In EuroMillions under the 5/50 + 2/9 · Feb 2004 – May 2011 rules — 378 draws, 5 from 1–50 (an earlier era).
39times drawn · chance expected 38 +0.21σ
11draws waiting · a wait this long: 35% for any number
9.5average wait between appearances · chance says 10.0
66longest completed wait · 4% chance of one at least that long
3 is drawn as often as chance explains
Drawn 39 times in 378 draws against 37.8 expected, +0.21σ. Each draw is independent: after 11 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 39 times in 378 draws · average wait 9.5 draws · longest completed wait 66 · waiting 11 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 1 of the other 49 numbers; chance expects about 2 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 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.