Number 21

In Eurojackpot under the 5/50 + 2/8 · Mar 2012 – Oct 2014 rules — 133 draws, 5 from 1–50 (an earlier era).

16times drawn · chance expected 13 +0.78σ

8draws waiting · a wait this long: 48% for any number

8.3average wait between appearances · chance says 10.0

19longest completed wait · 91% chance of one at least that long

21 is drawn as often as chance explains

Drawn 16 times in 133 draws against 13.3 expected, +0.78σ. Each draw is independent: after 8 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 21, draw by draw

Drawn 16 times in 133 draws · average wait 8.3 draws · longest completed wait 19 · waiting 8 draws now

a completed wait — darker is longer the wait still running — a lower bound, not a finished gap

Where it lands in a sorted draw

Sort a draw and 21 has a favourite seat — chance gives a small number the low positions more often. That is the shape of sorting, not of the machine.

1st smallest0 · chance 1.8
2nd smallest4 · chance 5.5
3rd smallest10 · chance 5.8
4th smallest2 · chance 2.5
5th smallest0 · chance 0.4

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 1.3 shared draws, and the leaders are simply the ones that came out ahead this time.

1 2 5 37 45 4

Never drawn alongside 10 of the other 49 numbers; chance expects about 13 such strangers by now. Every pair →

How many people play it

Under the crowd model, 21 is picked about 1.22× as often as an indifferent choice — 15th most popular of 50. That changes nothing about whether it comes up, and everything about how many ways a jackpot on it would be shared.

Numbers 1–31 — the birthday zone ×1.22

The model and its sources → · What people believe about 21 →

Every draw it appeared in

Date	Wait	Position	The draw
2014-08-08	11	3rd	15 19 21 34 40
2014-05-23	12	2nd	6 21 33 37 47
2014-02-28	1	3rd	2 17 21 22 45
2014-02-21	1	3rd	2 4

What this cannot tell you

Nothing here predicts the next draw. A number’s history is a record of a fair machine’s past, and the machine keeps none of it: 21 is drawn with probability 5/50 tonight whatever it did last week.