Number 31

In Mega Millions under the 5/50 + 1/25 · Sep 1996 – Jan 1999 rules — 172 draws, 5 from 1–50 (an earlier era).

16times drawn · chance expected 17 −0.30σ

2draws waiting · a wait this long: 90% for any number

11.1average wait between appearances · chance says 10.0

31longest completed wait · 48% chance of one at least that long

31 is drawn as often as chance explains

Drawn 16 times in 172 draws against 17.2 expected, −0.30σ. Each draw is independent: after 2 draws away it is exactly as likely tonight as a number drawn yesterday.

Number 31, draw by draw

Drawn 16 times in 172 draws · average wait 11.1 draws · longest completed wait 31 · waiting 2 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 0.3
2nd smallest6 · chance 2.2
3rd smallest5 · chance 5.6
4th smallest3 · chance 5.8
5th smallest2 · chance 2.1

Every position’s lane →

The company it keeps

Seen most often with these — chance gives every partner about 1.3 shared draws, and the leaders are simply the ones that came out ahead this time.

21 32 34 43 7 12

Never drawn alongside 15 of the other 49 numbers; chance expects about 13 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 50. 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
1999-01-05	3	2nd	4 31 32 34 43
1998-12-25	30	5th	6 8 17 21 31
1998-09-11	9	2nd	21 31 34 35 43
1998-08-11	5	2nd	7 31

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 5/50 tonight whatever it did last week.