Number 31

In Lotto under the 6/45 + 1/45 · Jan 2010 – Oct 2015 rules — 601 draws, 6 from 1–45 (an earlier era).

72times drawn · chance expected 80 −0.98σ

0draws waiting — it came up last time

7.9average wait between appearances · chance says 7.5

32longest completed wait · 57% chance of one at least that long

31 is drawn as often as chance explains

Drawn 72 times in 601 draws against 80.1 expected, −0.98σ. Each draw is independent: after 0 draws away it is exactly as likely tonight as a number drawn yesterday. It has also come out as the bonus ball 13 times, counted separately.

Number 31, draw by draw

Drawn 72 times in 601 draws · average wait 7.9 draws · longest completed wait 32 · drawn in the most recent draw

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 smallest1 · chance 0.1
2nd smallest3 · chance 2.0
3rd smallest9 · chance 10.5
4th smallest21 · chance 24.5
5th smallest27 · chance 25.4
6th smallest11 · chance 9.4

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 8.2 shared draws, and the leaders are simply the ones that came out ahead this time.

42 14 5 9 15 45

It has shared a draw with every one of the other 44 numbers; chance expected about 0.0 still unmet 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 45. 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
2015-10-03	1	4th	1 15 17 31 36 45
2015-09-30	4	4th	4 9 27 31 38 39
2015-09-16	27	6th	3 9 22 25 27 31
2015-06-13	7	4th

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 6/45 tonight whatever it did last week.

2013-10-26	1	5th	9 12 18 19 31 44
2013-10-23	10	2nd	14 31 32 34 35 40
2013-09-18	1	5th	10 12 14 15 31 36
2013-09-14	2	4th	5 9 15 31 35 43
2013-09-07	1	6th	7 10 15 18 25 31
2013-09-04	4	6th	2 4 9 12 28 31
2013-08-21	16	5th	14 21 24 26 31 38
2013-06-26	15	4th	6 20 29 31 35 42
2013-05-04	4	5th	12 16 18 21 31 45
2013-04-20	1	6th	3 7 8 15 28 31
2013-04-17	4	3rd	16 25 31 39 40 43
2013-04-03	4	6th	6 14 15 23 24 31
2013-03-20	21	3rd	16 22 31 33 34 43
2013-01-05	7	4th	12 14 23 31 32 44
2012-12-12	10	5th	3 9 12 15 31 33
2012-11-07	2	6th	4 5 9 20 27 31
2012-10-31	22	5th	14 16 20 22 31 43
2012-08-15	6	5th	2 11 16 26 31 36
2012-07-25	5	1st	31 34 39 42 44 45
2012-07-07	1	5th	17 20 21 28 31 37
2012-07-04	4	4th	7 13 21 31 36 42
2012-06-20	13	2nd	15 31 35 38 40 45
2012-05-05	5	4th	6 9 21 31 33 42
2012-04-18	2	6th	2 14 15 19 27 31
2012-04-11	2	3rd	7 26 31 33 42 45
2012-04-04	3	5th	5 7 23 26 31 45
2012-03-24	13	4th	1 3 20 31 34 38
2012-02-08	23	5th	1 5 7 20 31 40
2011-11-19	7	5th	3 10 24 30 31 39
2011-10-26	6	5th	14 21 25 28 31 36
2011-10-05	11	4th	5 8 19 31 34 45
2011-08-27	6	4th	17 18 19 31 32 44
2011-08-06	1	4th	9 21 26 31 39 42
2011-08-03	3	3rd	17 21 31 34 35 37
2011-07-23	31	5th	1 7 14 23 31 34
2011-04-06	4	5th	6 18 23 24 31 32
2011-03-23	1	5th	1 2 6 14 31 42
2011-03-19	5	3rd	2 12 31 37 39 45
2011-03-02	13	3rd	9 27 31 39 42 45
2011-01-15	10	5th	3 10 19 26 31 36
2010-12-11	4	4th	1 7 24 31 33 38
2010-11-27	2	6th	3 4 5 12 20 31
2010-11-20	8	4th	12 19 21 31 39 42
2010-10-23	19	5th	15 16 22 25 31 32
2010-08-18	10	4th	1 4 20 31 34 43
2010-07-14	13	3rd	5 13 31 36 42 43
2010-05-29	2	4th	3 9 19 31 33 34
2010-05-22	—	5th	6 21 26 27 31 45