Number 31

In Daily Million Plus 2pm under the 6/39 + 1/38 · Apr 2016 – Jul 2016 rules — 86 draws, 6 from 1–39 (an earlier era).

16times drawn · chance expected 13 +0.83σ

1draws waiting · a wait this long: >99% for any number

5.4average wait between appearances · chance says 6.5

18longest completed wait · 59% chance of one at least that long

31 is drawn as often as chance explains

Drawn 16 times in 86 draws against 13.2 expected, +0.83σ. Each draw is independent: after 1 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 16 times in 86 draws · average wait 5.4 draws · longest completed wait 18 · waiting 1 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 0.0
2nd smallest1 · chance 0.1
3rd smallest1 · chance 0.8
4th smallest2 · chance 3.6
5th smallest7 · chance 7.0
6th smallest5 · chance 4.5

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 2.1 shared draws, and the leaders are simply the ones that came out ahead this time.

11 8 16 17 23 35

Never drawn alongside 3 of the other 38 numbers; chance expects about 5 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 39. 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
2016-07-18	18	4th	7 24 30 31 34 38
2016-06-30	3	5th	10 16 21 29 31 38
2016-06-27	4	5th	9 14 15 23 31 34

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 6/39 tonight whatever it did last week.