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 Maximum Entropy Data Analysis

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.

From our estimate of the popularity of each of the 14 million tickets in the UK National Lottery, we deduce the popularity of individual numbers. The results were derived using a commodity supercomputer. Players prefer to pick lower numbers and those towards the centre of the ticket.

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Denis Nicole, Kenji Takeda, Ivan Wolton, Geoff Daniell


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., Manchester. p551-557

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.

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