Number 40

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

80times drawn · chance expected 78 +0.29σ

3draws waiting · a wait this long: 83% for any number

10.8average wait between appearances · chance says 11.2

37longest completed wait · 94% chance of one at least that long

40 is drawn as often as chance explains

Drawn 80 times in 869 draws against 77.6 expected, +0.29σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 40, draw by draw

Drawn 80 times in 869 draws · average wait 10.8 draws · longest completed wait 37 · 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 40 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 0.4
2nd smallest6 · chance 5.1
3rd smallest18 · chance 20.9
4th smallest33 · chance 34.3
5th smallest23 · chance 19.3

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 5.8 shared draws, and the leaders are simply the ones that came out ahead this time.

39 48 14 16 6 17

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, 40 is picked about 0.90× as often as an indifferent choice — 32nd 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 above 31 ×0.86
Round numbers (multiples of 10) ×1.05

The model and its sources → · What people believe about 40 →

Every draw it appeared in

Date	Wait	Position	The draw
2013-10-08	4	5th	6 15 19 23 40
2013-09-24	20	5th	4 11 32 39 40
2013-07-16	7	4th	10 14 21 40 53
2013-06-21	1	4th	3 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: 40 is drawn with probability 5/56 tonight whatever it did last week.

2011-05-10	9	4th	11 16 34 40 51
2011-04-08	29	2nd	6 40 45 50 56
2010-12-28	1	4th	6 18 36 40 49
2010-12-24	37	4th	15 16 27 40 52
2010-08-17	5	3rd	11 19 40 43 44
2010-07-30	21	3rd	11 30 40 48 52
2010-05-18	1	5th	11 13 19 37 40
2010-05-14	15	3rd	20 21 40 47 56
2010-03-23	8	5th	3 25 28 29 40
2010-02-23	15	4th	4 16 36 40 53
2010-01-01	16	4th	6 8 27 40 41
2009-11-06	21	4th	7 11 27 40 46
2009-08-25	11	5th	3 12 19 22 40
2009-07-17	22	3rd	8 17 40 47 50
2009-05-01	12	4th	9 16 24 40 43
2009-03-20	3	5th	15 16 20 39 40
2009-03-10	4	5th	2 27 31 39 40
2009-02-24	3	5th	1 27 28 35 40
2009-02-13	17	4th	25 36 37 40 51
2008-12-16	34	5th	10 14 16 29 40
2008-08-19	2	5th	9 18 19 26 40
2008-08-12	21	5th	2 7 23 38 40
2008-05-30	16	2nd	39 40 47 53 55
2008-04-04	2	3rd	3 5 40 45 49
2008-03-28	15	4th	7 26 27 40 43
2008-02-05	2	4th	4 5 17 40 51
2008-01-29	7	4th	8 23 39 40 42
2008-01-04	15	4th	24 31 39 40 56
2007-11-13	11	5th	15 26 36 39 40
2007-10-05	1	4th	10 19 37 40 48
2007-10-02	5	3rd	28 37 40 43 44
2007-09-14	4	5th	5 9 12 33 40
2007-08-31	1	4th	8 18 22 40 44
2007-08-28	16	2nd	37 40 48 53 56
2007-07-03	1	5th	21 35 37 39 40
2007-06-29	30	3rd	1 17 40 51 52
2007-03-16	8	4th	17 25 36 40 43
2007-02-16	4	3rd	17 35 40 46 48
2007-02-02	6	4th	22 33 35 40 53
2007-01-12	8	4th	12 14 26 40 42
2006-12-15	6	5th	6 7 17 28 40
2006-11-24	7	3rd	14 35 40 47 48
2006-10-31	6	3rd	5 34 40 45 46
2006-10-10	2	4th	14 30 35 40 43
2006-10-03	15	5th	6 19 32 33 40
2006-08-11	12	4th	14 16 38 40 49
2006-06-30	13	2nd	20 40 46 48 54
2006-05-16	27	3rd	7 24 40 48 50
2006-02-10	7	3rd	24 39 40 43 46
2006-01-17	5	5th	24 32 37 39 40
2005-12-30	3	4th	14 20 25 40 44
2005-12-20	10	4th	6 20 23 40 56
2005-11-15	16	4th	2 4 5 40 48
2005-09-20	8	3rd	35 36 40 42 52
2005-08-23	7	5th	6 7 8 13 40
2005-07-29	—	5th	4 16 23 25 40