I confess: I play the lottery. Each week, I spend £10 on lottery tickets, harboring the hope of one day winning a multi-million-pound jackpot. From a mathematical perspective, playing the lottery is a very poor use of one’s money. But how poor is it really?
Keep in mind that there are many different lottery games, but for the purposes of this article, I’m going to focus on a lottery that consists of numbers 1 to 49. What are your odds of winning a jackpot with those 49 numbers? As it turns out, they’re not so good.
In a lottery where participants choose six numbers from a possible 49, the probability of selecting all six winning numbers is 1 in 13,983,816. In other words, that’s a chance of one in nearly 14 million. If one were to buy a single lottery ticket per week under these odds, a win could theoretically be expected once every 269,000 years.
Earlier this year, I conducted a series of mathematics lessons on probability with my Year 8 children. During one of these lessons, I asked each child to choose their own lottery numbers. I then used an online ‘Lottery Simulator‘ (a U.S.-based tool, displaying winnings in dollars) to simulate multiple draws and determine how frequently they would win. Despite running millions of simulated draws, none of the students won (and, hypothetically, many millions of dollars were spent in the process). You can try the simulator yourself with your preferred numbers at the following link:
The purpose of the lesson was to show learners how futile it is to play the lottery. I then encouraged them to rather invest the same amount of money (leading into lessons about simple interest).
However, I clearly haven’t learnt my own lesson about playing the lottery!
