D'Alembert Calculator
The D'Alembert ladder raises your bet one unit after a loss and steps back down after a win. This calculator prices that ladder against a real casino: how deep your bankroll takes it, where the table max cuts it off first, and the exact odds of the streak that gets you there — in Classic and Contra (reversed) form.
01Casino
02System
03Your numbers
The ladder
| Step | Bet | Cumulative | Chance to reach |
|---|---|---|---|
Illustrative math, not advice: the house edge stays negative in both directions, and no ladder changes that. Preset limits and edges load from the same audited data as our dice simulator; the Generic chip is yours to fill in.
See the ladder on a live dice session
The calculator above is the math; the simulator below is the experience. Pick a casino, keep the D'Alembert strategy that's preloaded, and hit RUN to watch the ladder climb and fall on a real seeded session.
Casino
Stake
No session yet
- Final balance where the session ended
- Net profit against your starting bankroll
- Total wagered what the edge is charged on
- Max drawdown deepest peak-to-trough dip
- Longest streaks best win · loss run
Session detail
- Expected edge cost
- Net incl. rakeback
- Rakeback earned
- Win rate
- ROI (net / wagered)
- Session outcome
Illustrative RNG simulation — every run is a fresh random session, not a prediction or a profit guarantee. Payout multipliers are rounded the way each casino’s own panel displays them: that is a model of what the panel shows, measured in-account, and not a rounding we have confirmed against a settled bet.
How to use the D'Alembert calculator
- Pick your casino. The limits and house edge load from the same audited data our dice simulator uses.
- Choose the direction. Classic raises bets after losses; Contra raises them after wins — and Contra is what Stake actually ships under the D'Alembert name.
- Set your base bet, the unit, and your win chance. The payout line updates from the casino's edge.
- Enter your bankroll and how many bets you plan. The headlines show where the ladder dies and the odds of getting there.
- Read the ladder table before you play: every step shows the bet, the money already committed, and the chance of reaching that step.
Classic vs Contra
Classic D'Alembert raises your bet by one unit after every loss and lowers it by one unit after every win, so a single win only undoes a single loss. It is the gentlest of the progressive systems: no doubling, no explosive ladder, just a slow one-unit walk up and down.
Contra D'Alembert reverses the rule: raise by one unit after a win, lower by one unit after a loss. That means you bet more when you're already winning and less when you're already losing — a give-back risk, since a losing streak that follows a hot run gives back size at the top of the ladder instead of the bottom.
Here is the twist worth knowing: Stake’s own “D’Alembert” strategy is built as Contra, not Classic — the opposite of what the name traditionally means. Use the badge’s button to flip the math and compare both directly.
Note: limits and edges come live from the same data the simulator runs on, checked against the casinos’ real games. Casinos move their tables — the game’s own info panel is always the source of truth. Where no table max is published, the table-max line simply hides.
FAQ
Why does Stake's D'Alembert behave backwards?
We audited Stake’s shipped strategy and it raises the bet after a win and lowers it after a loss — that is Contra, not the textbook Classic D’Alembert. This calculator defaults to whichever direction matches what you came to check, and the Stake badge lets you flip between Classic and Contra with one click so you can compare both against the same casino.
What kills the ladder first — my bankroll or the table max?
Either can, and it’s not always the one you’d guess. The calculator prices both death points separately: the step where your bankroll runs out, and the step where the bet would exceed the casino’s published table max. Whichever comes first is the one that actually binds — a deep bankroll is no protection if the table max cuts the ladder off three steps earlier.
Does finishing at the base bet really mean profit?
In Classic D’Alembert, yes — if wins and losses land in equal numbers and the ladder walks back down to the base bet, the session nets a profit equal to one unit per matched win/loss pair. That parity identity is real math, not a promise: it only holds at an even-money payout, and it says nothing about how many bets it takes to get there or whether the table max lets you finish the walk at all.
Where do the limits come from?
The same live casino data that powers our dice simulator — table max, minimum bet and house edge, pulled from published, audited sources and refreshed as casinos change their tables. Nothing here is estimated for this calculator specifically.
Want the strategy itself, explained? Read the D’Alembert strategy page. Sizing a doubling ladder instead? The Martingale Calculator prices that one.