ΣLottosigma

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 (closed-form formulas over all 376,992 combinations), not simulated. The result in advance: everywhere, what we observe stays within the range of chance.

2769 draws · 10.03.2019 – 14.10.2026 · Exact expected values under the hypothesis of uniform 5-from-36 draws

How close together are the five numbers?

The linear span is the distance from the smallest to the largest number (end positions included). The circular span reads the numbers 1 to 36 on a circle where 36 touches 1: the draw 4, 5, 7, 34, 36 is then no longer spread over 33 positions but concentrated on 10. The bars show the distribution of draws by span, observed and expected.

Linear span

Mean: observed 25.6, expected 25.7

Observed Expected
5–9 18 / 14.8
10–14 113 / 115.4
15–19 345 / 337.3
20–24 622 / 625.2
25–29 856 / 832.3
30–34 685 / 719.9
35–36 130 / 124.1

Circular span

Mean: observed 21.2, expected 21.2

Observed Expected
5–9 19 / 18.5
10–14 155 / 170.6
15–19 651 / 620.1
20–24 1348 / 1,357.8
25–29 596 / 602.1

The tightest draws

A circular span of at most 10 has a probability of 1.20% for a random draw. We therefore expected 33.3 such draws; there were 27.

DateWinning numberscircularlinear
25.08.2019121516171877
08.08.2020303132343677
29.10.20192567988
12.10.2023679111388
31.03.202445691188
13.02.2025161819212388
12.11.2025252627283288
04.12.2019369101199
20.08.2020242630313299
24.03.2021252730323399
29.06.2021192124262799
30.03.202324581099

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 36, of which 5 are marked.

Exact repeats

Mean: observed 0.688, expected 0.694

Observed Expected
0 1279 / 1,247.5
1 1113 / 1,155.1
2 338 / 330.0
3 37 / 34.1
4–5 1 / 1.1

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.

1.151
Observed
1.159
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 36 numbers in six rows of six. The darker the cell, the more often the number was drawn. The expected value is the same for all; the differences are the normal spread of a binomial distribution.

All time

2769 draws · Expected: 384.6 / Number · min 350, max 432

139323943367439353926414
738683859402104321137612392
133711440615384163781735618363
193502037921390223822338624369
254202636827396283872937430378
313823237933379343763537836388

Last 100 draws

100 draws · Expected: 13.9 / Number · min 7, max 23

110214316410517616
71481091410151181216
131014191514161717121812
19102016212022723212412
252326142710281329133015
3119321733734153583616

The gap between the rarest and the most frequent number looks large, but it is exactly what you expect from 36 independent counts. Over the last 100 draws the relative spread is even larger 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 probability 5/36 ≈ 13.9% per draw: mean 7.2, and long absences are not rare, they are the rule.

13809 gaps measured · Mean: observed 7.18, expected 7.20

Observed Expected
1 1904 / 1,917.9
2 1657 / 1,651.5
3–4 2646 / 2,646.8
5–7 2707 / 2,744.6
8–10 1827 / 1,752.5
11–15 1649 / 1,629.9
16–20 751 / 771.7
21–30 515 / 538.4
31–40 119 / 120.7
41+ 34 / 34.9

The longest absence in the data is 76 draws. The probability that a given number stays absent that long is 0.00%; with 36 numbers it is bound to happen eventually. The longest current absence is 44 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 been drawn before? Which draws came closest?

Everything runs in your browser; nothing is stored or sent. That a combination has never been drawn is normal: out of 376,992 possible combinations only a tiny fraction has ever come up.

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