Willingness to pay and the demand for lotto

Abstract

Why do many bettors participate in an unfair gamble, in particular a lotto game, while at the same time purchase insurance? The willingness-to-pay for lotto is analysed to find a ‘rational’ explanation for a (local) risk-averter's participation in an unfair bet. A reasonable case is found where bettors’ preference can be approximately characterized as a locally risk-averse and sufficiently prudent cubic function. Such bettors dislike risk but prefer standard third moment of the payoff. The result suggests that the traditional effective price for lotto demand may omit important explanatory variables. We thus propose an alternative method to examine the demand for lotto by incorporating the second and the third moments of lotto's payoff. Evidence from Taiwan Lotto data supports that lotto bettors could be both (locally) risk-averse and rational.

Notes

¹ Golec and Tamarkin (1998), p. 210.

² The game structure also matters from this perspective, for example, whether a given lotto should be made more difficult by increasing its total numbers to be chosen. On the practical level, all these questions are interesting and important. This study only notes them in passing.

³ 50 NT dollars is approximately $1.47 or €1.31.

⁴ The rollover can last up to five turns. If no one wins the grand prizes in five consecutive turns, there are some additional complications. This scenario is ignored since no such event has happened so far.

⁵ The number of possible combinations is given by .

⁶ Surely this is inconsistent with the so-called ‘conscious selection’ phenomena (Cook and Clotfelter, 1993). However, Walker (1998) and Farrell et al. (1999) find that conscious selection has very little effect on the expected value of a lotto ticket at observed lotto sales magnitudes. An interesting paper, which adopts different perspective from the present study, is Papachristou (2004).

⁷ The calculation of the effective price departs from that of literature, which uses a Poisson distribution to approximate the binomial distribution. The departure is made because the same procedures will be used to calculate the second and third moments of the random payoff of a lotto ticket.

⁸ Forrest et al. (2000) experimented with four lags of the sales to capture a richer pattern of habit persistence. However, Forrest et al. (2000) and Forrest et al. (2002) find that lags of order two and above were jointly insignificant. To make a close comparison with Forrest et al. (2000), four lagged sales are still used.

⁹ The results are qualitatively the same when skewness instead of Standard Third Moment is used.