The short answer
Nothing in the archive suggests these draws are anything other than random. Across the 13 number pools of the six games, none shows a spread of counts outside the range chance usually produces (p below 0.05), and in every game consecutive draws share numbers at the rate independent draws should. That is what the tests can say. What they cannot say — and what this page is really about — is explained at the end.
What random actually looks like
A fair draw does not give every number the same count. Take Powerball: in 1,387 draws, each of the 69 white balls is expected 100.5 times. The real counts run from 76 to 127 — a gap that looks large, and that people often read as a pattern. But random counts are supposed to scatter: with a standard deviation of 9.7, about 95% of numbers should land within 19.3 of the expected count, and a handful outside it. 63 of the 69 do.
So the right question is never "why is this number ahead?" but "is the whole spread wider or narrower than chance produces?". That is what a chi-square test measures.
Test 1: do the counts spread the way chance predicts?
For each pool we compare every number's count with its expected count, using only draws made under the pool's current rules, and turn the total deviation into a p-value: the chance that a perfectly fair draw would look at least this uneven. Values near 0 mean "more uneven than chance usually produces"; anything above about 0.05 is ordinary.
| Game & pool | Draws | Expected per number | Lowest – highest count | Within 2 SD | p-value |
|---|---|---|---|---|---|
| Powerball white balls (5 of 69) | 1,387 | 100.5 | 76 – 127 | 63 of 69 | p = 0.10 |
| Powerball red Powerball (1 of 26) | 1,387 | 53.3 | 40 – 68 | 25 of 26 | p = 0.47 |
| Mega Millions white balls (5 of 70) | 934 | 66.7 | 53 – 87 | 68 of 70 | p = 0.61 |
| Mega Millions Mega Ball (1 of 24) | 158 | 6.6 | 2 – 13 | 23 of 24 | p = 0.36 |
| UK Lotto main numbers (6 of 59) | 1,125 | 114.4 | 94 – 132 | 58 of 59 | p = 0.94 |
| UK Lotto Bonus Ball (1 of 59) | 1,125 | 19.1 | 10 – 28 | 57 of 59 | p = 0.60 |
| EuroMillions main numbers (5 of 50) | 1,125 | 112.5 | 79 – 133 | 48 of 50 | p = 0.46 |
| EuroMillions Lucky Stars (2 of 12) | 1,048 | 174.7 | 157 – 204 | 11 of 12 | p = 0.16 |
| EuroJackpot main numbers (5 of 50) | 800 | 80.0 | 65 – 97 | 49 of 50 | p = 0.83 |
| EuroJackpot Euro Numbers (2 of 12) | 475 | 79.2 | 65 – 99 | 11 of 12 | p = 0.21 |
| SuperEnalotto main numbers (6 of 90) | 1,839 | 122.6 | 90 – 147 | 84 of 90 | p = 0.53 |
| SuperEnalotto Jolly (1 of 90) | 1,839 | 20.4 | 12 – 32 | 88 of 90 | p = 0.88 |
| SuperEnalotto SuperStar (1 of 90) | 1,839 | 20.4 | 12 – 34 | 85 of 90 | p = 0.28 |
Two things to keep in mind when reading it. First, with 13 tests, about one p-value below 0.1 and occasionally one below 0.05 is expected even if every draw is perfectly fair — so a single low value in a table like this is not evidence of anything. Second, the small pools with few draws (the Mega Ball since its April 2025 change, for instance) cannot detect much at all: each number is expected only a handful of times, and a test on counts that small has little power.
Test 2: does one draw remember the last?
If a machine had any memory — or if our data had copied one draw into the next — consecutive draws would share numbers more (or less) often than independent draws do. For independent draws the share of draws repeating 0, 1 or 2+ numbers from the previous draw follows the hypergeometric distribution, which depends only on the game's format.
| Game | Draw pairs | No repeat | 1 repeat | 2 or more | p-value |
|---|---|---|---|---|---|
| Powerball | 1,386 | 945 (940 expected) | 393 (392 expected) | 48 (54 expected) | p = 0.71 |
| Mega Millions | 933 | 626 (637 expected) | 275 (261 expected) | 32 (35 expected) | p = 0.54 |
| UK Lotto | 1,124 | 591 (573 expected) | 416 (430 expected) | 117 (122 expected) | p = 0.55 |
| EuroMillions | 1,124 | 659 (648 expected) | 389 (395 expected) | 76 (81 expected) | p = 0.76 |
| EuroJackpot | 799 | 461 (461 expected) | 278 (281 expected) | 60 (57 expected) | p = 0.93 |
| SuperEnalotto | 1,838 | 1,224 (1,200 expected) | 525 (547 expected) | 89 (91 expected) | p = 0.50 |
Observed and expected agree within normal chance variation for every game. For UK Lotto the test uses Round 1 draws only, so the two rounds of one night are never compared with each other.
What this does — and does not — tell you
Passing these tests does not prove a draw is random; no finite set of results can. It means the archive gives no reason to think otherwise, and that a number's high or low count is the ordinary scatter of chance. It also means the reverse of what many "lottery statistics" suggest: if the draws are behaving randomly, then past counts carry no information about the next draw. A number that has been drawn often is not more likely to come up, and one that has been missing is not "due". We tested that directly in Hot and cold numbers, tested.
Operators certify their draw equipment and hold draws under independent supervision; that is where fairness is actually guaranteed. What a public archive like ours can do is let anyone check the published results for themselves — each game's Statistics page runs the same test on its own pools, and the formulas are on the methodology page.