Are the govt lottery results really fair?
The government lottery results on February 1, 2013 were as follows: the first prize number was 565566 and the two-digit prize number was 66. The last two digits of both prizes correspond to the last two digits of the prime minister's auto licence plate.
On the February 16 draw, the first prize and the two-digit prize numbers were 368257 and 09, respectively. The last two digits of the prizes corresponded to the age (57) and the ballot number (09) of one candidate in Bangkok’s gubernatorial election.
The above phenomena may make one wonder whether the lottery results are fair. In particular, the first phenomenon might seem especially amazing because the probability of this event happening is quite low – equal to 0.0001 per cent, or one in 10,000 draws. With only two lottery draws every month, the probability is only once in 417 years.
The statistical tests used in this article are employed to determine if the draws are fair. The tests concentrate only on some important lottery prizes, for example the first prize, three-digit prize, and two-digit prize. The tests cover four periods. The first period started when the Government Lottery Office began to use the “Ladkrabang 6” lottery drawing machine. The first period spans June 16, 2002 to February 16, 2013 (257 draws). The second period covers the tenure of the former government, starting from December 30, 2008 to June 16, 2011 (60 draws). The third period covers the present government taking office, starting July 1, 2011, to February 16, 2013. The fourth period covers June 16, 2001 to June 1, 2002 (24 draws).
This research article uses a statistical method called the Chisquare test. The question as to the fairness of the results is an important one. If the results are not fair, somebody might be able to take advantage of the results, such as operators of the underground lottery. The results from the investigation are as follows. For the first period, the draws for the first prize are unfair, at a statistically significant level of 95 per cent confidence. The deviation from a fair result is the highest at last digit position and the third-from-last digit position.
The two-digit prize is also unfair, at an 80 per cent level, especially the deviation in the second-from-last digit position. For the second period, the first prize is unfair, at a 95 per cent confidence level, especially the deviation in the last digit position. For the third period, the first prize is unfair, at an 85 per cent confidence level, especially the deviation in the third-from-last digit position. Moreover, the two-digit prize is also unfair, with the same confidence level as the result for the first prize, especially the deviation in the last digit position.
Lastly, in the fourth period, every important prize result (first prize, three-digit prize, and two-digit prize) are fair, at a 95 per cent confidence level.
For the first period, the results for the first prize or two-digit prize show repeated digit results 47 times out of 257 draws. This is a frequency equal to 18 per cent. The phenomenon, similar to the February 1, 2013 draw, occurred on the October 1, 2003 draw. The number 66 has occurred five times in the last 10 years, which is about two times the expected frequency. Similarly, repeated digit results occurred in the second and third periods with a frequency twice that expected.
Theeraporn Verathaworn
Assoc Prof Chulalongkorn University’s Department of Statistics.
