In Mega Millions under the 5/75 + 1/15 · Oct 2013 – Oct 2017 rules — 420 draws, 5 from 1–75 (an earlier era).
29times drawn · chance expected 28 +0.20σ
40draws waiting · a wait this long: 7% for any number
13.5average wait between appearances · chance says 15.0
41longest completed wait · 84% chance of one at least that long
3 is drawn as often as chance explains
Drawn 29 times in 420 draws against 28.0 expected, +0.20σ. Each draw is independent: after 40 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 29 times in 420 draws · average wait 13.5 draws · longest completed wait 41 · waiting 40 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 13 of the other 74 numbers; chance expects about 15 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 75. 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 5/75 tonight whatever it did last week.