Math And The Lottery!

 

I don't know about you but when I go through a state that offers lottery tickets, I indulge and buy one or two with the idea that maybe (yeah, right) I'll win and become a multimillionaire. I also know that the US is not the only country with a chance to win the lottery. When I was in Madrid, there was a line at this one lottery shop because more people had purchased winning tickets and wanted to win.

Not long ago, 433 people won the government backed lottery in the Philippines.  The 236 million peso prize would be shared among those 433 people. Since this many people won, there were calls for the government to investigate because 433 people should not win.  The odds appear impossible. If you take probability into account, it really isn't impossible. 

Lets look at this in detail.  Every person who buys a lottery ticket chooses six numbers between 1 and 55. The numbers are drawn randomly so the winner is the person whose six numbers match the six drawn numbers.  So mathematically, you have to multiply the 6 in 55 times 5 in 54 times 4 in 53 times 3 in 52 times 2 in 51 times 1 in 50 or you have a chance of 1 in 28,989,675 of winning the lottery.  Although it is not known how many tickets were actually sold, it is estimated that around 10 million were sold.  

It is assumed that every person who purchases a ticket has an equal chance of selecting each of the possible 28,989,675 combinations but that doesn't agree with human nature since there are certain combinations that are more popular than others.  This is why experts recommend one use a random number generator when buying the ticket since it won't increase your chances of winning, it will decrease your chance of having the share the prize with someone else.

The numbers that actually won this drawing were 9, 18, 27, 36, 45, and 54 which are all multiples of nine. Since it is a recognizable sequence, it is a sequence that many people would have chosen for themselves. The same thing happened back in 2018 in the United Kingdom when the winning tickets were multiples of seven or in 2020 when the numbers ended up being consecutive from 5 to 10 in a drawing in South Africa.

The thing is the chances of drawing 9, 18, 27, 36, 45, 54, are exactly the same as drawing the numbers of 3, 12, 13, 25, 36, 37, and 55 although to the human mind, the second set is seen as more random than the first set.  This is because the human mind really has no concept of what is truly random. One study indicates a person is more likely to choose an odd number if asked to select a random number leading the the assumption that certain numbers feel more "random" than others. 

It is possible that these 433 people chose these numbers "randomly" or the numbers were "randomly" generated but either way, people have trouble wrapping their minds around the fact that 433 people all ended up with the same numbers so in their mind, something weird is going on.  This may be why people are calling for an investigation.  Let me know what you think I'd love to hear.  Have a great day.