Gamblers Never Change their Habits

Abstract

In the game ‘6 out of 45’ the gambler has to guess 6 different numbers out of 45. These guesses are far from being uniformly distributed, instead gamblers prefer certain numbers and avoid others. This paper discusses the influence of the gamblers’ behavior on the probability that no one will guess all 6 numbers correctly. This probability is important because if such an event occurs the turnover of the next round will be significantly increased. Furthermore a fast simulation program is described that was developed on the basis of the above mentioned analysis and which aims to predict the behavior of the game during longer periods of time.