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Reading the draws and working out what chance predicts.
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Reading the draws and working out what chance predicts.
Balls versus RNG
A lottery is drawn one of two ways: balls tumbling in a machine, or a certified random number generator. The failure modes have nothing in common. A ball can be a fraction heavier than its siblings; software cannot. Software can be seeded from the clock, or have a back door written into it by the man who wrote it; a ball machine cannot.
Balls versus RNG76 draws
Scroll the chart sideways →
| Game | Slots | Days | Correlation | Adjusted p |
|---|---|---|---|---|
| Pick 3 | morning / night | 1,174 | 0.184 | 0.000 |
| Pick 2 | day / evening | 2,000 | -0.058 | 0.757 |
| Cash 3 | evening / midday | 1,475 | 0.033 | 1.000 |
| Cash 4 | evening / midday | 1,474 | -0.018 | 1.000 |
| Pick 3 | evening / midday | 102 | -0.101 | 1.000 |
| Pick 4 | evening / midday | 101 | 0.006 | 1.000 |
| Daily 3 | evening / midday | 1,627 | -0.016 | 1.000 |
| Pick 3 | evening / midday | 1,088 | -0.032 | 1.000 |
| Play 3 | day / night | 2,000 | 0.002 | 1.000 |
| Play 4 | day / night | 2,000 | -0.011 | 1.000 |
| DC-3 | 1_50pm / 7_50pm | 2,000 | 0.010 | 1.000 |
| DC-4 | 1_50pm / 7_50pm | 2,000 | 0.021 | 1.000 |
| DC-5 | 1_50pm / 7_50pm | 2,000 | 0.040 | 1.000 |
| Play 3 | day / night | 2,000 | -0.000 | 1.000 |
| Play 4 | day / night | 2,000 | -0.000 | 1.000 |
| Pick 2 | evening / midday | 2,000 | -0.019 | 1.000 |
| Pick 3 | evening / midday | 2,000 | -0.013 | 1.000 |
| Pick 4 | evening / midday | 2,000 | -0.007 | 1.000 |
| Pick 5 | evening / midday | 2,000 | 0.023 | 1.000 |
| Cash 3 | evening / midday | 2,000 | 0.019 | 1.000 |
No game shows any relationship between its own draws of the day. Across 75 games the correlations run from -0.101 to 0.056, which is what independent draws look like.
One limitation worth stating. A generator so badly broken that it emitted the same draw twice a day would look exactly like a duplicating feed, and its evidence would be excluded with theirs. From the numbers alone the two are identical, so the duplication rate is reported as its own finding rather than folded away.
Cross-slot and method comparisondraw-method-v1
Balls versus RNG17 draws
| Game | Identical days | Rate |
|---|---|---|
| Pick 4 | 1,495 | 59.5% |
| Pick 3 | 1,494 | 58.5% |
| Pick 3 | 1,489 | 57.8% |
| Cash 4 | 1,568 | 51.5% |
| Cash 3 | 1,567 | 51.5% |
| Pick 3 | 1,490 | 48.9% |
| Daily 3 | 1,488 | 47.8% |
| Numbers Game | 1,486 | 47.7% |
| Pick 3 | 413 | 26% |
| Cash 3 | 99 | 7.8% |
| Cash 4 | 96 | 7.6% |
| Pick 3 | 76 | 3.7% |
| Pick 4 | 76 | 3.7% |
| Cash 3 | 52 | 2.5% |
| Cash 4 | 49 | 2.4% |
| Pega 2 | 7 | 1.6% |
| Pick 2 | 22 | 1.1% |
This is a fault in the record, not in the machine, and it is severe: on the worst games the second slot is a copy of the first on well over half the days. Those pairs are excluded from the correlation above — left in, they produced correlations of 0.4 to 0.63 on games that are almost certainly fine.
Balls versus RNG0 draws
Not enough games have a draw method on record yet to compare the two populations. The five seeded below are the ones whose own results name the machine and ball set that drew them, which is the operator stating it draw by draw.
Which games are drawn by ball and which by software is not in any feed. It has to be read from each operator’s published draw procedure, one at a time, with the source recorded — so this table fills up slowly and is honest about being mostly empty. A game with nothing on record is left out, never assumed.
Balls versus RNG76 draws
Cross-slot and method comparisondraw-method-v1
The test. For a game drawing twice a day, pair the two slots by date, take each draw's digit sum, and compute Pearson's correlation between the two series. Under independence it is zero; a generator seeded from the date would make it positive.
The p-value comes from shuffling one series against the other rather than from a table. The digit sum of three digits is bounded, discrete and not quite normal at these sizes, and a permutation needs no assumption at all:
The correction has to be achievable. Seventy-four games are tested, so each p is multiplied by seventy-four and read against a plain 5%. A permutation p cannot fall below , so with 199 shuffles the smallest possible adjusted p would be — the test could never fire. Two thousand shuffles put the floor at 0.037, under the level. This is the same arithmetic that governs every corrected permutation test on this site, and it is easy to get wrong in the direction that silently disables the instrument.
Identical pairs are excluded, and counted separately. Two independent three-digit draws match on about one day in a thousand. In this archive fourteen games match on far more than that — several on more than half of all days — because one physical draw has been filed under two slot names. Those pairs are removed before the correlation, because leaving them in produced correlations of 0.4 to 0.63 on games that are almost certainly fine.
Grouping by draw method. One omnibus fairness p per game, grouped by whether the game is drawn with balls or by software, compared with a two-sample Kolmogorov-Smirnov test. Under the null that both methods are fair, every p is uniform on and the two groups are the same distribution, so the KS asks exactly the right question. It needs the method table filled in, which is human work and is mostly not done.
This page was built to ask whether it matters how a lottery is drawn — balls in a machine, or software. That question turns out to need something no data feed contains: which games use which. It has to be read out of each operator's published draw procedure, one at a time, and that work is barely begun.
But the other half of the page needed nothing curated at all, and it found something.
About seventy-four games in this archive draw twice or three times a day. If a generator were seeded from the date — the single commonest way to get this wrong, and the shape of the fault Eddie Tipton built deliberately — then the day's draws would be related to each other. So: pair the slots by date, correlate their digit sums, and shuffle the days apart to see what chance produces.
The first run came back with nine games showing correlations between 0.4 and 0.63. A correlation of 0.63 between two draws that are supposed to be independent would be the largest finding this site has ever made.
It was not a finding. It was the record.
Fourteen games file one physical draw under two slot names. North Carolina's Pick 4 has an identical "midday" and "evening" result on every single day from 2017 through 2021, then stops dead on 22 November 2022 — the date a data feed changed format. Kansas, Colorado, Rhode Island, Arkansas, New Mexico and California carry the same thing. Twelve and a half thousand pairs in all.
Two independent three-digit draws come out identical about one day in a thousand. These games do it on half of them. That is not a machine failing; it is a row being written twice.
With those pairs excluded, the correlations collapse to a range of −0.075 to +0.056, averaging 0.0009. Not one game of the seventy-four shows any relationship between its own draws of the day. That is the honest headline, and it is a good one.
There is a limitation to state plainly. A generator so badly broken that it emitted the same draw twice a day would look exactly like a duplicating feed, and this page would exclude its evidence along with theirs. From the numbers alone the two situations are identical. So the duplication rate is reported here as a finding in its own right rather than quietly filtered away, and a reader can judge which explanation they believe.
The duplication is almost certainly the record. But this page is not in a position to prove it, and says so.