Benford's law and number selection in fixed-odds numbers game

Area of Science:

• Mathematics
• Statistics
• Behavioral Economics

Background:

• Fixed-odds games present risks for both players and operators due to luck.
• Operators often limit liability with sales caps, potentially losing business.
• Determining optimal sales limits is a key challenge for game operators.

Purpose of the Study:

• To investigate the relationship between player number selection behavior and sales limit setting.
• To quantify the phenomenon of players favoring numbers linked to real-world events.
• To connect this player behavior to Benford's Law for a novel modeling approach.

Main Methods:

• Empirical analysis of player betting patterns in fixed-odds numbers games.
• Quantification of non-uniform number selection probabilities.
• Application of Benford's Law to model player choices.
• Development of a choice model for sales limit optimization.

Main Results:

• Empirical evidence shows players do not select numbers uniformly.
• Players exhibit a bias towards smaller numbers associated with personal events (e.g., birthdays).
• This selection bias is quantifiable and relates to Benford's Law.

Conclusions:

• Player number selection is not random and can be predicted.
• A novel model connecting player behavior and Benford's Law can inform sales limit strategies.
• This approach allows operators to set more effective sales limits, balancing liability and revenue.