The D’Alembert strategy is one of the most “peaceful” ways to manage a bankroll on bets with nearly even probabilities. Unlike Martingale, it doesn’t try to “break” variance with one or two aggressive pushes; it proceeds steadily: after a loss the stake increases by a fixed step, after a win it decreases by the same step. Because it uses an arithmetic rather than a geometric progression, the load on the bankroll is spread smoothly and sessions last longer. It doesn’t promise miracles like guaranteed profit, but it helps keep risk in check and instills discipline.
What Exactly Is the D’Alembert Progression
The system rests on a simple idea: work with a “betting unit” (unit). You choose the size of the unit, and then:
- loss → the next spin’s stake increases by +1 unit;
- win → the stake decreases by −1 unit (you don’t go below 1 unit).
This is an arithmetic progression: changes happen by a fixed amount, not by multiplication. Unlike Martingale, where after a string of losses the stake snowballs, in D’Alembert the growth rate is moderate. The upshot is simple: when wins and losses are close in number, you often finish the cycle around breakeven or with a small profit — thanks to the symmetry of steps up and down.
Where the Strategy Fits and Why “Even Chances” Aren’t Truly 50/50
D’Alembert is used where there are even-money (1:1) outcomes: “red/black,” “even/odd,” “low/high.” In roulette these markets pay 1:1, but the expected value is slightly negative because of zero:
- European roulette (single 0): 18 winning numbers out of 37 → probability ≈ 48.65%, house edge ≈ 2.70%.
- American roulette (0 and 00): 18 out of 38 → probability ≈ 47.37%, house edge ≈ 5.26%.
The lower the house edge, the healthier a long progression will be. That’s why a single-zero wheel and, where available, “En Prison/La Partage” rules are preferable for D’Alembert.
The Algorithm, Without the Fluff
- Set your bankroll. The sum you’re comfortable spending for the session.
- Choose your unit — 1–2% of the bankroll. This helps you withstand long streaks.
- Place the first bet = 1 unit on the chosen even-money outcome.
- Adjust the stake: +1 unit after a loss, −1 unit after a win (but not below 1).
- Define stop-loss and take-profit. For example, −10 units and +10–15 units for the session.
- Respect table limits. If your next step hits the maximum, end the cycle and restart from 1 unit.
A Worked Scenario: How the “Steady” Ladder Plays Out
Suppose your bankroll is $1,200 and your unit is $40 (≈ 1/30 of the bank). You bet on “red.”
- Spin 1: stake 1U ($40). Win → bankroll $1,240. Next stake remains 1U (you can’t go lower).
- Spin 2: 1U ($40). Loss → bankroll $1,200. Next stake 2U.
- Spin 3: 2U ($80). Loss → bankroll $1,120. Next 3U.
- Spin 4: 3U ($120). Loss → bankroll $1,000. Next 4U.
- Spin 5: 4U ($160). Win → bankroll $1,160. Next 3U.
- Spin 6: 3U ($120). Win → bankroll $1,280. Next 2U.
- Spin 7: 2U ($80). Win → bankroll $1,360. Next 1U.
After a brief downswing followed by three wins in a row, you’re up 4 units (+$160) from the start. Important note: an equal number of wins and losses doesn’t always yield zero — thanks to the stepped stake structure, a cycle often closes with a small profit.
Strengths, Weak Spots, and Common Pitfalls
Advantages:
- Low aggression. Growth is gentle; the bankroll lasts longer than with geometric scaling.
- Easy calculations. No multipliers required — the step is always fixed.
- Psychological comfort. It’s easier to endure streaks knowing the next step won’t “eat half the bank.”
Disadvantages:
- Doesn’t offset all losses with a single win. You may need a run of wins to get positive.
- Variance and house edge dominate. House edge doesn’t vanish; over the long run EV is negative.
- Table limits are real. A long losing streak can push you into the max, halting the progression.
Pitfalls to Avoid:
- Oversized unit (more than 2–3% of the bank) — the strategy loses its “steady” character.
- No stop-loss/take-profit — sessions drag on and emotional load increases.
- Switching markets on emotion mid-cycle — it breaks the logic of the progression.
- Playing American roulette when European is available — you’re voluntarily giving up extra edge.
Getting the Most Out of This “Steady” Progression
- Play single-zero. If La Partage/En Prison are offered, take them — they reduce the cost of zero.
- Keep records. Track the sequence of stakes and the unit-based balance — it’s easier to close a cycle on time.
- Cap your stake. Pre-set a unit ceiling (e.g., 6–8U). On reaching it — stop and start a new series at 1U.
- Flexible take-profit. When you’ve banked +8–12U, don’t hesitate to leave the table. In these systems, discipline beats “chasing one more unit.”
- Same logic every spin. Treat zero as a loss for even-money bets — with no exceptions.
Reverse D’Alembert: When It Makes Sense to Flip the Logic
In the mirror version known as Reverse D’Alembert, you increase the stake by +1U after a win and decrease it by −1U after a loss (down to the minimum). The idea is to ride a streak by scaling up when the wheel “gives.” But this variant is more volatile and demands a firm take-profit; otherwise a single pullback can wipe out the cushion. If you’re new to progressions, start with the classic version — it’s about resilience, not aggression.
Should You Add D’Alembert to Your Toolkit
If a measured style suits you and you’re ready to be disciplined, D’Alembert is a worthy tool for structuring sessions on even-money markets. It doesn’t promise to beat mathematics or the house edge, but it helps you ride out variance without “burning” the bank in a couple of spins. Keys to a sensible outcome are a small unit, European roulette, a stake cap, pre-set loss/profit levels, and strict sequential execution. In this format, the strategy turns from a “quick way to win back losses” (which it is not) into a practical risk-management framework. Please play responsibly and remember: the aim isn’t to trick the wheel — it’s to help you stay rational at the table.
