Number 21

In Mega Millions under the 5/50 + 1/25 · Sep 1996 – Jan 1999 rules — 172 draws, 5 from 1–50 (an earlier era).

16times drawn · chance expected 17 −0.30σ

1draws waiting · a wait this long: >99% for any number

9.3average wait between appearances · chance says 10.0

22longest completed wait · 82% chance of one at least that long

21 is drawn as often as chance explains

Drawn 16 times in 172 draws against 17.2 expected, −0.30σ. Each draw is independent: after 1 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 21, draw by draw

Drawn 16 times in 172 draws · average wait 9.3 draws · longest completed wait 22 · waiting 1 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 small number the low positions more often. That is the shape of sorting, not of the machine.

1st smallest2 · chance 1.8
2nd smallest12 · chance 5.5
3rd smallest1 · chance 5.8
4th smallest1 · chance 2.5
5th smallest0 · chance 0.4

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 1.3 shared draws, and the leaders are simply the ones that came out ahead this time.

31 43 48 8 12 17

Never drawn alongside 17 of the other 49 numbers; chance expects about 13 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 50. 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
1999-01-08	4	2nd	5 21 23 26 37
1998-12-25	1	4th	6 8 17 21 31
1998-12-22	1	2nd	17 21 33 42 44
1998-12-18	5	2nd	10 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 5/50 tonight whatever it did last week.