Friday, September 22, 2023

How many times do you have to play the lottery to win it?

The mathematicians of the Manchester University have answered the question: How many lottery tickets do you need to buy to guarantee winning something in the UK National Lottery?

Focusing on the flagship “Lotto” game, which draws six random numbers from 1 to 59, Dr. David Stewart and Dr. David Cushing discovered that 27 is the lowest possible number of tickets needed to guarantee a prize, though, more importantly, with no guarantee of making the initial spend profitable.

They describe the solution using a mathematical system called finite geometry, which is centered around a triangle-like structure called the Fano plane. Each point of the structure is drawn with pairs of numbers and connected with lines: each line generates a set of six numbers, which is equal to one ticket.

Three Fano planes and two triangles are needed to cover all 59 numbers and generate 27 sets of tickets.

Choosing tickets in this way guarantees that no matter which of the 45,057,474 possible draws occurs, at least one of the tickets will have at least two numbers in common. From any drawing of six, two numbers must appear in one of the five geometric structureswhich ensures they appear on at least one ticket.

But Stewart and Cushing say the hard work is actually showing that it is not possible to achieve the same result with 26 tickets.

Stewart, a reader in pure mathematics at the University of Manchester, said in a statement: “Fundamentally, there is a tension that comes from the fact that there are only 156 entries on 26 tickets. This means that many numbers cannot appear once. many times. Eventually you will see that you will be able to find six numbers that do not appear on any ticket together. In terms of graph theory, we ended up proving the existence of an independent set of size six.

Although a win is guaranteedthe researchers say that the chances of making a profit are highly unlikely and should not be used as a reason to gamble.

The 27 lottery tickets it would cost 54 pounds. And Peter Rowlett, a mathematician at The Aperiodical website, has shown that in almost 99% of cases, he would not get that money back.

By testing the theory in the draw lottery from July 1, 2023; the researchers hit just two balls on three of the tickets, the reward being three lucky guesses in a subsequent lottery, each resulting in nothing.

The researchers say the finding is computationally interesting. They use a fifty-year-old programming language called Prolog, which they say makes it one of the oldest examples of real artificial intelligence.


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