In Powerball under the 5/45 + 1/45 · Jan 2009 – Mar 2013 rules — 218 draws, 5 from 1–45 (an earlier era).
21times drawn · chance expected 24 −0.69σ
0draws waiting — it came up last time
10.3average wait between appearances · chance says 9.0
36longest completed wait · 28% chance of one at least that long
3 is drawn as often as chance explains
Drawn 21 times in 218 draws against 24.2 expected, −0.69σ. Each draw is independent: after 0 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 21 times in 218 draws · average wait 10.4 draws · longest completed wait 36 · drawn in the most recent draw
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 7 of the other 44 numbers; chance expects about 7 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 45. 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 5/45 tonight whatever it did last week.