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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.
Déjà vu
Players avoid last week’s numbers because they feel spent, and treat a repeated draw as proof of tampering. Both instincts come from expecting the machine to remember what it did. It has no memory at all — and that single fact makes the first belief backwards and the second one arithmetic.
A number repeating from the last draw is the normal case, not a warning. A whole draw repeating is rare but not suspicious — and most apparent repeats are recording errors, not miracles.
The last fourteen draws
Lit numbers also appeared in the draw above. In a 5-from-50 game chance says 42% of draws will hold at least one number over — then switch to a shuffled history and try to tell the difference.
The most recent draws, oldest first. Lit numbers were also in the draw above.
5 of 13 of these draws repeated at least one number from the draw before it — 38.5% against the 42.3% chance predicts. Switch to a shuffled history and the behaviour does not change.
The machine has no memory. Repeats are normal, and most apparent ones are recording errors.
Every draw, against the model
205 consecutive pairs of Euro Millions Plus draws, beside what a machine with no memory would produce. The average number held over is exactly 5²/50 — 0.500 — and the data agrees to two decimal places.
numbers held over from the previous draw
The machine has no memory. Repeats are normal, and most apparent ones are recording errors.
The coincidence ladder
Nothing in that formula required the two draws to be consecutive, so the same distribution describes every pair of draws in the history — a decade apart just as well as a week. The top rung is the same draw, twice.
21,115 pairs of draws in this history, by how many numbers the two draws had in common.
| Numbers in common | Pairs of draws | Chance predicts | Ratio |
|---|---|---|---|
| 0 | 12,089 | 12,176 | 0.99× |
| 1 | 7,483 | 7,424 | 1.01× |
| 2 | 1,424 | 1,414 | 1.01× |
| 3 | 116 | 99 | 1.18× |
| 4 | 3 | 2.24 | 1.34× |
| 5the same draw twice | 0 | 0.01 | 0.00× |
Every rung is the same hypergeometric formula, evaluated at a different overlap. The machine has no memory of how long ago a draw was, so the distribution that governs consecutive draws governs draws a decade apart just as well — including the top rung, where the two draws are identical.
The machine has no memory. Repeats are normal, and most apparent ones are recording errors.
Has it ever happened?
The instinct is to reach for 1 in 2,118,760 and conclude it could not have. That is the answer to a different question — whether the next draw matches one you name. Drag the history length and watch the real question behave completely differently.
The machine has no memory. Repeats are normal, and most apparent ones are recording errors.
The register
Every combination this game has produced more than once — and a verdict on each. The verdicts exist because the first version of this scan found seven times more repeats than chance allows, and almost all of the excess was bad data rather than remarkable luck.
Euro Millions Plus has never repeated a draw — which is what you would expect, because chance predicted 0.01 of them by now.
The machine has no memory. Repeats are normal, and most apparent ones are recording errors.
Reading the main draw, 206 draws over 2 years. Carry-over is only meaningful within a single draw series — mixing a game’s sub-draws would make “the previous draw” mean the previous different game.
The two layers underneath
Everything on this page is the same formula asked three times.
Take a draw of numbers from a pool of . Now take another draw, made by a machine with no memory of the first. How many numbers do they share?
The second draw is a uniform -subset, and the first draw's numbers are a fixed target inside the pool. That is a hypergeometric setup — drawing without replacement from a population split into "was in the last draw" and "wasn't":
The mean simplifies to something worth remembering:
Each of your numbers has probability of being among the next draw's , and expectation adds regardless of the dependence between them. For a 6/49 that is numbers carried over per draw.
The quantity players actually care about is , and it is the complement of a single term:
For a 6/49: .
More often than not, a 6/49 draw repeats a number from the draw before it. For a 7-from-52 game it is about 66%; for a 5-from-69 game, where the pool is sparse relative to the pick, it drops to 32%. The belief that a number is "used up" for a while has the arithmetic exactly inverted, and the strength of the effect is a property of the format rather than of the balls.
Nothing in that derivation used the fact that the two draws were consecutive. The machine has no memory of a week ago and none of a decade ago either, so the same distribution describes every pair of draws in the history.
