Number 31

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

9times drawn · chance expected 13 −1.24σ

4draws waiting · a wait this long: 73% for any number

14.0average wait between appearances · chance says 10.0

33longest completed wait · 24% chance of one at least that long

31 is drawn as often as chance explains

Drawn 9 times in 133 draws against 13.3 expected, −1.24σ. Each draw is independent: after 4 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 9 times in 133 draws · average wait 14.0 draws · longest completed wait 33 · waiting 4 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 31 has a favourite seat — chance gives a large number the high positions more often. That is the shape of sorting, not of the machine.

1st smallest0 · chance 0.2
2nd smallest4 · chance 1.2
3rd smallest2 · chance 3.2
4th smallest2 · chance 3.3
5th smallest1 · chance 1.2

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 0.7 shared draws, and the leaders are simply the ones that came out ahead this time.

33 37 3 6 9 12

Never drawn alongside 24 of the other 49 numbers; chance expects about 24 such strangers by now. Every pair →

How many people play it

Under the crowd model, 31 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 31 →

Every draw it appeared in

Date	Wait	Position	The draw
2014-09-05	18	2nd	26 31 33 39 40
2014-05-02	33	2nd	9 31 32 33 34
2013-09-13	18	4th	3 10 18 31 43
2013-05-10	5	3rd	6 9

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: 31 is drawn with probability 5/50 tonight whatever it did last week.