DISTRIBUTION AND RUN TESTS OF THE LAST TWO DIGITS IN GOVERNMENT LOTTERY RESULTS
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Abstract
This research aims to: 1) analyze the frequency distribution of the last two digits of the first prize and the two-digit lottery prizes, 2) study the correlation between the digit positions of the last two digits in the first prize and the two-digit prizes, and 3) test the runs of high digits (5-9) and low digits (0-4) for the last two digits of the first prize and the two-digit prizes. This study examines 825 government lotteries drawn from the past 35 years (1990 to 2024), analyzing the last two digits of both the first prize and the two-digit prizes. The statistical methods used include frequency classification, percentage, chi-square test, Pearson correlation coefficient, Z-test, and run test.
The research results revealed that 1) regarding the frequency distribution, for the first prize’s last two digits, the most frequently drawn digits in the tens and units positions were 5 and 7, and 7 and 4, respectively; for the two-digit prize, the most frequently drawn digits in the tens and units positions were 9 and 6, and 9 and 5, respectively; the frequency analysis showed significant deviations uniform distribution for the first prize’s units digit and both digits of the two-digit prize (χ2 = 22.430, 22482 and 17.582, p-value < 0.05), 2) regarding the parity analysis (odd-even distribution), the draws of the last two digits for both the first prize and the two-digit prize showed similar occurrences of odd and even numbers; chi-square tests for the parity relationship across the four positions found no statistically significant correlation; correlation coefficient analysis between the four positions also indicated no statistically significant relationship, and 3) regarding the run test for high and low digits, the analysis of runs for high (5-9) and low (0-4) digits from January 16, 1990 to May 16, 2024 showed random patterns in the arrangement of these digits in both the first prize and the two-digit prizes indicating no significant patterns. The conclusion of the statistical analysis of the last two digits for the first prize and the two-digit prizes indicates transparency in the lottery drawing process, as observed through the randomness and lack of systematic patterns in the results.
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