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.

993 draws · 23.03.2012 – 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 34.9, expected 35.0

Observed Expected
5–9 4 / 1.4
10–14 6 / 11.6
15–19 32 / 36.9
20–24 82 / 77.9
25–29 150 / 129.4
30–34 174 / 180.1
35–39 218 / 213.1
40–44 192 / 205.6
45–49 126 / 128.9
50–50 9 / 8.1

Circular span

Mean: observed 28.9, expected 28.8

Observed Expected
5–9 4 / 1.6
10–14 10 / 15.1
15–19 49 / 55.0
20–24 146 / 135.8
25–29 268 / 270.7
30–34 356 / 369.2
35–39 160 / 145.1
40–41 0 / 0.6

The tightest draws

A circular span of at most 10 has a probability of 0.30% in a random draw. So 3.0 were expected; there have been 5.

DateWinning numberscircularlinear
19.04.2013171822242599
14.05.2024192223242799
20.08.2024252829313399
21.03.20258912141699
25.08.202645748501047
22.01.202138404146481111
28.10.201614612131313
22.02.201914162125261313
07.06.2022574548491345
03.08.201212151824251414
22.11.20131383942471447
02.06.2023891113501443

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 0.500, expected 0.500

Observed Expected
0 576 / 572.0
1 340 / 348.8
2 72 / 66.4
3 4 / 4.6
4–5 0 / 0.1

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.

0.861
Observed
0.880
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

993 draws · Expected: 99.3 / Number · min 79, max 115

110429439441015906997104810491011093
111101297131031410515991610917113181081910020115
2111022962310624902588268927892888299630108
31923294339534113351143686371023899391034096
41107429343994493451024610347964879491075089

Last 100 draws

100 draws · Expected: 10.0 / Number · min 5, max 16

110293941351169778997109
1171271381491591611171618111910208
211222102314247251226627112892973015
317327331034103516369371638739114011
4113429431044845124611471348104955013

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.

4915 gaps measured · Mean: observed 9.92, expected 10.00

Observed Expected
1 496 / 491.5
2 463 / 442.3
3–4 735 / 756.4
5–7 914 / 873.9
8–10 628 / 637.1
11–15 672 / 701.8
16–20 415 / 414.4
21–30 388 / 389.2
31–40 123 / 135.7
41+ 81 / 72.6

The longest absence in history is 80 draws. The probability that a given number stays absent that long is 0.02%; with 50 numbers over 14 years, it is bound to happen eventually. The longest current absence is 29 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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