In Powerball under the 6/40 + 1/20 · Mar 2013 – Apr 2018 rules — 267 draws, 6 from 1–40 (an earlier era).
45times drawn · chance expected 40 +0.85σ
0draws waiting — it came up last time
5.8average wait between appearances · chance says 6.7
21longest completed wait · 82% chance of one at least that long
31 is drawn as often as chance explains
Drawn 45 times in 267 draws against 40.0 expected, +0.85σ. Each draw is independent: after 0 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 45 times in 267 draws · average wait 5.8 draws · longest completed wait 21 · drawn in the most recent draw
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.
It has shared a draw with every one of the other 39 numbers; chance expected about 0.1 still unmet 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 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: 31 is drawn with probability 6/40 tonight whatever it did last week.