With draws there are pairs, and the expected number sharing exactly numbers is . That is the ladder on this page — and its top rung, , is two draws that were completely identical.
Here is where intuition fails hardest.
Asked whether a lottery has ever repeated a draw, people reach for — one in 13,983,816 for a 6/49 — and conclude it could not have happened. But that is the answer to "will the next draw match this specific one?" The real question is whether any of the pairs match, and that count grows quadratically while the space stays fixed.
The expected number of repeats after draws is
and, treating them as approximately Poisson,
Even odds arrive when , which gives
For a 6/49 that is 4,404 draws — around forty years of twice-weekly play. Not the geological timescale the one-in-fourteen-million figure suggests. A game that has been running since the 1980s is not unlikely to have repeated itself; it is roughly a coin flip.
There is one more step, and this page learned it the hard way.
When you hunt for coincidences across many games at once, the expected count rises with every game you add — but so does the number of ways your data can be wrong. Scanning every lottery in this database for repeated draws returns about a third more than chance allows, and essentially none of the excess is remarkable: it is one physical draw recorded under two slot names, or a result posted to two consecutive dates.
The statistical lesson generalises well beyond lotteries. At the scale where coincidences become expected, data errors become expected faster, because they are not competing against a one-in-fourteen-million denominator. Any anomaly hunt that does not model its own error rate will find its bugs first and report them as discoveries.
On 6 September 2009 the Bulgarian national lottery drew 4, 15, 23, 24, 35 and 42. Nobody won.
Four days later, on 10 September, the machine produced 4, 15, 23, 24, 35 and 42 again. This time eighteen people had the ticket.
The reaction was immediate and entirely predictable. The country's sports minister ordered an investigation; commentators explained that the odds were millions to one and that such a thing could not happen by accident. The investigation found no evidence of manipulation, and mathematicians pointed out what the arithmetic on this page says: across the thousands of draws held every week by hundreds of lotteries worldwide, a repeat somewhere is not merely possible but expected.
The Bulgarian case is famous because it was consecutive, which is genuinely rarer than a repeat separated by years. But the instinct it provoked — a coincidence this striking must have a cause — is the one this whole playground exists to examine.
Lottery players hold two convictions about repetition, and they contradict each other.
The first is that a number which came up last week is spent, and should be avoided. This is the gambler's fallacy in its most common costume, and the arithmetic is not close: in a 6/49 game, more than half of all draws repeat a number from the draw before. The "unlikely" thing is the one that happens most weeks.
The second is that a whole draw repeating would be proof of a rigged machine. That one is wrong in the other direction — a repeat is exactly what a fair machine produces once a game has run long enough, and the point at which it becomes likely is far nearer than anybody guesses.
Both beliefs come from the same place: a sense that the machine ought to remember what it has already done. It doesn't. It has no state at all between draws, which is what makes both the carry-over and the eventual repeat inevitable.
Building this page produced a small object lesson, and it seemed dishonest to leave it out.
The first version simply hunted for repeated draws across every game in this database. It found 10,400 of them, against roughly 1,455 that chance allows — a sevenfold excess that, taken at face value, would be the largest anomaly ever reported in a lottery dataset.
It was not an anomaly. It was three separate bugs.
Some games run several sub-draws under one name — South Africa's Lotto has a main draw, Plus 1, Plus 2 and a 5 Max — and the same physical result was filed under two of those slot names, so it looked like the machine had repeated itself within a second. Another game had a stretch in 2024 where results were posted to two consecutive dates, producing sixteen "one in 177,100" events in a single spring. And the search itself had a flaw: it packed each draw into a 64-bit mask, which silently dropped every number above 64, making Powerball's 65 to 69 invisible and manufacturing a clean, plausible, entirely fictional deviation.
Only the last of those was our own code, and it was the most dangerous, because it did not look like a bug. It looked like a finding.
Every claim on this site is an anomaly hunt of some kind: is this number hot, is this pair unusual, is this machine fair. The honest version of that work spends most of its effort on the boring question — could this be an artifact? — because at the scale where genuine coincidences start appearing, mistakes are appearing much faster.
The register on this page is what survived that question. It shows the repeats we believe, the number chance predicted, and the ones we threw out and why. It is a shorter list than the first version produced. It is also true.