In Texas Two Step under the 4/35 + 1/0 · Nov 2022 – Sep 2025 rules — 296 draws, 4 from 1–35 (an earlier era).
37times drawn · chance expected 34 +0.58σ
3draws waiting · a wait this long: 78% for any number
7.8average wait between appearances · chance says 8.8
28longest completed wait · 75% chance of one at least that long
31 is drawn as often as chance explains
Drawn 37 times in 296 draws against 33.8 expected, +0.58σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 37 times in 296 draws · average wait 7.8 draws · longest completed wait 28 · 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 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 34 numbers; chance expected about 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 35. 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 4/35 tonight whatever it did last week.