Number 31

In PowerBall under the 5/45 + 1/20 · Oct 2009 – Jun 2018 rules — 896 draws, 5 from 1–45 (an earlier era).

117times drawn · chance expected 100 +1.85σ

3draws waiting · a wait this long: 79% for any number

7.7average wait between appearances · chance says 9.0

29longest completed wait · 99% chance of one at least that long

31 is drawn as often as chance explains

Drawn 117 times in 896 draws against 99.6 expected, +1.85σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 117 times in 896 draws · average wait 7.7 draws · longest completed wait 29 · waiting 3 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 smallest4 · chance 0.9
2nd smallest7 · chance 9.4
3rd smallest37 · chance 34.1
4th smallest44 · chance 49.0
5th smallest25 · chance 23.6

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 10.6 shared draws, and the leaders are simply the ones that came out ahead this time.

37 2 20 12 45 4

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
2018-06-12	4	3rd	3 5 31 35 37
2018-05-29	11	3rd	12 21 31 37 41
2018-04-20	3	4th	5 13 20 31 35
2018-04-10	4	4th	2 14

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 5/45 tonight whatever it did last week.

2016-11-04	6	4th	5 14 23 31 36
2016-10-14	22	3rd	4 12 31 38 40
2016-07-29	3	3rd	4 12 31 41 42
2016-07-19	1	2nd	2 31 34 38 39
2016-07-15	1	3rd	2 14 31 34 37
2016-07-12	14	4th	4 12 23 31 41
2016-05-24	8	5th	8 12 23 24 31
2016-04-26	7	5th	1 3 16 19 31
2016-04-01	16	3rd	11 15 31 37 43
2016-02-05	6	4th	6 15 16 31 40
2016-01-15	17	4th	4 9 19 31 32
2015-11-13	15	4th	2 11 16 31 45
2015-09-22	6	5th	2 21 22 25 31
2015-09-01	1	3rd	23 30 31 44 45
2015-08-28	1	5th	10 16 18 20 31
2015-08-25	26	5th	2 11 19 20 31
2015-05-26	1	4th	12 13 20 31 36
2015-05-22	8	2nd	9 31 32 40 41
2015-04-24	2	4th	4 13 20 31 38
2015-04-17	10	4th	5 6 26 31 41
2015-03-10	3	4th	24 26 27 31 33
2015-02-27	5	4th	4 9 27 31 41
2015-02-10	4	4th	10 20 27 31 33
2015-01-27	2	4th	12 26 28 31 35
2015-01-20	3	4th	3 4 23 31 35
2015-01-09	3	5th	2 13 15 17 31
2014-12-30	2	4th	8 15 25 31 40
2014-12-23	17	3rd	2 25 31 32 36
2014-10-24	1	3rd	7 21 31 37 44
2014-10-21	19	4th	26 28 30 31 32
2014-08-15	1	2nd	19 31 40 41 43
2014-08-12	11	5th	10 17 26 29 31
2014-07-04	1	4th	4 19 25 31 36
2014-07-01	10	5th	1 10 19 21 31
2014-05-27	8	5th	4 11 24 26 31
2014-04-29	29	3rd	12 20 31 40 44
2014-01-14	4	1st	31 34 37 42 43
2013-12-31	6	4th	6 14 20 31 34
2013-12-10	1	4th	1 16 21 31 37
2013-12-06	4	5th	13 15 21 28 31
2013-11-22	2	5th	11 15 16 20 31
2013-11-15	11	2nd	3 31 35 37 45
2013-10-08	3	1st	31 39 42 43 45
2013-09-27	14	5th	6 13 21 28 31
2013-08-09	7	4th	10 22 23 31 45
2013-07-16	9	4th	5 7 8 31 37
2013-06-14	5	3rd	15 23 31 32 35
2013-05-28	8	4th	25 26 29 31 34
2013-04-30	9	4th	12 24 28 31 32
2013-03-26	10	3rd	1 18 31 37 40
2013-02-19	8	4th	1 5 6 31 42
2013-01-22	25	5th	3 10 11 28 31
2012-10-23	6	4th	8 23 24 31 42
2012-10-02	27	4th	11 18 23 31 45
2012-06-29	11	5th	2 4 6 19 31
2012-05-22	8	4th	1 3 22 31 38
2012-04-24	18	4th	3 5 22 31 45
2012-02-17	1	3rd	8 26 31 38 45
2012-02-14	29	3rd	20 30 31 32 44
2011-11-04	6	3rd	9 25 31 34 42
2011-10-14	7	4th	15 20 21 31 35
2011-09-20	8	4th	8 10 23 31 38
2011-08-23	4	5th	4 17 20 22 31
2011-08-09	2	1st	31 37 38 43 45
2011-08-02	8	5th	3 9 16 27 31
2011-07-05	1	3rd	2 30 31 34 42
2011-07-01	2	3rd	2 9 31 35 37
2011-06-24	6	4th	6 18 28 31 36
2011-06-03	4	3rd	6 30 31 33 36
2011-05-20	3	4th	3 7 10 31 42
2011-05-10	17	3rd	1 17 31 41 43
2011-03-08	3	3rd	17 21 31 34 41
2011-02-25	2	3rd	3 24 31 37 41
2011-02-18	2	5th	2 7 12 17 31
2011-02-11	2	4th	14 25 27 31 34
2011-02-04	12	4th	11 12 16 31 37
2010-12-24	1	3rd	26 30 31 33 40
2010-12-21	2	3rd	19 25 31 39 40
2010-12-14	13	3rd	12 30 31 32 35
2010-10-29	8	2nd	10 31 32 39 45
2010-10-01	3	5th	16 22 28 30 31
2010-09-21	11	1st	31 33 36 40 42
2010-08-13	1	4th	8 9 10 31 39
2010-08-10	11	3rd	9 19 31 33 45
2010-07-02	2	5th	2 6 7 9 31
2010-06-25	22	3rd	13 23 31 40 42
2010-04-09	26	5th	2 16 27 30 31
2010-01-05	5	3rd	1 8 31 43 44
2009-12-15	5	3rd	7 29 31 32 39
2009-11-27	6	3rd	12 18 31 37 45
2009-11-06	2	4th	10 17 23 31 42
2009-10-30	1	5th	11 14 16 30 31
2009-10-27	—	4th	5 15 17 31 37