Number 21

In Daily Million Plus 2pm under the 6/39 + 1/38 · Apr 2016 – Jul 2016 rules — 86 draws, 6 from 1–39 (an earlier era).

15times drawn · chance expected 13 +0.53σ

5draws waiting · a wait this long: 51% for any number

5.1average wait between appearances · chance says 6.5

11longest completed wait · 95% chance of one at least that long

21 is drawn as often as chance explains

Drawn 15 times in 86 draws against 13.2 expected, +0.53σ. Each draw is independent: after 5 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 21, draw by draw

Drawn 15 times in 86 draws · average wait 5.1 draws · longest completed wait 11 · waiting 5 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 21 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 0.3
2nd smallest1 · chance 1.8
3rd smallest6 · chance 4.6
4th smallest4 · chance 5.2
5th smallest2 · chance 2.6
6th smallest2 · chance 0.5

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 2.0 shared draws, and the leaders are simply the ones that came out ahead this time.

10 16 18 22 30 3

Never drawn alongside 6 of the other 38 numbers; chance expects about 5 such strangers by now. Every pair →

How many people play it

Under the crowd model, 21 is picked about 1.22× as often as an indifferent choice — 15th most popular of 39. 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 21 →

Every draw it appeared in

Date	Wait	Position	The draw
2016-07-14	6	3rd	5 20 21 30 32 38
2016-07-08	7	4th	10 16 20 21 24 30
2016-07-01	1	6th	1 2 7 10 17 21

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: 21 is drawn with probability 6/39 tonight whatever it did last week.