In Powerball under the 5/45 + 1/45 · Apr 1992 – Nov 1997 rules — 578 draws, 5 from 1–45 (an earlier era).
58times drawn · chance expected 64 −0.82σ
3draws waiting · a wait this long: 79% for any number
9.8average wait between appearances · chance says 9.0
37longest completed wait · 56% chance of one at least that long
40 is drawn as often as chance explains
Drawn 58 times in 578 draws against 64.2 expected, −0.82σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday. It has also come out as the bonus ball 14 times, counted separately.
40
Number 40, draw by draw
Drawn 58 times in 578 draws · average wait 9.8 draws · longest completed wait 37 · 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 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.
It has shared a draw with every one of the other 44 numbers; chance expected about 0.2 still unmet 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 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: 40 is drawn with probability 5/45 tonight whatever it did last week.