In Powerball under the 5/59 + 1/39 · Jan 2009 – Jan 2012 rules — 316 draws, 5 from 1–59 (an earlier era).
26times drawn · chance expected 27 −0.16σ
2draws waiting · a wait this long: 92% for any number
11.8average wait between appearances · chance says 11.8
44longest completed wait · 43% chance of one at least that long
21 is drawn as often as chance explains
Drawn 26 times in 316 draws against 26.8 expected, −0.16σ. Each draw is independent: after 2 draws away it is exactly as likely tonight as a number drawn yesterday.
21
Number 21, draw by draw
Drawn 26 times in 316 draws · average wait 11.8 draws · longest completed wait 44 · waiting 2 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.
Never drawn alongside 7 of the other 58 numbers; chance expects about 10 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 59. 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 5/59 tonight whatever it did last week.