In Mega Millions under the 5/56 + 1/46 · Jun 2005 – Oct 2013 rules — 869 draws, 1 from 1–46 (an earlier era).
20times drawn · chance expected 19 +0.26σ
126draws waiting · a wait this long: 6% for any number
38.7average wait between appearances · chance says 46.0
144longest completed wait · 57% chance of one at least that long
2 is drawn as often as chance explains
Drawn 20 times in 869 draws against 18.9 expected, +0.26σ. Each draw is independent: after 126 draws away it is exactly as likely tonight as a number drawn yesterday.
2
Number 2, draw by draw
Drawn 20 times in 869 draws · average wait 38.7 draws · longest completed wait 144 · waiting 126 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 2 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 45 of the other 45 numbers; chance expects about 45 such strangers by now. Every pair →
How many people play it
Under the crowd model, 2 is picked about 1.34× as often as an indifferent choice — 6th most popular of 46. 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: 2 is drawn with probability 1/46 tonight whatever it did last week.