The numbers

Is it random?

The standard tests, and what they say about these draws.

Please read

For important limitations, see the Disclaimer.

How to read this page. A fair lottery should pass these tests — that is the expected result. If one does flag something, likely reasons include sample size, an uneven number of draws per lottery, or how the source documents were read.

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Are the digits evenly spread?

Checks whether digits 0–9 appear about equally often. A p-value of 0.05 or above is consistent with chance.

Statistic
49.964
p-value
0.0000
Critical value (0.05)
16.919
Sample
324,863

The observed distribution differs from a perfectly even spread.

The same test, position by position

Position Statistic p-value Sample Looks like chance?
Position 1 from the right 106.538 0.0000 79,689 Deviates (p < 0.05)
Position 2 from the right 127.086 0.0000 79,689 Deviates (p < 0.05)
Position 3 from the right 126.613 0.0000 79,689 Deviates (p < 0.05)
Position 4 from the right 51.574 0.0000 79,689 Deviates (p < 0.05)
Position 5 from the right 117.094 0.0000 3,054 Deviates (p < 0.05)
Position 6 from the right 642.765 0.0000 3,053 Deviates (p < 0.05)

How much variety is there?

Measures how evenly the digits are spread. 1.0 is perfectly even.

Entropy (bits)
3.3218
Normalised
1.0000

Entropy summarises how evenly digits are spread. A value near 1 is close to even.

Do odd and even alternate the way chance predicts?

Checks whether the last digit alternates between odd and even as often as independent draws would.

Runs
9,770
Expected by chance
10,000.8
p-value
0.0011

The alternation differs from the usual random range. Review the ordering and sample size alongside it.

Does one draw hint at the next?

Checks whether one draw’s last digit carries information about the next. In a fair lottery it should not.

The relationship falls outside the usual range. Review the sample size and ordering alongside it.

Gap Correlation Outside the expected band?
1 0.01858 Yes
2 0.02837 Yes
3 0.02999 Yes
4 0.02522 Yes
5 0.01595 Yes
6 0.00986 No
7 0.00916 No
8 0.01337 No
9 0.01223 No
10 0.00139 No

Based on 20,000 ordered observations. Even random data puts roughly 1 lag in 20 outside the expected band.