In Fantasy 5 under the 5/39 · Apr 2010 – Mar 2011 rules — 285 draws, 5 from 1–39 (an earlier era).
31times drawn · chance expected 37 −0.98σ
11draws waiting · a wait this long: 25% for any number
8.8average wait between appearances · chance says 7.8
29longest completed wait · 48% chance of one at least that long
31 is drawn as often as chance explains
Drawn 31 times in 285 draws against 36.5 expected, −0.98σ. Each draw is independent: after 11 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 31 times in 285 draws · average wait 8.8 draws · longest completed wait 29 · waiting 11 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 1 of the other 38 numbers; chance expects about 1 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 39. 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 5/39 tonight whatever it did last week.