Number 31

In Mega Millions under the 5/56 + 1/46 · Jun 2005 – Oct 2013 rules — 869 draws, 5 from 1–56 (an earlier era).

81times drawn · chance expected 78 +0.41σ

9draws waiting · a wait this long: 47% for any number

10.5average wait between appearances · chance says 11.2

39longest completed wait · 90% chance of one at least that long

31 is drawn as often as chance explains

Drawn 81 times in 869 draws against 77.6 expected, +0.41σ. Each draw is independent: after 9 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 81 times in 869 draws · average wait 10.5 draws · longest completed wait 39 · waiting 9 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 smallest2 · chance 3.0
2nd smallest17 · chance 16.4
3rd smallest30 · chance 31.0
4th smallest23 · chance 24.1
5th smallest9 · chance 6.5

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 5.9 shared draws, and the leaders are simply the ones that came out ahead this time.

36 12 24 27 11 56

It has shared a draw with every one of the other 55 numbers; chance expected about 0.2 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 56. 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
2013-09-17	10	4th	6 15 27 31 39
2013-08-13	17	2nd	2 31 32 37 41
2013-06-14	22	3rd	2 5 31 33 34
2013-03-29	18	2nd	25 31

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 5/56 tonight whatever it did last week.

2010-12-14	7	4th	18 22 25 31 38
2010-11-19	7	3rd	7 14 31 51 54
2010-10-26	3	4th	15 21 30 31 32
2010-10-15	1	4th	9 10 13 31 50
2010-10-12	27	2nd	10 31 36 37 43
2010-07-09	19	2nd	1 31 33 34 50
2010-05-04	5	3rd	9 21 31 36 43
2010-04-16	4	3rd	10 16 31 48 50
2010-04-02	4	5th	2 17 22 30 31
2010-03-19	4	2nd	10 31 45 50 54
2010-03-05	15	2nd	11 31 34 44 52
2010-01-12	1	3rd	5 9 31 37 56
2010-01-08	7	3rd	18 20 31 36 43
2009-12-15	12	2nd	27 31 32 36 47
2009-11-03	6	4th	5 18 23 31 38
2009-10-13	7	2nd	17 31 34 45 51
2009-09-18	6	3rd	18 27 31 36 52
2009-08-28	19	3rd	1 17 31 37 54
2009-06-23	4	4th	12 14 16 31 50
2009-06-09	24	3rd	5 17 31 36 56
2009-03-17	2	5th	9 15 24 28 31
2009-03-10	9	3rd	2 27 31 39 40
2009-02-06	17	5th	2 12 18 28 31
2008-12-09	15	4th	11 12 26 31 33
2008-10-17	6	5th	7 15 27 28 31
2008-09-26	39	4th	6 13 14 31 36
2008-05-13	1	4th	20 24 27 31 47
2008-05-09	5	2nd	16 31 43 46 56
2008-04-22	3	3rd	3 22 31 48 54
2008-04-11	1	4th	14 18 27 31 42
2008-04-08	27	3rd	8 9 31 37 44
2008-01-04	14	2nd	24 31 39 40 56
2007-11-16	17	4th	12 13 30 31 39
2007-09-18	25	3rd	20 24 31 34 49
2007-06-22	1	5th	11 14 21 24 31
2007-06-19	2	3rd	5 16 31 49 54
2007-06-12	1	4th	3 13 19 31 50
2007-06-08	11	4th	6 26 29 31 39
2007-05-01	4	3rd	11 16 31 52 53
2007-04-17	14	4th	1 4 11 31 47
2007-02-27	11	2nd	18 31 44 45 48
2007-01-19	11	4th	4 28 30 31 35
2006-12-12	37	3rd	20 30 31 35 49
2006-08-04	9	3rd	2 24 31 50 55
2006-07-04	13	3rd	9 15 31 42 45
2006-05-19	5	3rd	5 12 31 51 56
2006-05-02	7	5th	7 11 22 27 31
2006-04-07	5	3rd	1 18 31 46 52
2006-03-21	9	5th	4 16 17 28 31
2006-02-17	4	3rd	16 25 31 43 46
2006-02-03	3	2nd	29 31 32 41 52
2006-01-24	11	1st	31 34 36 51 55
2005-12-16	2	4th	14 25 26 31 56
2005-12-09	4	3rd	14 15 31 32 43
2005-11-25	9	3rd	5 25 31 33 34
2005-10-25	14	4th	7 12 18 31 55
2005-09-06	—	4th	1 8 27 31 50