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 2,118,760 combinations), not simulated. The result in advance: everywhere, what we observe stays within the range of chance.

868 draws · 19.06.2018 – 13.10.2026 · Exact expected values under the hypothesis of uniform 5-from-50 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 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 on 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 3 / 1.2
10–14 9 / 10.1
15–19 31 / 32.3
20–24 75 / 68.1
25–29 107 / 113.1
30–34 162 / 157.4
35–39 188 / 186.3
40–44 177 / 179.7
45–49 111 / 112.7
50–50 5 / 7.1

Circular span

Mean: observed 28.8, expected 28.8

Observed Expected
5–9 3 / 1.4
10–14 12 / 13.2
15–19 41 / 48.0
20–24 130 / 118.7
25–29 235 / 236.6
30–34 315 / 322.7
35–39 131 / 126.8
40–41 1 / 0.5

The tightest draws

A circular span of at most 10 has a probability of 0.30% for a random draw. We therefore expected 2.6 such draws; there were 4.

DateWinning numberscircularlinear
01.12.20205678955
01.01.2019424446474877
27.08.2019459101188
17.04.202016192023251010
30.10.201819202427291111
08.11.202278910171111
07.10.202513182123241212
01.02.202231333740431313
11.09.2020141012491449
09.03.202128303637411414
28.05.202131333638441414
06.12.2022191047501450

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 0.483, expected 0.500

Observed Expected
0 505 / 499.9
1 310 / 304.8
2 47 / 58.1
3 5 / 4.1
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.

0.878
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 in rows of ten. 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

868 draws · Expected: 86.8 / Number · min 64, max 107

16428031014885916837758849921085
1178128113107147215105169417811894199620100
21892295237524105258126692783288429973079
31873288337634783587368337793810139894090
4190428243954479457946884784489049995088

Last 100 draws

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

182113948512677588911106
1112128131514915101615171618819132010
2172211238241425132672711281329103011
3113328338348359367379381139154013
4184274313445458469471148949105013

The gap between the rarest and the most frequent number looks large, but it is exactly what you expect from 50 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 5/50 ≈ 10.0% per draw: mean 10.0, and long absences are not rare, they are the rule.

4290 gaps measured · Mean: observed 9.90, expected 10.00

Observed Expected
1 419 / 429.0
2 407 / 386.1
3–4 683 / 660.2
5–7 767 / 762.8
8–10 535 / 556.1
11–15 624 / 612.6
16–20 329 / 361.7
21–30 353 / 339.7
31–40 113 / 118.4
41+ 60 / 63.4

The longest absence in the data is 82 draws. The probability that a given number stays absent that long is 0.02%; with 50 numbers it is bound to happen eventually. The longest current absence is 40 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 2,118,760 possible combinations only a tiny fraction has ever come up.

▲