In Powerball under the 5/59 + 1/39 · Jan 2009 – Jan 2012 rules — 316 draws, 5 from 1–59 (an earlier era).
25times drawn · chance expected 27 −0.36σ
4draws waiting · a wait this long: 77% for any number
11.5average wait between appearances · chance says 11.8
35longest completed wait · 70% chance of one at least that long
40 is drawn as often as chance explains
Drawn 25 times in 316 draws against 26.8 expected, −0.36σ. Each draw is independent: after 4 draws away it is exactly as likely tonight as a number drawn yesterday.
40
Number 40, draw by draw
Drawn 25 times in 316 draws · average wait 11.5 draws · longest completed wait 35 · 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 40 has a favourite seat — chance gives a large number the high positions more often. That is the shape of sorting, not of the machine.
Never drawn alongside 8 of the other 58 numbers; chance expects about 10 such strangers by now. Every pair →
How many people play it
Under the crowd model, 40 is picked about 0.90× as often as an indifferent choice — 32nd most popular of 59. 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: 40 is drawn with probability 5/59 tonight whatever it did last week.