Wanna Win The Lottery? Mathematicians Tell Us How Many Tickets You Need

Mathematical researchers from The University of Manchester have provided an answer to the inquiry: What is the minimum number of lottery tickets one must purchase to ensure a win on the U.K. National Lottery?

Concentrating their study on the primary “Lotto” game of the National Lottery, which selects six random numbers ranging from 1 to 59, Dr. David Stewart and Dr. David Cushing determined that a total of 27 tickets represents the lowest quantity required to guarantee a win. It’s worth noting, however, that this guarantee pertains solely to achieving a win, not necessarily a profit.

For a definite victory in the Lotto, Dr. David Stewart and Dr. David Cushing have deciphered a strategy to secure at least two correct numbers out of the vast pool of 45,057,474 potential combinations. Astonishingly, this feat can be accomplished with just 27 tickets.

To depict these myriad combinations, the researchers employed Fano planes—a geometric construction wherein pairs of numbers are situated on or within triangles, connected by straight lines or circles. These lines traverse through three pairs each, thereby generating one of the conceivable winning sets of six numbers.

From a mathematical perspective, the intriguing aspect was not the act of winning the lottery, but rather determining the smallest conceivable number of tickets needed. Interestingly, establishing that winning is impossible with only 26 tickets posed a considerable challenge.

Mathematician Peter Rowlett estimated, as reported in The Aperiodical, that in about 99 percent of instances, the investment would not yield profits commensurate with the expenses. While victories might occur, they tend to be relatively modest. However, recognizing that theory can only provide limited insight, the researchers decided to put their theories into practical application.

They procured a total of 27 lottery tickets for the draw scheduled on July 1, 2023. The expenditure amounted to £54 ($68.61). Out of these tickets, three were winners, with each one matching a pair of numbers. This type of win grants the recipient a complimentary randomly generated ticket for the subsequent lottery draw. Unfortunately, none of the three bonus tickets resulted in a win.