In Powerball under the 5/55 + 1/42 · Aug 2005 – Jan 2009 rules — 350 draws, 5 from 1–55 (an earlier era).
27times drawn · chance expected 32 −0.90σ
15draws waiting · a wait this long: 26% for any number
12.8average wait between appearances · chance says 11.0
56longest completed wait · 13% chance of one at least that long
1 is drawn as often as chance explains
Drawn 27 times in 350 draws against 31.8 expected, −0.90σ. Each draw is independent: after 15 draws away it is exactly as likely tonight as a number drawn yesterday.
1
Number 1, draw by draw
Drawn 27 times in 350 draws · average wait 12.8 draws · longest completed wait 56 · waiting 15 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 1 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 9 of the other 54 numbers; chance expects about 7 such strangers by now. Every pair →
How many people play it
Under the crowd model, 1 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: 1 is drawn with probability 5/55 tonight whatever it did last week.