June 2, 2023

# That freak lottery win sounds impossible. A mathematician explains why it isn’t : ScienceAlert

Many eyebrows were raised over the weekend when it was reported that 433 people won the jackpot of a government-backed lottery in the Philippines – sharing 236 million pesos (about US\$4 million).

Perhaps unsurprisingly, this has led to calls for research into how this seemingly “almost improbable” result could occur.

However, a basic understanding of probability and human psychology helps explain why this outcome is not as unlikely as you might think.

## How the lottery works

Each person to buy a lottery ticket chooses six numbers between 1 and 55. The order of the jackpot is drawn randomly. A ticket wins the jackpot if the six numbers on it are the same as the six numbers drawn.

So each ticket has:

• six in 55 chances of drawing the first number, multiplied by
• five in 54 chance of getting the second, multiplied by
• four in 53 chances of getting the third, multiplied by a factor
• three in 52 chances of getting the fourth. is multiplied by
• two in 51 chances of getting the fifth, multiplied by
• one in 50 chance of getting the last one.

Together, this means that any given ticket has a 1 in 28,989,675 chance of winning the jackpot. So how is it possible that 433 tickets have done this?

## What are the odds?

Without knowing how many tickets were actually sold, we cannot know the exact probability of getting 433 winning tickets.

A widely circulated estimate this week assumed there were about 10 million ticket sales and argued the odds were as slim as “one in one followed by 1,224 zeroes” – a truly absurd number. That’s less than the odds of flipping a typical coin 2,800 times in a row and seeing tails every time.

However, this assessment ignores substantial empirical evidence about human behavior and psychology. It naively assumes that each person who buys a ticket has an equal chance of choosing each of the 28,989,675 possible combinations of numbers.

All over the world, it has been clearly observed that some combinations are much more popular than others.

This is why some experts often advocate using a random number generator when redeeming a ticket. While it won’t increase your chances of matching winning prices, it can reduce the chance of having to share any winnings with several other players if you do.

## More psychology than chance

A closer look at the winning numbers – 9, 18, 27, 36, 45 and 54 – may give some idea of ​​a possible explanation. Those of you who paid attention when learning your nine times table will recognize a clear pattern in the seemingly randomly drawn numbers.

It is possible that this pattern is what has attracted people and why more people will have chosen this particular sequence of numbers. Rather than providing a smoking gun to suggest impropriety, this pattern may actually explain the high number of winning tickets.

A similarly unusual surge of winners was seen in the UK in 2018, when five of the six numbers were multiples of seven. In 2020, a series of consecutive numbers (5, 6, 7, 8, 9, 10) resulted in many jackpot winners in South Africa.

Also, you must remember that the winning sequence is the Philippine lotto is no less likely to be drawn than any other sequence of numbers. The odds of drawing 9, 18, 27, 36, 45 and 54 are exactly the same as, say, 1, 18, 19, 28, 30 and 46.

However, many people would perceive (incorrectly) that the latter sequence is more likely to occur by chance.

In general, humans have proven to be surprisingly bad judges of what a set of truly random numbers would look like. In fact, the humble pigeon even outperformed them in simple possible pattern matching.

In one study, participants were more than twice as likely to choose an odd number than an even number when asked to think of a random number, suggesting that some numbers may “feel” more random than others, despite the apparent absurdity.

## Could foul play be involved?

The fact that 433 winning tickets were sold is far from conclusive evidence of any wrongdoing. It would be interesting to know how many people bought this same number pattern in previous weeks, or what other combinations are also attracting several hundred ticket sales.

Based on anecdotal evidence from other lotteries, this number may not be unusual at all.

We must also consider the many thousands of similar lotteries that are drawn around the world each year, almost all of which receive no international press. While such results are extremely unlikely for any given draw, the sheer number of total lotteries means that it’s actually quite possible that at least one of them will have a notable result just by chance.

There are often accusations when notable lottery results are announced, perhaps most infamously when FC Barcelona legend Xavi was declared the winner of a private lottery shortly after moving to Qatar.

But overall it’s very plausible the only real statistical anomaly at play here is how so many people’s perception of randomness drew them into the same pattern of numbers. That said, I won’t be rushing out to buy a lottery ticket anytime soon.

Stephen Woodcock, Associate Professor of Mathematical Sciences, University of Technology Sydney