In Powerball under the 5/59 + 1/39 · Jan 2009 – Jan 2012 rules — 316 draws, 1 from 1–39 (an earlier era).
9times drawn · chance expected 8 +0.32σ
3draws waiting · a wait this long: 95% for any number
33.6average wait between appearances · chance says 39.0
109longest completed wait · 39% chance of one at least that long
2 is drawn as often as chance explains
Drawn 9 times in 316 draws against 8.1 expected, +0.32σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.
2
Number 2, draw by draw
Drawn 9 times in 316 draws · average wait 33.6 draws · longest completed wait 109 · 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 2 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 38 of the other 38 numbers; chance expects about 38 such strangers by now. Every pair →
How many people play it
Under the crowd model, 2 is picked about 1.34× as often as an indifferent choice — 6th most popular of 39. 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: 2 is drawn with probability 1/39 tonight whatever it did last week.