Number 31

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

7times drawn · chance expected 8 −0.52σ

23draws waiting · a wait this long: 9% for any number

9.5average wait between appearances · chance says 9.8

23longest completed wait · 45% chance of one at least that long

31 is drawn as often as chance explains

Drawn 7 times in 83 draws against 8.4 expected, −0.52σ. Each draw is independent: after 23 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 7 times in 83 draws · average wait 9.5 draws · longest completed wait 23 · waiting 23 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 31 has a favourite seat — chance gives a large number the high positions more often. That is the shape of sorting, not of the machine.

1st smallest0 · chance 0.2
2nd smallest3 · chance 0.9
3rd smallest1 · chance 2.2
4th smallest0 · chance 2.3
5th smallest3 · chance 1.2
6th smallest0 · chance 0.2

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 0.6 shared draws, and the leaders are simply the ones that came out ahead this time.

38 46 13 15 58 3

Never drawn alongside 30 of the other 58 numbers; chance expects about 32 such strangers by now. Every pair →

How many people play it

Under the crowd model, 31 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 31 →

Every draw it appeared in

Date	Wait	Position	The draw
2010-07-28	8	5th	3 8 12 15 31 51
2010-06-30	15	5th	4 6 27 28 31 38
2010-05-08	23	2nd	7 31 33 38 45 46

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