In Mega Millions under the 5/50 + 1/36 · Jan 1999 – May 2002 rules — 348 draws, 1 from 1–36 (an earlier era).
15times drawn · chance expected 10 +1.74σ
6draws waiting · a wait this long: 87% for any number
23.2average wait between appearances · chance says 36.0
58longest completed wait · 96% chance of one at least that long
3 is drawn as often as chance explains
Drawn 15 times in 348 draws against 9.7 expected, +1.74σ. 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 15 times in 348 draws · average wait 23.2 draws · longest completed wait 58 · 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.
Never drawn alongside 35 of the other 35 numbers; chance expects about 35 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 36. 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 1/36 tonight whatever it did last week.