In Powerball under the 5/49 + 1/42 · Nov 1997 – Oct 2002 rules — 514 draws, 5 from 1–49 (an earlier era).
45times drawn · chance expected 52 −1.09σ
16draws waiting · a wait this long: 20% for any number
11.3average wait between appearances · chance says 9.8
41longest completed wait · 45% chance of one at least that long
21 is drawn as often as chance explains
Drawn 45 times in 514 draws against 52.4 expected, −1.09σ. Each draw is independent: after 16 draws away it is exactly as likely tonight as a number drawn yesterday.
21
Number 21, draw by draw
Drawn 45 times in 514 draws · average wait 11.3 draws · longest completed wait 41 · waiting 16 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.
It has shared a draw with every one of the other 48 numbers; chance expected about 1 still unmet 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 49. That changes nothing about whether it comes up, and everything about how many ways a jackpot on it would be shared.
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 5/49 tonight whatever it did last week.