In Powerball under the 5/55 + 1/42 · Aug 2005 – Jan 2009 rules — 350 draws, 5 from 1–55 (an earlier era).
38times drawn · chance expected 32 +1.15σ
3draws waiting · a wait this long: 83% for any number
9.2average wait between appearances · chance says 11.0
26longest completed wait · 97% chance of one at least that long
2 is drawn as often as chance explains
Drawn 38 times in 350 draws against 31.8 expected, +1.15σ. 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 38 times in 350 draws · average wait 9.2 draws · longest completed wait 26 · 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 4 of the other 54 numbers; chance expects about 3 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 55. 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 5/55 tonight whatever it did last week.