Number 21

In New York Lotto under the 6/59 + 1/55 · Jan 2010 – Oct 2010 rules — 83 draws, 6 from 1–59 (an earlier era).

8times drawn · chance expected 8 −0.16σ

7draws waiting · a wait this long: 53% for any number

10.4average wait between appearances · chance says 9.8

32longest completed wait · 23% chance of one at least that long

21 is drawn as often as chance explains

Drawn 8 times in 83 draws against 8.4 expected, −0.16σ. Each draw is independent: after 7 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 21, draw by draw

Drawn 8 times in 83 draws · average wait 10.4 draws · longest completed wait 32 · waiting 7 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 21 has a favourite seat — chance gives a small number the low positions more often. That is the shape of sorting, not of the machine.

1st smallest1 · chance 0.9
2nd smallest3 · chance 2.6
3rd smallest3 · chance 2.8
4th smallest1 · chance 1.4
5th smallest0 · chance 0.3
6th smallest0 · chance 0.0

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 0.7 shared draws, and the leaders are simply the ones that came out ahead this time.

9 51 15 23 27 30

Never drawn alongside 27 of the other 58 numbers; chance expects about 29 such strangers by now. Every pair →

How many people play it

Under the crowd model, 21 is picked about 1.22× as often as an indifferent choice — 15th most popular of 59. That changes nothing about whether it comes up, and everything about how many ways a jackpot on it would be shared.

Numbers 1–31 — the birthday zone ×1.22

The model and its sources → · What people believe about 21 →

Every draw it appeared in

Date	Wait	Position	The draw
2010-09-22	1	3rd	4 18 21 30 44 59
2010-09-18	3	1st	21 23 26 42 51 58
2010-09-08	5	3rd	2 3 21 25 45 53

What this cannot tell you

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: 21 is drawn with probability 6/59 tonight whatever it did last week.