Published:
Oct 7, 2022 16:08 GMT
A mathematician gives a logical explanation for why it is not unlikely that 433 people chose the winning combination of numbers, as happened last Saturday in the Philippines.
The result of a lottery draw generated surprise and suspicion in the Philippines, where on October 1, 433 people shared the 4 million jackpot. This high number of lucky winners (each pocketing around $8,400) led many in the Asian country to believe that something was amiss with the Philippine Charity Raffle Office raffle. The repercussion was such that a senator, Aquilino ‘Koko’ Pimentel, even demanded a research officer to clarify the case, which he defined as “strange and unusual”.
However, a mathematics professor at the University of Technology in Sydney, Australia, says that probabilities and psychology can explain this seemingly implausible result, publish The Conversation this Thursday.
What were the possibilities?
Professor Stephen Woodcock explains that each person who buys a lottery ticket chooses six numbers between 1 and 55, with the jackpot winner being the ticket that matches the sequence of six randomly drawn numbers. In this way, at least mathematically, each ticket has a 1 in 28,989,675 chance of winning the jackpot.
Woodcock analyzed a estimatewidely spread on the Internet, according to which, if 10 million tickets had been sold, the possibility of 433 winning tickets coming out with that combination was “one in a one followed by 1,224 zeros”.
The mathematician refutes this calculation, since the estimate assumes that each of the 28,989,675 possible number combinations has the same chance of being chosen by lottery buyers; while at the moment of truth (Woodcock argues), human psychology plays a very important role in choosing the numbers, and it has been clearly observed that some combinations are much more popular than othersand therefore have more chances of being chosen.
Interesting numbers and patterns
Woodcock draws attention to the winning combination in the Philippines last Saturday: 9, 18, 27, 36, 45 and 54. The relationship between the numbers in the series is obviously that they are all multiples of 9. And the mathematician reasons that more people would have chosen this particular sequence of numbers attracted by this interesting pattern, which would ultimately explain the large number of tickets. winners. The mathematician recalls other occasions when similar cases occurred, such as in 2018 in the United Kingdom, where there was an unusual number of winners when five of the six numbers were multiples of seven; or in 2020 in South Africa, where a streak of consecutive numbers (5, 6, 7, 8, 9, 10) produced multiple jackpot winners.
The mathematician points out that, although humans believe that combinations made up of consecutive numbers or multiples of the same number are less likely to coincide on a winning ticket, in reality they are no less likely than any other combination. But since human understandable combinations are more popular among lottery buyers, to avoid (in case of winning) having to share the prize with many more players, the ideal is to use a random number generator, as experts suggest. , although that does not mean a higher probability of winning.
traps?
The analyst dismisses the possibility of foul play in the Philippine lottery result and reasons that the fact that 433 winning tickets were sold in a particular sequence is not an argument that there was cheating. To support his position, he stresses that it would be interesting to know how many people bought that same pattern of numbers in previous weeks and were not winners. Also, it could clarify this situation a little to know what other combinations also attract massive ticket sales. Finally, he argues that there are a large number of lotteries in the world, many of which do not have an international echo; and while it is unlikely that any given draw would produce a result like the one in the Philippines, it is not unreasonable to think that at least one of them has ever had an outcome just as surprising.
