We have used
the Maximum Entropy method to estimate the probability of each
of the 14 million tickets being chosen by players in the UK National
Lottery. As data, we used the numbers of winners in the 3, 4,
and 5-match categories and the total number of tickets sold in
each of the first 113 draws. We have computed the marginal distributions
for players choosing single numbers and pairs of numbers. A striking
conclusion is that players preferentially pick numbers towards
the centre of the ticket. By choosing unpopular combinations of
numbers, one’s expected winnings can be doubled. This work
was performed in collaboration with the Physics department.
Nicole, D.A., Takeda, K, Wolton, I.C.W., and Cox, S.J., 1998.
HPC on DEC Alphas and Windows NT. Proc. HPCI 1998 Conf.,
Cox, S.J., Nicole, D.A., and Takeda, K., 1998. Commodity High
Performance Computing at Commodity Prices. WoTUG-21, Proceedings
of the 21st World occam and Transputer User Group Technical Meeting.
(IOS Press) 19-26.
Cox, S.J., Daniell, G.J., and Nicole, D.A., 1998. Maximum Entropy,
Parallel Computation and Lotteries. Proc. International Conference
on Parallel and Distributed Processing Techniques and Applications
(PDPTA '98). 1252-1258.
Cox, S.J., Daniell, G.J., and Nicole, D.A., 1998. Using Maximum
Entropy to Double One’s Expected Winnings in the UK National
Lottery. Journal of the Royal Statistical Society D.
47 (4) 629-641.