Lottochaos

Analyses: observed versus expected

Each statistic on this page is shown next to the value you would expect if the draws were purely random. The expected values are calculated exactly (by counting all 2,118,760 combinations or by closed-form formulas), not simulated. The result in advance: everywhere, the observed values stay within the range of chance.

1988 draws · 13.02.2004 – 09.10.2026 · Exact expected values assuming uniform 5 from 50 draws

Are the five numbers clustered?

The linear span is the distance from the smallest to the largest number (end positions included). The circular span reads the numbers 1 to 50 on a circle where 50 touches 1: the draw 4, 5, 7, 48, 50 is then no longer spread over 47 positions but concentrated in 10. The bars show the distribution of draws by span, observed and expected.

Linear span

Mean: observed 35.1, expected 35.0

Observed Expected
5–9 0 / 2.8
10–14 22 / 23.2
15–19 68 / 73.9
20–24 157 / 156.0
25–29 260 / 259.0
30–34 367 / 360.5
35–39 423 / 426.7
40–44 402 / 411.7
45–49 271 / 258.0
50–50 18 / 16.2

Circular span

Mean: observed 29.0, expected 28.8

Observed Expected
5–9 0 / 3.3
10–14 28 / 30.3
15–19 102 / 110.0
20–24 277 / 271.9
25–29 537 / 541.9
30–34 751 / 739.1
35–39 292 / 290.4
40–41 1 / 1.2

The tightest draws

A circular span of at most 10 has a probability of 0.30% in a random draw. So 5.9 were expected; there have been 1.

DateWinning numberscircularlinear
04.06.201331333437401010
23.04.201314710501150
09.09.202217232426271111
07.05.202435364142451111
16.07.201038394546491212
11.02.201112141519231212
06.07.201231323840421212
19.05.201526303135371212
09.10.20151404243471247
11.09.202034384243451212
03.02.202626272834371212
19.03.200433363742451313

What carries over from the previous draw?

For each draw, we count how many of its five numbers were already in the immediately preceding draw. The expected distribution is hypergeometric: 5 drawn from 50, of which 5 are marked.

Exact repeats

Mean: observed 0.494, expected 0.500

Observed Expected
0 1146 / 1,145.8
1 706 / 698.6
2 129 / 133.1
3 6 / 9.3
4–5 0 / 0.2

Neighbours of the previous draw

Average number of winning numbers that are direct neighbours (±1, circular) of a number in the previous draw, without having been drawn in it themselves.

0.896
Observed
0.882
Expected

The last draw contains no information about the next one. Replaying the latest numbers or their neighbours gives exactly the same chances as any other combination.

The slip as a heat map

The 50 numbers laid out as on the play slip (five rows of ten). The darker the cell, the more often the number has been drawn. The expected value is the same for all; the differences are the normal scatter of a binomial distribution.

All time

1988 draws · Expected: 198.8 / Number · min 157, max 227

11872186319442015204619372058193918610219
11194122001320414206152021619617218181781922020204
21213221572322324202252092620627206281922921930199
31189321803317434199352093618537212382023919740180
41182422244318044227452104617747188481974919950213

Last 100 draws

100 draws · Expected: 10.0 / Number · min 4, max 16

1621037412514610711814971016
118121013111415156161017161810199205
21522923824925102612271028112912307
31103243383411351236637123883910408
4112421143744154512461247144812498508

The gap between the rarest and the most frequent number looks large, but it is exactly what you would expect from 50 independent counts. Over the last 100 draws, the relative scatter is even greater because the sample is smaller.

How long does a number stay absent?

For each number, we measure the gap in draws between two appearances. If the draws are independent, this gap follows a geometric distribution with a probability of 1/10 per draw: mean 10, and long absences are not rare, they are the rule.

9890 gaps measured · Mean: observed 9.95, expected 10.00

Observed Expected
1 982 / 989.0
2 902 / 890.1
3–4 1505 / 1,522.1
5–7 1775 / 1,758.5
8–10 1301 / 1,281.9
11–15 1421 / 1,412.2
16–20 860 / 833.9
21–30 745 / 783.1
31–40 240 / 273.1
41+ 159 / 146.2

The longest absence in history is 88 draws. The probability that a given number stays absent that long is 0.01%; with 50 numbers over 14 years, it is bound to happen eventually. The longest current absence is 42 draws. A number that has been absent for a long time is therefore not "due": the balls have no memory.

My combination

Enter five numbers: has this combination ever been drawn? Which draws came closest to it?

The calculation is done entirely in your browser; nothing is saved or transmitted. A combination never having been drawn is the normal case: out of 2,118,760 possible combinations, fewer than a thousand have been drawn so far.

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