Statistical improbability or a miracle? Statisticians, experts weigh in on the P236M Grand Lotto issue

"Rare, but not impossible"

"The chance that a number combination can win is 1 in 28,989,675… or approximately 1 in 29 million so you see it’s really difficult to win in lotto." University of the Philippines Los Baños (UPLB) Mathematics Biology professor Dr. Jomar Fajardo Rabajante shared with PhilSTAR L!fe "What more if we have 2 or more (eg, 433) winners, it seems very very unlikely."

However, Rabajante added that PCSO's lotto betting isn't just one time and people can be regular bettors. The chance a combination will show up such the multiples of 9 combinations is also possible in the long run.

"The story becomes different if a basic pattern will show up," he explained.

In an interview with CNN Philippines' The Source, OCTA Research fellow and UP Professor of Mathematics, Dr. Guido David likewise called the instance "highly unusual" but did not rule it impossible.

"Wala naman impossible, it can happen," Guido shared with Pinky Webb. "In itself, it is not unusual to have a winning sequence [of 9] like this because this is as likely as any other combination."

"Maybe more people bet on this sequence because it's something most people can understand and it's Lucky 9. So that makes it a bit more of a likely combination, but the probability of that happening is still very, very small."

People want to know the probability of 433 6-55 winners. It is 1 to 1.87e-1224. That is 1 out of 1 followed by 1224 zeros. The age of the universe is 4.3e17 seconds (17 zeros). However, the winning combination, divisible by 9, could mean more people bet on it. #dzbb @DZAR1026 pic.twitter.com/N22G7BP43k

— Dr. Guido David (@iamguidodavid) October 3, 2022

The human nature of choosing 'Lucky' numbers

The winning numbers all being divisible by 9 were also called out, but it has long been considered a lottery favorite for it's so-called "lucky" nature.

"When we see the combinations being 09-18-27-36-45-54, which are multiples of 9 or digits adding up to 9, and when you see the lotto entry form where these digits often are arranged diagonally, it explains that it is a very human thing to do," Peter Julian Cayton, associate professor of UP’s School of Statistics shared.

"The lotto selects numbers randomly through drawing balls, but we humans choose numbers based on patterns and order that we can easily make, especially when we like to participate daily."

"The combination has a chance of only 1/28,989,675, the denominator being all possible 6-number combinations in the 6/55. However, that is different from what people would choose as their 6-number ticket."

"Again, people will choose numbers based on their preferred pattern or order. People are not random number thinkers. Many people can be loyal or consistent in their choice of numbers, especially if they would be regularly joining the lotto," Cayton added.

Rabajante likewise pointed out that regular bettors have an "alaga" or typical combinations that they choose. In the PCSO Lotto tickets, the Oct. 1 winning combination is laid out in a clear diagonal line.

"Swertihan talaga na lumabas ang pattern — the sad news is many selected that basic pattern so ma-divide ang prize. Some combinations might not be as common for bettors to bet, but some are common due to their pattern," he said.

Ultimately, Rabajante, like Guido, said that the instance was "rare but not impossible."

PCSO General Manager Melquiades Aypa Robles that the numbers people were chose were usually also "loyalty-based."

“Maraming tumataya ng alagang numero," he said during an Oct. 2 press conference. It’s not only good to be loyal to your wives and husbands, it’s also good to be loyal to your numbers."

The call to probe

On the other hand, it is also human nature to probe these seemingly-impossible occurrences, as several lawmakers have called to investigate the PCSO and whether or not anomalies will come up in the machines.

"Talagang marami po ang nagtaka, na medyo nagulat because statistically speaking, this is a very rare event," Senate Majority Leader Aquilino "Koko" Pimentel said on Sunday.

"Let us take this opportunity to investigate so that ang purpose natin to ensure the integrity of our lotto games."

Sen. Risa Hontiveros also moved to investigate the matter "rule out any doubts" for the public.

"We just want rule out any doubts in the public mind that the results have been manipulated. While we recognize that people tend to bet in patterns, we also want to make sure the system is secure, free from glitches, and trustworthy," she said.

2022 Presidential candidate Panfilo "Ping" Lacson suggested that authorities ought to start by looking at the "common denominator" among the 433 winners.

433 winners in one 6/55 lotto draw is highly improbable, if not impossible. If I were to investigate this apparent PCSO anomaly, I’d start by looking for a common denominator of these “lucky ones”.

— PING LACSON (@iampinglacson) October 2, 2022

Albeit saying that it isn't impossible, Guido David also supported the call for looking into anomalies: "Any time something happens that is not within the realm of expectations of probability, usually there is going to be an audit or investigation so I don't blame that people would want to know if everything is above board."

"I'm not saying that there is going to be an anomaly, it can happen, it's possible. But there will be an investigation when things don't align with the probabilities."

Meanwhile, the PCSO has shared photos of the few anonymous announced winners coming forward to the PCSO Mandaluyong main office.