The British gambler's fallacy

Abstract

People facing choices under uncertainty, and gamblers in particular, are often subject to statistical fallacies. This paper explores the hypothesis that if lotto players were subject to the ‘gambler's fallacy’, predictable fluctuations in the number of jackpots would occur. Evidence, based on a Poisson regression model in which the number of winning bets is conditional on the history of draws, indicates that number selection in the UK is only marginally affected by the history of draws.

Acknowledgements

The author would like to thank Dimitri Mavridis for his assistance in collecting and processing the data.

Notes

The basic references in the literature of Poisson regression and count data are Gourieroux et al. (1984) and Cameron and Trivedi (1986). Most of what follows is based on Cameron and Trivedi (1998) and the references cited therein.

Although the size and statistical significance of the intersect is irrelevant for the hypothesis in hand, a significantly negative intersect would indicate that popular numbers exist.

Data and information on the UK National Lottery is available from Camelot's official site http://www.national-lottery.co.uk. However, data are stored in a more convenient format in http://lottery.merseyworld.com.

Maximum likelihood estimates were obtained using the Raphson–Newton algorithm given the analytical expressions for the gradient and the Hessian of the log-likelihood function; standard errors were obtained under various specifications of the variance matrix. All calculations were performed in Matlab™.

Data and information on the Greek 6/49 Lotto were obtained from Papachristou and Karamanis (1998).