Double Diamond Simulator — it's just math

A reconstruction of IGT's Double Diamond Deluxe, the three-reel machine whose real design document — a PAR sheet — was obtained by researchers under freedom-of-information law. There is no secret algorithm, no "hot" or "cold" cycle, no memory of what you did before, and nothing that reacts to how you play. Every spin is three independent random numbers between 1 and 72. Every figure below is computed on this page by enumerating all 373,248 possible outcomes.

Reel weights reverse-engineered from Harrigan, K. A., & Dixon, M. (2009). PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling. Journal of Gambling Issues, 23, 81–110.

The machine

Three approved versions of the same game. Identical cabinet, identical glass, identical pay table, identical jackpot odds. Only the hidden reel weights differ — and the player has no way to tell which one they are sitting at.

Credits

100

Bet

Paid

Insert coin — good luck.

Spins

Wagered

Returned

—

Near misses

2 diamonds + 1 off the line

Watch the diamonds. The Double Diamond symbol is deliberately surrounded by a cluster of blank stops, so it lands just above or just below the payline many times more often than on it. You are meant to feel like you nearly won. Nothing nearly happened.

Nudges. Spin at normal speed and some reels stop on a blank, pause, then shunt one position so a symbol slides onto the payline. A marker shows what is about to happen: diamond pointing down means the symbol will drop onto the line, pointing up means it will rise onto it, and no marker means the reel has already finished. Real machines do this without warning. Critically, the nudge changes nothing — the three numbers were drawn before the reels stopped moving, and the payout is calculated from the final position either way. It exists to make a decided outcome feel like it is still being decided.

Pay table · one payline

Combination	1 credit	2 credits	3 credits	Odds

The Double Diamond is wild and substitutes for any symbol. One diamond in a winning combination doubles the prize, two diamonds quadruple it. The jackpot pays a bonus at three credits (2,500 instead of 2,400) — that is the entire mathematical basis of "always bet max", and it is worth 0.07%.

Simulation

Starting credits

Bet per spin

Credit value

Cash out at a gain of

Walk away at a loss of

Repeat this session how many times

Every session is played independently under the same rules, then averaged. Each is capped at spins.

Balance over time

individual sessions average of all sessions mathematical expectation cash-out goal walk-away floor

Where the sessions ended

Distribution of final balances. Bars left of the dashed line finished behind, bars right of it finished ahead.

The math — computed live, nothing hard-coded

Pays (per credit)	Combinations	Probability	1 in	Share of payback

The machine does not decide whether you win. It draws three numbers, reads them off three fixed strips, and pays exactly what the table says. Play once and anything can happen. Play a hundred thousand times and it converges on 92.6% — every time, on every machine of this type, forever.

Each physical reel has 22 stops. The computer picks a number from 1 to 72 and a weighted map converts it into one of those 22 stops — so the stops are not equally likely. This is the most misunderstood fact about slot machines: the thing you watch spinning is not the thing being randomised. Stops shown faded are never selected at all.

Blank stops are stacked around the Double Diamond, so it lands just off the payline far more often than on it.

Reel	Diamond on the payline	Diamond just above/below	Seen but not paid

A player who sees two diamonds and a third one a hair above the line feels like they almost won. Statistically nothing almost happened — the outcome was fixed the instant the three numbers were drawn. Near misses exist because they make people keep playing.

The single most important finding in the research: a casino can put several versions of the same game side by side and the player cannot tell them apart.

Version	Payback	House edge	Hit frequency	Jackpot odds	Cost per hour at $0.75/spin	Hours a $100 bankroll lasts

Same cabinet, same artwork, same pay table, same jackpot odds — and on the 85% machine your money disappears roughly four times faster than on the 96.2% one. Nothing on the outside of the machine tells you which is which.

What this machine costs to play

Based on 600 spins per hour, the speed of play the researchers measured on mechanical three-reel machines.

How long "luck" lasts

Spins played	Payback could be as low as	…or as high as

90% confidence interval from the volatility index (10.4) — the same calculation the manufacturer prints on its own PAR sheet. Short sessions are wild. Long ones are not.

The point. A 92.6% machine keeps 7.4 cents of every dollar staked — but you re-stake your winnings, so you do not lose 7.4% of what you walked in with, you lose 7.4% of everything you ever push through it. That is why the average session above ends far below −7.4%, and why "I was up earlier" is true for most players and irrelevant to all of them.