In Powerball under the 5/53 + 1/42 · Oct 2002 – Aug 2005 rules — 302 draws, 5 from 1–53 (an earlier era).
18times drawn · chance expected 28 −2.07σ
3draws waiting · a wait this long: 82% for any number
16.5average wait between appearances · chance says 10.6
79longest completed wait · 0.7% chance of one at least that long
3 is drawn as often as chance explains
Drawn 18 times in 302 draws against 28.5 expected, −2.07σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 18 times in 302 draws · average wait 16.5 draws · longest completed wait 79 · waiting 3 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 13 of the other 52 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 53. 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 5/53 tonight whatever it did last week.