In Eurojackpot under the 5/50 + 2/8 · Mar 2012 – Oct 2014 rules — 133 draws, 2 from 1–8 (an earlier era).
33times drawn · chance expected 33 −0.05σ
3draws waiting · a wait this long: 56% for any number
3.9average wait between appearances · chance says 4.0
12longest completed wait · 75% chance of one at least that long
3 is drawn as often as chance explains
Drawn 33 times in 133 draws against 33.3 expected, −0.05σ. Each draw is independent: after 3 draws away it is exactly as likely tonight as a number drawn yesterday.
3
Number 3, draw by draw
Drawn 33 times in 133 draws · average wait 3.9 draws · longest completed wait 12 · waiting 3 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 7 numbers; chance expected about 0.1 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 8. 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 2/8 tonight whatever it did last week.