Playing the lottery has always been seen as a game of chance.
“You can’t predict the lottery,” they say. However, a team of mathematicians at the University of Manchester has challenged this conventional wisdom.
The old joke that suggests the lottery is a tax on people who can’t do math might have just got a twist.
But, spoiler alert, the method that guarantees a win might not necessarily secure a jackpot or even a significant monetary return.
Dr David Stewart and Dr David Cushing focused their study on the UK National Lottery’s Lotto game, where players select six numbers from 1 to 59 with the goal of matching the drawn numbers.
The spectrum of possible winnings ranges from getting a pair right, which rewards the player with a free randomly generated ticket for the following lottery, to the jackpot for matching all six numbers. The jackpot, as of the week of the research, stood at an enticing £7.8 million ($9.9 million).
Analyzing the complex probability of the game, the mathematicians worked out how to get at least two numbers right out of all 45,057,474 possible combinations. They found that the magic number of tickets one needs to purchase to guarantee a win is 27.
This minimum number of tickets was determined by applying Fano planes – geometrical constructions where pairs of numbers are plotted on or inside triangles, and straight lines or circles connect them.
Each line passes through three pairs, producing one of the possible winning sextets. This approach, while fascinating, created tension with the mathematical landscape of the lottery.
As Stewart, a Reader in Pure Mathematics at The University of Manchester, explained in a statement, “Fundamentally there is a tension which comes from the fact that there are only 156 entries on 26 tickets.
This means a lot of numbers can’t appear a lot of times. Eventually, you see that you’ll be able to find six numbers that don’t appear on any ticket together. In graph theory terms, we end up proving the existence of an independent set of size six.”
The tension Stewart speaks of highlights the challenge of the task, the difficulty of proving that you can’t win with only 26 tickets. The team’s discovery effectively bridges the gap between theory and practice, providing an intriguing mathematical solution. However, is it a viable money-making scheme?
According to mathematician Peter Rowlett, who commented on the findings in The Aperiodical, in 99 percent of cases, the investment won’t match the profit. In other words, while you’re guaranteed to win, you’re not guaranteed to make money.
The University of Manchester team put their theory into practice ahead of the July 1, 2023, draw. They purchased the magic number, 27 tickets, at a cost of £54 ($68.61).
Indeed, they scored three winning tickets, each matching a pair, thus winning three more tickets for the following lottery. However, none of these newly won tickets proved successful.
So, what does this mean for avid lottery players and potential mathematician gamblers? The study presents a compelling intersection of mathematics and gambling, providing a method to guarantee a win, yet it simultaneously dispels the myth of using such an approach as a get-rich-quick scheme.
While it seems the old joke about the lottery remains true to an extent, the University of Manchester’s findings shed light on the complex probability involved in such a game.
While the research remains not yet peer-reviewed and is available at arXiv, it undeniably creates an engaging dialogue about applying mathematical principles to traditionally chance-based activities.
As Stewart and Cushing demonstrated, you can use math to win the lottery – just don’t count on buying that beachfront mansion with the proceeds.