In Montana Cash under the 5/37 · Apr 2010 – May 2014 rules — 428 draws, 5 from 1–37 (an earlier era).
64times drawn · chance expected 58 +0.87σ
1draws waiting · a wait this long: >99% for any number
6.3average wait between appearances · chance says 7.4
37longest completed wait · 29% chance of one at least that long
31 is drawn as often as chance explains
Drawn 64 times in 428 draws against 57.8 expected, +0.87σ. Each draw is independent: after 1 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 64 times in 428 draws · average wait 6.3 draws · longest completed wait 37 · waiting 1 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.
It has shared a draw with every one of the other 36 numbers; chance expected about 0.0 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 37. 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 5/37 tonight whatever it did last week.