Number 3

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

9times drawn · chance expected 8 +0.20σ

9draws waiting · a wait this long: 42% for any number

8.8average wait between appearances · chance says 9.8

30longest completed wait · 31% chance of one at least that long

3 is drawn as often as chance explains

Drawn 9 times in 83 draws against 8.4 expected, +0.20σ. Each draw is independent: after 9 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 3, draw by draw

Drawn 9 times in 83 draws · average wait 8.8 draws · longest completed wait 30 · waiting 9 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.

1st smallest8 · chance 7.5
2nd smallest1 · chance 1.4
3rd smallest0 · chance 0.1
4th smallest0 · chance 0.0
5th smallest0 · chance 0.0
6th smallest0 · chance 0.0

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 0.8 shared draws, and the leaders are simply the ones that came out ahead this time.

40 4 5 8 14 18

Never drawn alongside 27 of the other 58 numbers; chance expects about 27 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 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
Numbers 1–12 — day and month overlap ×1.10
Culturally lucky numbers 3, 8, 9 ×1.10

The model and its sources → · What people believe about 3 →

Every draw it appeared in

Date	Wait	Position	The draw
2010-09-15	2	1st	3 17 37 44 46 57
2010-09-08	10	2nd	2 3 21 25 45 53
2010-08-04	2	1st	3 7 18 36 44 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: 3 is drawn with probability 6/59 tonight whatever it did last week.