In EuroMillions under the 5/50 + 2/11 · May 2011 – Sep 2016 rules — 562 draws, 5 from 1–50 (an earlier era).
52times drawn · chance expected 56 −0.59σ
17draws waiting · a wait this long: 19% for any number
10.7average wait between appearances · chance says 10.0
48longest completed wait · 30% chance of one at least that long
3 is drawn as often as chance explains
Drawn 52 times in 562 draws against 56.2 expected, −0.59σ. Each draw is independent: after 17 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 52 times in 562 draws · average wait 10.7 draws · longest completed wait 48 · waiting 17 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 0.7 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.