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How to buy a winning ticket on the National Lottery

Published online by Cambridge University Press:  01 August 2016

J. Brinkman ,
D. E. Hodgkinson  and
J. F. Humphreys
J. Brinkman
Affiliation:
Department of Mathematics, Liverpool Hope University College, Hope Park, Liverpool LI 6 9JD
D. E. Hodgkinson
Affiliation:
Dept. of Mathematical Sci., The University, P.O. Box 147, Liverpool L69 3BX
J. F. Humphreys
Affiliation:
Dept. of Mathematical Sci., The University, P.O. Box 147, Liverpool L69 3BX
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Extract

In this article, we discuss a combinatorial problem arising from the National Lottery. The question considered is the following: Given a works (or any other) National Lottery syndicate of say n persons, how small can n be and still allow to ensure that at least one person in the syndicate has a winning ticket? Of course we will only be able to ensure that the required ticket wins the minimum prize of £10. However, we will show that a system to achieve this end can be constructed using some remarkable combinatorics which are well-known parts of modern mathematics. In fact, the system we propose for this problem has n = 290 and at least two tickets will win £10 prizes. It will be perfectly possible that the system will result in some members of the syndicate winning a fourth, third, second or even first prize. Although the combinatorics are quite interesting, it is not possible to ‘beat’ the National Lottery using our system. We have applied our system to the actual results of the National Lottery since its inception. Our experimental evidence shows that even using our seemingly efficient scheme, payout averages only about 28% of expenditure (showing an average loss of about 72%). However, in a typical draw, our system would actually have produced 5 or so ‘winning’ tickets for the syndicate.

Type
Articles
Information
The Mathematical Gazette , Volume 85 , Issue 503 , July 2001 , pp. 202 - 207
Copyright
Copyright © The Mathematical Association 2001

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References

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