In Powerball under the 5/59 + 1/35 · Jan 2012 – Oct 2015 rules — 388 draws, 5 from 1–59 (an earlier era).
33times drawn · chance expected 33 +0.02σ
6draws waiting · a wait this long: 64% for any number
10.8average wait between appearances · chance says 11.8
67longest completed wait · 9% chance of one at least that long
3 is drawn as often as chance explains
Drawn 33 times in 388 draws against 32.9 expected, +0.02σ. Each draw is independent: after 6 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 33 times in 388 draws · average wait 10.8 draws · longest completed wait 67 · waiting 6 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 3 of the other 58 numbers; chance expects about 6 such strangers by now. Every pair →
How many people play it
Under the crowd model, 3 is picked about 1.16× 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.