台灣樂透市場投注者選號行為之研究

Abstract

Although lotto games are better suited for testing the nature of human rationality than stock markets or laboratory designs in experimental psychology, insufficient attention has been given to the quantitative analysis of the lotto players’ behavior. This may be due to the fact that analyzing the behavior of lotto participants requires the exact frequencies of numbers chosen by the players and, unfortunately, lottery operators seldom release such data. The most well-known cognitive bias exhibited by lotto players is the gambler’s fallacy, which infers that people underestimate the repetition of recent signals from a random binary series. In the first part, we introduce a method that enables us to test whether the numbers drawn in the past have any impact on the players’ selection of numbers without using the exact distribution of the numbers chosen. We apply this method to the Taiwan 6/42 lotto game and obtain two main findings. First, we show that the short horizon betting behavior of Taiwan lotto players is strongly consistent with the gambler’s fallacy. Second, consistent with the notion of Type II gambler’s fallacy (Keren and Lewis, 1994), these same players tend to pick those numbers that have been drawn most frequently in the past. The gambler’s fallacy can be explained by the representativeness heuristic, while the type II gambler’s fallacy in number selection may be resulted by the availability heuristic, since winning numbers with higher occurrence rates come to mind more easily than those with low occurrence frequencies. Our finding is the first in the literature that presents statistically significant evidence of lotto players falling in two types of fallacies both. The purpose of the second part is to study the behavior of the Taiwan lotto players by developing various dynamic regression models. The data collected for our analysis are accurate and precise since we exhaust a large database of lotto players choices of the number combinations maintained by the only lottery operator in Taiwan. There are three main results in this study. First, the gambler’s fallacy temporarily influences players’ selection of lotto numbers. Second, such negative influence can be partially offset by picking the numbers that appeared more frequently in the past. Third, the players using the system bet strategy have more misconceptions about random processes than the players using the ordinary bet strategy. The first two findings are related to Rabin and Vayanos (2005) model, which states that people judge the performance of a signal depending not only on the luck with reversals, but also on the underlying state with persistence.