The memoryless machine

“That number is due.”

It is the most persistent feeling in the game, and Cash 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.

Somebody has to be the straggler

Longest current waits across 37 numbers and 5,246 draws.

A given number waiting 2,527 draws happens <0.1% of the time. But the chance that some number among all 37 is at least this overdue right now is <0.1%. The board is never empty. Somebody always has to be at the top of it.

Number 6, draw by draw

Drawn 730 times in 5,246 draws · average wait 7.2 draws · longest completed wait 48 · waiting 17 draws now

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

Does waiting help?

Cash 55/37 era · since Jan 20105,246 draws

Scroll the chart sideways →

If “due” were real, this line would climb to the right. Each point is every occasion in 5,246 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 2431 of 2435 points sit outside the rule’s 95% interval, about the 122 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

Cash 55/37 era · since Jan 20105,246 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 (60 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.

37 has been waiting 2,527 draws — the era’s worst. A fair machine’s worst drought over this many draws lands between 63–88, 71. This one is outside that band: 1.7% of fair eras produced a drought at least this long. Before reading anything into it, see the look-elsewhere note in the maths.

p = 0.017Flagged honestly, and measured against 60 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 37 numbers and 5,246 draws.

372,527drawslast seen 2018-09-19 · 2,948 days341.5× the average<0.1%how likely
362,526drawslast seen 2018-09-20 · 2,947 days341.4× the average<0.1%how likely
2523drawslast seen 2026-09-18 · 27 days3.1× the average3.5%how likely
1622drawslast seen 2026-09-19 · 26 days3.0× the average4.1%how likely
617drawslast seen 2026-09-25 · 20 days2.3× the average8.5%how likely
715drawslast seen 2026-09-28 · 17 days2.0× the average11.3%how likely

Real records

Against the longest drought a provably fair machine produces over the same number of draws (60 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 = 0.017Flagged honestly, and measured against 60 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 37 numbers and 5,246 draws.

936drawslast seen 2026-09-03 · 42 days4.9× the average0.5%how likely
1931drawslast seen 2026-09-09 · 36 days4.2× the average1.1%how likely
1725drawslast seen 2026-09-16 · 29 days3.4× the average2.7%how likely
419drawslast seen 2026-09-23 · 22 days2.6× the average6.3%how likely
2616drawslast seen 2026-09-26 · 19 days2.2× the average9.8%how likely
214drawslast seen 2026-09-29 · 16 days1.9× the average13.1%how likely

A given number waiting 36 draws happens 0.5% of the time. But the chance that some number among all 37 is at least this overdue right now is 18.1%. 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 (60 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.

16 waited 66 draws — the era’s worst. A fair machine’s worst drought over this many draws lands between 63–88, 71. 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 37 numbers for 5,246 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 6, 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