In Powerball Double Play under the 5/69 + 1/26 · since Aug 2021 rules — 810 draws, 1 from 1–26.
35times drawn · chance expected 31 +0.70σ
18draws waiting · a wait this long: 51% for any number
22.8average wait between appearances · chance says 26.0
105longest completed wait · 44% chance of one at least that long
3 is drawn as often as chance explains
Drawn 35 times in 810 draws against 31.2 expected, +0.70σ. Each draw is independent: after 18 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 35 times in 810 draws · average wait 22.8 draws · longest completed wait 105 · waiting 18 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 3 has a favourite seat — chance gives a small number the low positions more often. That is the shape of sorting, not of the machine.
Never drawn alongside 25 of the other 25 numbers; chance expects about 25 such strangers by now. Every pair →
How many people play it
Under the crowd model, 3 is picked about 1.48× as often as an indifferent choice — 2nd most popular of 26. 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: 3 is drawn with probability 1/26 tonight whatever it did last week.