In Powerball under the 5/59 + 1/39 · Jan 2009 – Jan 2012 rules — 316 draws, 5 from 1–59 (an earlier era).
20times drawn · chance expected 27 −1.37σ
7draws waiting · a wait this long: 59% for any number
16.2average wait between appearances · chance says 11.8
46longest completed wait · 30% chance of one at least that long
31 is drawn as often as chance explains
Drawn 20 times in 316 draws against 26.8 expected, −1.37σ. Each draw is independent: after 7 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 20 times in 316 draws · average wait 16.2 draws · longest completed wait 46 · waiting 7 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 31 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 14 of the other 58 numbers; chance expects about 15 such strangers by now. Every pair →
How many people play it
Under the crowd model, 31 is picked about 1.22× as often as an indifferent choice — 15th 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: 31 is drawn with probability 5/59 tonight whatever it did last week.