In Powerball under the 5/53 + 1/42 · Oct 2002 – Aug 2005 rules — 302 draws, 5 from 1–53 (an earlier era).
29times drawn · chance expected 28 +0.10σ
4draws waiting · a wait this long: 74% for any number
10.1average wait between appearances · chance says 10.6
31longest completed wait · 77% chance of one at least that long
1 is drawn as often as chance explains
Drawn 29 times in 302 draws against 28.5 expected, +0.10σ. Each draw is independent: after 4 draws away it is exactly as likely tonight as a number drawn yesterday.
1
Number 1, draw by draw
Drawn 29 times in 302 draws · average wait 10.1 draws · longest completed wait 31 · waiting 4 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 6 of the other 52 numbers; chance expects about 6 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 53. 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 5/53 tonight whatever it did last week.