433 people win a lottery jackpot. Impossible? Probability and psychology suggest it’s more likely than you’d think

More than a few eyebrows were raised over the weekend when it was reported that as many as 433 people won the jackpot of a government sponsored lottery in the Philippines – with a share of 236 million pesos (about A$6.2 million).

Perhaps unsurprisingly, this has led to phone calls for an investigation how this seemingly “almost impossible” outcome could have come about.

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

How the lottery works

Each person who buys a ticket chooses six numbers between 1 and 55. The winning jackpot sequence is drawn at random. A ticket wins the jackpot if the six numbers on it are equal to the six numbers drawn.

So each ticket has:

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

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

What are the odds?

Without knowing how many tickets have actually been sold, we cannot know the exact chance of getting 433 winning tickets.

A widely circulated estimate this week assumed there were about 10 million ticket sales, and claimed the odds were as slim as “one to one followed by 1,224 zeros” – a truly absurd number. This is less than the chance of flipping a typical coin 2,800 times in a row and seeing coin every time.

People want to know the probability of 433 6-55 winners. It’s 1 to 1.87e-1224. That’s 1 to 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

However, this estimate ignores substantial empirical evidence on human behavior and psychology. It naively assumes that every person who buys a ticket has an equal chance of selecting any of the 28,989,675 possible number combinations.

It has been clearly observed around the world that some combinations much more popular than others.

This is why some experts often advocate the use of a random number generator when redeeming a ticket. While it won’t increase your chance of matching the winning values, if you do, it can reduce your chance of having to share winnings with multiple other gamblers.

More psychology than probability

A closer look at the winning numbers – 9, 18, 27, 36, 45 and 54 – can give a clue to a possible explanation. Those of you who have paid close attention when learning your table of nine will recognize a distinct pattern in the apparently randomly drawn numbers.

It is likely that this pattern has appealed to people, and why more people will have chosen this particular set of numbers. Rather than offering a smoking gun to suggest impropriety, this pattern may indeed explain the high number of winning tickets.

An equally unusual spike of winners was observed 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) yielded multiple jackpot winners in South Africa.

You should also remember that the winning sequence of the Philippine lotto is no less likely 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.

Still, many people would (wrongly) see that the last sequence would appear rather random.

In general, people have been shown to be surprisingly poor judges of what a set of truly random numbers would look like. In fact, they have even outsmarted them in simply comparing probabilistic patterns by: the humble dove.

In one study, participants were more than twice as likely to have a odd number than an even number when asked to come up with a random number, suggesting that some numbers “feel” more random than others, despite the obvious absurdity of this.

Could there be malicious intent?

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 have bought the same pattern of numbers in the past few weeks, or what other combinations also bring in 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 every year around the world, almost all of which receive no international press. While such outcomes are highly unlikely for any given draw, the sheer number of total lotteries means it actually is very likely at least one of them will produce a remarkable result only by chance.

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

But overall, it’s highly plausible that the only real statistical anomaly at play here is how so many people’s perception of randomness led them to the same number pattern. That said, I won’t be in a hurry to buy a lottery ticket.

This article was republished from The conversation under a Creative Commons license. Read the original article.