In Powerball under the 5/59 + 1/39 · Jan 2009 – Jan 2012 rules — 316 draws, 5 from 1–59 (an earlier era).
22times drawn · chance expected 27 −0.97σ
2draws waiting · a wait this long: 92% for any number
14.2average wait between appearances · chance says 11.8
51longest completed wait · 22% chance of one at least that long
3 is drawn as often as chance explains
Drawn 22 times in 316 draws against 26.8 expected, −0.97σ. Each draw is independent: after 2 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 22 times in 316 draws · average wait 14.2 draws · longest completed wait 51 · 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 3 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 12 of the other 58 numbers; chance expects about 13 such strangers by now. Every pair →
How many people play it
Under the crowd model, 3 is picked about 1.48× as often as an indifferent choice — 2nd 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: 3 is drawn with probability 5/59 tonight whatever it did last week.