Trying To Be Random in Selecting Numbers for Lotto

Abstract

In the lottery game Lotto n/N, the winning n numbers are selected randomly and without replacement from {1, 2, 3, ..., N}. The selection of the winning numbers is normally done with a highly sophisticated mechanical device, and one of the appealing aspects of Lotto is that this procedure is seen to be fair and unbiased. An important perceived consequence is that no one (for a given amount of money) is seen to have a better chance of winning than anyone else. Few people would be willing to let an individual perform this task because of possible bias, but do we really know how difficult it is for an individual to be random in selecting numbers? In an experiment to observe the types and degrees of bias an individual might possess, data were collected from students who were asked to perform as 'random' number generators for the Lotto 6/42 game. Data consisting of the winning numbers from the Irish National Lottery game Lotto 6/42 were obtained from previous years, and a statistical package (in this case, S-Plus) was used to generate other simulated data. A comparison of the three sets of data using many of the basic tools in descriptive statistics together with some goodness of fit tests provides a useful exercise for students to test their intuition about randomness and to discover some of the inherent (and sometimes subtle) biases individuals possess when they attempt to be random.

Keywords:

• Bias
• Boxplots
• Chi-squared tests
• Lottery
• Minimum gap
• QQ plots