In PowerBall under the 5/50 + 1/20 · since Jun 2018 rules — 866 draws, 1 from 1–20.
37times drawn · chance expected 43 −0.98σ
5draws waiting · a wait this long: 81% for any number
23.6average wait between appearances · chance says 20.0
110longest completed wait · 13% chance of one at least that long
3 is drawn as often as chance explains
Drawn 37 times in 866 draws against 43.3 expected, −0.98σ. Each draw is independent: after 5 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 37 times in 866 draws · average wait 23.6 draws · longest completed wait 110 · waiting 5 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 19 of the other 19 numbers; chance expects about 19 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 20. 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 1/20 tonight whatever it did last week.