Abstract
This chapter applies Benford's law to study how players choose numbers in fixed-odds number lottery games. Empirical data suggests that not all players choose numbers with equal probability in lottery games. Some of them tend to bet on (smaller) numbers that are closely related to events around them (e.g., birthdays, anniversaries, addresses, etc.). In a fixed-odds lottery game, this small-number phenomenon imposes a serious risk on the game operator of a big payout if a very popular number is chosen as the winning number. The chapter quantifies this phenomenon and develops a choice model incorporating a modified Benford's law for lottery players to capture the magnitude of the small-number phenomenon observed in the empirical data.
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