Investigating the behavioural characteristics of lottery players by using a combination preference model for conscious selection
Summary.  Conscious selection describes the process by which lottery players choose numbers non-randomly on their tickets. The only theoretical model that has been produced to date models conscious selection as number preference; for example players may tend to choose ‘lucky’ numbers. This model, however, does not fit the observed distributions of the numbers of winners of prizes well. We present a theoretical model in which clusters of similar number combinations are preferentially chosen. This three-parameter model gives a convincing visual fit to the long-tailed distributions of numbers of winners and accurately reproduces the correlations between the numbers of winners of the various tiers of prize. Our model is fitted to lottery data and the fit is compared with those of previous models that have been employed for conscious selection. We then use the model to contrast features of lottery player behaviour in two of the biggest lotteries in the world: the UK National Lottery game, lotto, and Spain's El Gordo de la Primitiva. Finally, we use the model to detect any changes in UK player behaviour over time.