In Powerball under the 6/40 + 1/20 · Mar 2013 – Apr 2018 rules — 267 draws, 6 from 1–40 (an earlier era).
32times drawn · chance expected 40 −1.38σ
3draws waiting · a wait this long: 72% for any number
8.3average wait between appearances · chance says 6.7
25longest completed wait · 47% chance of one at least that long
40 is drawn as often as chance explains
Drawn 32 times in 267 draws against 40.0 expected, −1.38σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.
40
Number 40, draw by draw
Drawn 32 times in 267 draws · average wait 8.3 draws · longest completed wait 25 · 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.
Never drawn alongside 1 of the other 39 numbers; chance expects about 0.6 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 40. 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 6/40 tonight whatever it did last week.