Modelling of how lotto players select their number combinations dynamically

ABSTRACT

By examining a unique dataset, the authors build a time series model that can describe the dynamics of lotto players’ betting behaviour. The results are derived from a database maintained by a lottery operator in Taiwan, which consists of number combinations selected by players for 203 consecutive draws in 2 years, including those placed through certain systematic schemes. The dynamic models that the authors established show that the players’ number selection over time is influenced by three factors: the numbers that they chose in the last draw, the winning numbers of the previous draw and the numbers with the highest observed winning frequencies in the past. The first factor reflects the mean-reverting nature of the lotto players’ selection behaviour. The second reaffirms the well-known gambler’s fallacy in which players believe that they can improve their chances of winning by avoiding numbers that recently won. The third exhibits the players’ bias towards certain numbers with an above-average probability to be drawn. The two latter types of misconceptions are found to be more predominant in systematic betters, which suggests that the extent of the lotto players’ behavioural biases may vary according to how they place their bets.

KEYWORDS:

• Bias
• decisions
• gambling
• lotteries
• cognition

Acknowledgements

We are indebted to the editor and the three anonymous referees for their comments and suggestions that have led to significant improvements in the article.

Conflicts of interest

Competing interests

The authors have no conflicts of interest to declare in relation to this article.

Constraints on publishing

The authors declare that there were no constraints on publishing

Notes

1. As explained in the next section, our dataset, which consists of all number combinations selected by lotto purchasers, contains no background information about the players. Therefore, throughout this article, the term ‘lotto players’ is interpreted as the collection of all tickets instead of participants. In other words, the behavioural patterns that we conclude are on ticket basis and aim to infer general trends for the market or the player population as a whole.

2. We also investigate the ranks of picking frequencies during the winning-number announcements. The picking frequencies are ranked from 1 (least picking frequency) to 42 (most picking frequency). The result of the significant drop is similar to those reported in Figure 1. The average picking frequency on winning numbers drops immediately from a rank of 21.2 at the hitting draw to 10.4 after the first day of the draw.

3. One explanation for this is the difference between the rules of the two games. The probability that the three-digit winning numbers would repeat is lower than that for an individual winning number for the lotto game.

4. The last 99 draws represent one year of observations.

5. We also analyse the player’s reaction to winning number hits by investigating ‘Hot winner’ and ‘Cold winner’ groups. The ranked frequencies are assigned to six quintile groups according to winning frequencies within the last 99 draws. The highest quintile group is called the ‘Hot winner’ group, and the lowest quintile group is called the ‘Cold winner’ group. The results are not presented here because they are similar to those in Figure 3.

6. Using a hot number defined by the top 5 or 10 winning numbers produces similar figures.

7. In the case where the dummy variable HOT is defined for the last 30, 50 or 150 draws, the results are similar.

Additional information

Funding

This work was partially supported by the Ministry of Science and Technology, R.O.C. (Taiwan) [grant number MOST 106-218-M-001-008].

Notes on contributors

Hwai-Chung Ho

Hwai-Chung Ho, PhD, is a professor of finance at the National Taiwan University and a research fellow of the Institute of Statistical Science, Academia Sinica. His major research areas are time series analysis, financial statistics and behavioural finance. He had served as co-editor of an international statistical journal, Statistica Sinica, and as supervisor and board director of the Taiwan Financial Holding Company.

Shih-Chin Lee

Shih-Chin Lee, PhD, is an associate professor of finance at Chihlee Institute of Technology, Taiwan. His main research interests include lottery gambling, decision-making and behavioural finance. He has conducted research projects on lottery players’ behaviours funded by the Ministry of Science and Technology, and was invited to participate in a research project aimed to invent an effective method to detect abnormal trading transactions in a major Taiwan stock exchange.

Hsiou-wei Lin

Hsiou-wei Lin received his PhD in business from Stanford University. He is currently a professor at the Department of International Business, National Taiwan University, and a professor and dean of the College of Business, Chinese Culture University. His interest in the fields of finance and accounting is broad, but with a focus on strategic and behavioural issues regarding security analysts’ forecast reports, multiple hypothesis testing (multiple comparisons) bias, venture capital finance, and public offering of firms.