and 1s?
The last concern the reader had was about the frequency of the numbers themselves.
He saw a lot of 0s coming up in the past couple of months. Indeed, the number 0 has been selected a lot, making up about 12 percent of all number selections since Jan. 1, when it should be only 10 percent. The number 1 appeared 9.59 percent of the time.
“Over the next 9 months of draws, it will not be surprising to see one digit (not necessarily the zero) appear much more often than the others, or to see one digit (not necessarily the 2) appear much less often than the others,” Neath wrote.
The reader also said that Pick 3 sets with either a repeating number or a 0 or a 1 — a combination that casts a wide net — hovered around 90 percent.
The observed results, however, were 77 percent since Aug.16, and since Jan. 1, they were 68 percent.
As far as what the actual probability is, well, that’s a longer math problem, but, suffice it to say, Neath showed in an email that the result would be 65.6 percent.
“Our minds are so inclined to look for patterns in our observations, it is easy to think that such clusters are meaningful,” Neath wrote. But, “an observed 68 percent is not out of line with the expected.”
In conclusion, no nefarious activity is going on.