The memoryless machine

“That number is due.”

It is the most persistent feeling in the game, and Pick 5 has a number to hang it on right now. Here is the board. Then here is the era’s own history, asked whether waiting has ever made the slightest difference.

Reading the evening draw only — 3,657 draws. This game also runs 1 separate series (midday), left out on purpose: waits only mean something inside one draw series.

Somebody has to be the straggler

Longest current waits across 10 numbers and 3,657 draws.

A given number waiting 5 draws happens 3.1% of the time. But the chance that some number among all 10 is at least this overdue right now is 27.2%. The board is never empty. Somebody always has to be at the top of it.

Number 2, draw by draw

Drawn 1,878 times in 3,657 draws · average wait 1.9 draws · longest completed wait 20 · waiting 2 draws now

a completed wait — darker is longer the wait still running — a lower bound, not a finished gap

Does waiting help?

Pick 55/9 era · since Sep 20123,657 draws

Scroll the chart sideways →

If “due” were real, this line would climb to the right. Each point is every occasion in 3,657 draws when a number had waited at least that long, and how often it turned up in the very next draw. It wanders, because every point is a sample — but 11 of 12 points sit outside the rule’s 95% interval, about the 1 chance alone predicts. The whiskers are those 95% intervals; the gold point gathers every longer wait there is, and the chart stops where too few occasions remain to say anything honest.

How long numbers actually wait

Pick 55/9 era · since Sep 20123,657 draws

Scroll the chart sideways →

Most waits are short. The long ones are what people notice.

Every completed wait in this era, against the geometric curve chance predicts. Switch to the log scale to watch the tail — the part nobody checks — fall on the same line as the rest.

The record book

Against the longest drought a provably fair machine produces over the same number of draws (200 simulated eras).

The band is the range for a fair machine’s single worst drought, so only the top row is measured against it. The rows beneath are this era’s runners-up, and they fall short of it by construction.

2 waited 20 draws — the era’s worst. A fair machine’s worst drought over this many draws lands between 13–19, 15. This one is outside that band: 4.0% of fair eras produced a drought at least this long. Before reading anything into it, see the look-elsewhere note in the maths.

p = 0.040Flagged honestly, and measured against 200 simulated eras — which is the resolution limit, not a claim of proof.

Now the same thing, with nothing behind it

The right-hand era never happened. It came out of a random number generator moments ago, so there is provably no bias, no worn ball, no pattern of any kind in it. Compare the two boards.

The real era

Somebody has to be the straggler

Longest current waits across 10 numbers and 3,657 draws.

05drawslast seen 2026-10-23 · 5 days2.5× the average3.1%how likely
93drawslast seen 2026-10-25 · 3 days1.5× the average12.5%how likely
22drawslast seen 2026-10-26 · 2 days1.0× the average25.0%how likely
32drawslast seen 2026-10-26 · 2 days1.0× the average25.0%how likely
51drawslast seen 2026-10-27 · 1 days0.5× the average50.0%how likely
10drawslast seen 2026-10-28 · 0 days0.0× the average>99.9%how likely

Real records

Against the longest drought a provably fair machine produces over the same number of draws (200 simulated eras).

The band is the range for a fair machine’s single worst drought, so only the top row is measured against it. The rows beneath are this era’s runners-up, and they fall short of it by construction.

p = 0.040Flagged honestly, and measured against 200 simulated eras — which is the resolution limit, not a claim of proof.

A machine we know is fair

Somebody has to be the straggler

Longest current waits across 10 numbers and 3,657 draws.

13drawslast seen 2026-10-25 · 3 days1.5× the average12.5%how likely
63drawslast seen 2026-10-25 · 3 days1.5× the average12.5%how likely
92drawslast seen 2026-10-26 · 2 days1.0× the average25.0%how likely
21drawslast seen 2026-10-27 · 1 days0.5× the average50.0%how likely
51drawslast seen 2026-10-27 · 1 days0.5× the average50.0%how likely
00drawslast seen 2026-10-28 · 0 days0.0× the average>99.9%how likely

A given number waiting 3 draws happens 12.5% of the time. But the chance that some number among all 10 is at least this overdue right now is 73.7%. The board is never empty. Somebody always has to be at the top of it.

Simulated records

Against the longest drought a provably fair machine produces over the same number of draws (200 simulated eras).

The band is the range for a fair machine’s single worst drought, so only the top row is measured against it. The rows beneath are this era’s runners-up, and they fall short of it by construction.

3 waited 13 draws — the era’s worst. A fair machine’s worst drought over this many draws lands between 13–19, 15. It is comfortably inside the band. Nothing to explain.

Both boards have a straggler. Both have a drought that would make a headline. Drama is not evidence — it is what watching 10 numbers for 3,657 draws looks like.

The two layers underneath

The maths, in plain language

The story behind it

Monte Carlo Casino, 18 August 1913: 26 consecutive blacks — the origin of the “Monte Carlo fallacy”.
Italy, Venice wheel: number 53 absent for 182 draws to 9 February 2005; ≈€3.5bn staked; bankruptcies and deaths reported in the Italian and international press (incl. The Guardian, February 2005).
Clotfelter, C. & Cook, P. “The ‘Gambler’s Fallacy’ in Lottery Play.” Management Science 39(12), 1993.

“That number is due.”

Somebody has to be the straggler

Number 2, draw by draw

Does waiting help?

How long numbers actually wait

The record book

Now the same thing, with nothing behind it

Somebody has to be the straggler

Real records

Somebody has to be the straggler

Simulated records

Every draw is a fresh coin

The mean is not the typical wait

Memorylessness — the whole argument

Why a long drought is guaranteed

Two honest caveats

Monte Carlo, 18 August 1913

Italy, 2003 to 2005

Why the intuition exists at all

The one real effect