In Texas Two Step under the 4/35 + 1/35 · since Sep 2025 rules — 113 draws, 4 from 1–35.
12times drawn · chance expected 13 −0.27σ
2draws waiting · a wait this long: 89% for any number
9.9average wait between appearances · chance says 8.8
55longest completed wait · 2% chance of one at least that long
31 is drawn as often as chance explains
Drawn 12 times in 113 draws against 12.9 expected, −0.27σ. Each draw is independent: after 2 draws away it is exactly as likely tonight as a number drawn yesterday.
31
Number 31, draw by draw
Drawn 12 times in 113 draws · average wait 9.9 draws · longest completed wait 55 · waiting 2 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 11 of the other 34 numbers; chance expects about 12 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 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.