In Lotto under the 6/52 + 1/25 · Oct 2012 – Jan 2015 rules — 339 draws, 6 from 1–52 (an earlier era).
44times drawn · chance expected 39 +0.83σ
5draws waiting · a wait this long: 61% for any number
7.6average wait between appearances · chance says 8.7
25longest completed wait · 90% chance of one at least that long
51 is drawn as often as chance explains
Drawn 44 times in 339 draws against 39.1 expected, +0.83σ. Each draw is independent: after 5 draws away it is exactly as likely tonight as a number drawn yesterday.
51
Number 51, draw by draw
Drawn 44 times in 339 draws · average wait 7.6 draws · longest completed wait 25 · waiting 5 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 51 has a favourite seat — chance gives a large number the high positions more often. That is the shape of sorting, not of the machine.
It has shared a draw with every one of the other 51 numbers; chance expected about 0.7 still unmet by now. Every pair →
How many people play it
Under the crowd model, 51 is picked about 0.86× as often as an indifferent choice — 34th most popular of 52. 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: 51 is drawn with probability 6/52 tonight whatever it did last week.