In Mega Millions under the 5/50 + 1/36 · Jan 1999 – May 2002 rules — 348 draws, 5 from 1–50 (an earlier era).
31times drawn · chance expected 35 −0.68σ
6draws waiting · a wait this long: 59% for any number
11.1average wait between appearances · chance says 10.0
49longest completed wait · 17% chance of one at least that long
3 is drawn as often as chance explains
Drawn 31 times in 348 draws against 34.8 expected, −0.68σ. Each draw is independent: after 6 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 31 times in 348 draws · average wait 11.1 draws · longest completed wait 49 · waiting 6 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.
It has shared a draw with every one of the other 49 numbers; chance expected about 4 still unmet 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 50. 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 5/50 tonight whatever it did last week.