More than a few eyebrows were raised at the weekend when it was reported that more than 400 people won the lottery in the Philippines.
This result has led to calls for an inquiry into how it could have happened.
A basic understanding of probability and human psychology helps explain why this outcome is plausible.
There are six numbers for the lottery ticket. There is a random drawing for the winning sequence. If the six numbers on the ticket are the same as the six numbers drawn, it will win the lottery.
The tickets have:
Any ticket has a 1 in 28 million chance of winning the prize. There are 433 tickets that have done this.
We don't know how many tickets were sold because we don't know how likely they are to win.
A widely circulating estimate assumed there were around 10 million ticket sales and claimed the chances were as little as one out of one followed by 1,224 zeros. The chance of flipping a coin 2,800 times in a row and seeing tails is much higher.
The estimate ignores empirical evidence about human behavior. The assumption is that each person has an equal chance of selecting a number.
Some combinations are more popular than others.
The use of a random number generator is advocated by some experts. It won't increase your chance of matching the winning values, but it might reduce your chance of having to share any winnings with other gamblers.
The winning numbers are 9, 18, 27, 36, 45 and 54. Those of you who paid attention will see a clear pattern in the numbers.
More people will choose this sequence of numbers because it is appealing to them. This pattern may explain why there are so many winning tickets.
In the United Kingdom, five of the six numbers were multiples of seven in a single year. Multiple jackpot winners were produced in South Africa in the year 2020.
The winning sequence is more likely to be drawn than any other sequence of numbers. The chances are the same for 9, 18, 27, 36, 45 and 54.
Many people think the latter sequence is more likely to happen randomly.
Humans are not very good at judging a string of random numbers. They have been outsmarted by the pigeon.
According to a study, participants were more likely to pick an odd number than an even number when asked to think of a random number.
Winning tickets are not evidence of wrongdoing. It would be interesting to know how many people bought the same pattern of numbers in the previous week.
There is anecdotal evidence that this number is not unusual.
Almost all of the lotteries drawn around the world receive no international press. It is quite likely that at least one of the total lotteries will produce a remarkable outcome by chance.
When FC Barcelona legend Xavi was announced the winner of a private lottery, he was accused of being a fraud.
The only real statistical anomalies at play are how many people's perception of randomness draws them to the same pattern. I will not be rushing to buy a lottery ticket in the near future.
Stephen Woodcock is an associate professor of mathematical sciences.
Under a Creative Commons license, this article is re-posted. The original article is worth a read.
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