D'Alembert — Add one unit after a loss, subtract one after a win.

BeginnerRisk: MediumNegative progressions

Strategy guide

D'Alembert

Add one unit after a loss, subtract one after a win.

Best for: Players who want a structured even-money progression that grows more slowly than Martingale and is easier on a mid-sized bankroll.

Overview

D'Alembert is a classic negative-progression system named after the French mathematician Jean le Rond d'Alembert. On roulette it is applied to even-money bets: you choose a fixed unit size, start at one unit (or another agreed starting level), increase the next bet by one unit after a loss, and decrease by one unit after a win, never dropping below your base unit. The intellectual appeal is equilibrium—if wins and losses roughly alternate, the up-and-down steps may balance.

Compared with Martingale, stake growth is linear rather than geometric. After losses of one unit each time, you might climb 1 to 2 to 3 to 4 to 5 units instead of 1 to 2 to 4 to 8 to 16. That usually means slower recovery of a deep hole, but also a much lower chance of a single catastrophic sequence relative to pure doubling. Table limits still matter eventually, yet you typically get more spins before hitting a wall.

The equilibrium story is incomplete at a roulette table. Even-money bets are not fair coin flips: European single-zero wheels embed about a 2.70% house edge (about 1.35% with La Partage/En Prison on some even-money rules), and American double-zero wheels about 5.26%. Over time you expect slightly more losing units than winning units, so the progression tends to drift upward more than theory's balance suggests.

Session results under D'Alembert often look moderate: neither the tiny steady drip of flat betting nor the boom-and-bust of Martingale. A cluster of losses raises the stake gradually; a cluster of wins walks it back down. Because a win only reduces the stake by one unit, digging out of a long losing run can take many successful spins—patience is part of the design, not a bug.

Use D'Alembert as a bankroll-management framework and learning tool, not as a claim of advantage. Keep units small (often 1% or less of session funds), prefer European wheels, set stop-loss and stop-win points, and avoid inventing due outcomes. The system organizes bet size; it does not predict the next color.

Visual progression

D'Alembert +1 after loss / −1 after win (units)

How it works

Select an even-money outside bet and a unit size small enough for a long climb (for example $5 if your session bankroll is several hundred dollars).
Start the first spin at one unit (some players start at two or three units; pick one rule and keep it).
If the spin loses, increase the next bet by exactly one unit.
If the spin wins, decrease the next bet by exactly one unit, but not below your base unit.
Stay on the same even-money bet type for the sequence so the progression remains meaningful.
Optional: when you return to base unit with a net session profit, you may treat that as a completed cycle and reset goals.
If the next unit step would exceed table max or remaining bankroll, stop or drop to a planned maximum—do not improvise wild jumps.
End the session at predetermined profit/loss limits rather than waiting for perfect balance that may never arrive.

Worked $5-unit D'Alembert sequence

Spin 1: Bet $5 on even — lose. Net -$5. Next bet = $10.
Spin 2: Bet $10 on even — lose. Net -$15. Next bet = $15.
Spin 3: Bet $15 on even — lose. Net -$30. Next bet = $20.
Spin 4: Bet $20 on even — win. Net -$10. Next bet = $15.
Spin 5: Bet $15 on even — win. Net +$5. Next bet = $10.
Spin 6: Bet $10 on even — win. Net +$15. Next bet = $5 (back at base).
Spin 7: Bet $5 — lose. Net +$10. Climb resumes at $10; notice recovery took several wins after the three-loss hole.

Pros

Much milder stake growth than Martingale or Grand Martingale, reducing blow-up frequency.
Easy arithmetic: only add or subtract one unit after each result.
Works with modest bankrolls better than geometric doubling systems.
Gives a structured way to vary bets without complex cancellation lists.
Table limits are less likely to interrupt early compared with aggressive doublings.

Cons

Deep losing runs still raise stakes and can produce large drawdowns over many spins.
Recovery can be slow because each win only trims one unit from the stake level.
Does not cancel the house edge; long-run expected value stays negative.
False sense of balance may encourage longer sessions than flat betting would.
Less exciting for players seeking rapid recovery of a big early hole.

Bankroll & table limits

Keep the unit at roughly 0.5%-1% of session bankroll so a climb to 8-12 units remains survivable.
Simulate a worst reasonable climb (for example ten losses shifting you from 1u toward 11u) and ensure you can fund those bets.
European single-zero tables reduce the rate at which the progression is pushed upward by the edge compared with American wheels.
Set a maximum stake level in advance (for example never above 8 units) even if the pure system would continue rising.

Full bankroll guide →

Common mistakes

Starting with a unit that is already several percent of the bankroll, so a normal losing cluster hurts too much.
Jumping more than one unit after a loss to get even faster, which abandons D'Alembert for a hybrid mess.
Decreasing below the base unit or resetting inconsistently after wins, breaking the progression logic.
Believing that after several losses a win is due, so larger units feel safe—independence still holds.

FAQ

Can table limits stop a D'Alembert progression?

Yes, but usually later than with Martingale. If you keep adding a unit after every loss, a long cold run can still push the required stake to the table maximum. When that happens, you can no longer follow the pure +1 rule. Cap your climb before the max, or stop the session rather than inventing a new staking rule under pressure.

How does D'Alembert compare with Martingale?

Martingale doubles after each loss and aims to erase the whole streak with one win for about one unit of profit. D'Alembert moves one unit at a time, so risk per streak is lower and recovery is slower. Neither overcomes the house edge; D'Alembert is generally the medium-risk choice for players who find doubling too severe.

Is D'Alembert better on European or American roulette?

European single-zero is preferable. Even-money house edge is about 2.70% versus about 5.26% on American double-zero. The higher American edge means more losing results on average, which nudges a negative progression upward more often and costs more over time. Use La Partage/En Prison tables when available for even money, knowing the edge shrinks but does not disappear.

What bankroll suits D'Alembert?

Enough to fund a multi-unit climb without panic—often 50+ base units for a learning session, depending on how high you allow the stake to go. Because steps are linear, mid-sized bankrolls are more realistic than for Grand Martingale, but more realistic is not the same as safe from loss.

Does balancing wins and losses mean D'Alembert breaks even?

No. That is the central myth. Even if wins and losses alternate perfectly, the presence of zero(s) makes a true long-run balance of even-money outcomes unlikely, and every dollar wagered still carries a negative expectation. D'Alembert can smooth how losses appear; it cannot create a break-even game against the house.