In Powerball under the 5/45 + 1/45 · Jan 2009 – Mar 2013 rules — 218 draws, 5 from 1–45 (an earlier era).
34times drawn · chance expected 24 +2.11σ
14draws waiting · a wait this long: 22% for any number
5.5average wait between appearances · chance says 9.0
16longest completed wait · >99% chance of one at least that long
2 is drawn as often as chance explains
Drawn 34 times in 218 draws against 24.2 expected, +2.11σ. Each draw is independent: after 14 draws away it is exactly as likely tonight as a number drawn yesterday.
2
Number 2, draw by draw
Drawn 34 times in 218 draws · average wait 5.5 draws · longest completed wait 16 · waiting 14 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.
It has shared a draw with every one of the other 44 numbers; chance expected about 2 still unmet 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 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: 2 is drawn with probability 5/45 tonight whatever it did last week.