Number 12

In Montana Cash under the 5/37 · Apr 2010 – May 2014 rules — 428 draws, 5 from 1–37 (an earlier era).

56times drawn · chance expected 58 −0.26σ

3draws waiting · a wait this long: 75% for any number

7.7average wait between appearances · chance says 7.4

31longest completed wait · 51% chance of one at least that long

12 is drawn as often as chance explains

Drawn 56 times in 428 draws against 57.8 expected, −0.26σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 12, draw by draw

Drawn 56 times in 428 draws · average wait 7.7 draws · longest completed wait 31 · 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 12 has a favourite seat — chance gives a small number the low positions more often. That is the shape of sorting, not of the machine.

1st smallest18 · chance 12.0
2nd smallest23 · chance 24.1
3rd smallest13 · chance 15.7
4th smallest1 · chance 3.9
5th smallest1 · chance 0.3

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 6.2 shared draws, and the leaders are simply the ones that came out ahead this time.

28 1 16 25 36 5

It has shared a draw with every one of the other 36 numbers; chance expected about 0.1 still unmet by now. Every pair →

How many people play it

Under the crowd model, 12 is picked about 1.34× as often as an indifferent choice — 6th most popular of 37. 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
Numbers 1–12 — day and month overlap ×1.10

The model and its sources → · What people believe about 12 →

Every draw it appeared in

Date	Wait	Position	The draw
2014-04-30	8	1st	12 20 29 32 37
2014-04-02	2	2nd	6 12 13 15 34
2014-03-26	8	2nd	5 12 20 27 37
2014-02-26	14	1st	12 16

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: 12 is drawn with probability 5/37 tonight whatever it did last week.

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