The "balanced" system that increases bets after losses and decreases after wins.
Named after French mathematician Jean-Baptiste le Rond d'Alembert, this system is based on the theory of equilibrium. The idea is that wins and losses should eventually balance out, so you increase bets by one unit after losses and decrease by one unit after wins.
| Spin | Bet | Outcome | Win/Loss | Running Total | Next Bet |
|---|---|---|---|---|---|
| 1 | $1 | Loss | -$1 | -$1 | $2 |
| 2 | $2 | Loss | -$2 | -$3 | $3 |
| 3 | $3 | Win | +$3 | $0 | $2 |
| 4 | $2 | Win | +$2 | +$2 | $1 |
| 5 | $1 | Loss | -$1 | +$1 | $2 |
Result: After 5 spins with 3 losses and 2 wins, we're ahead $1. Notice how the bet sizes change gradually (+1 after loss, -1 after win).
D'Alembert believed in the "law of equilibrium" - that if you flip a coin and get several heads, tails becomes more likely to "balance things out."
Reality Check: This is the gambler's fallacy. Each spin is independent, and past results don't affect future outcomes.
Despite the flawed theory, the system creates a much gentler progression than Martingale:
Bets increase slowly and predictably
Easy rules: +1 after loss, -1 after win
Lower risk than exponential systems
Can't lose everything in one bad sequence
Equilibrium theory doesn't apply to roulette
Extended losing runs increase bet sizes
Still lose 2.7% of total bets over time
Takes longer to recoup losses than Martingale
| Factor | D'Alembert | Martingale |
|---|---|---|
| Progression Type | Linear (+1/-1) | Exponential (x2) |
| After 10 losses | $11 bet | $1,024 bet |
| Total risk (10 losses) | $55 | $1,023 |
| Recovery time | Slower | Immediate |
| Risk level | Medium | Very High |
Key Insight: D'Alembert is much safer in terms of bet size progression, but it's still a progressive system that can lead to losses during long unfavorable streaks.
Some players use the "Reverse D'Alembert" (also called "Contra D'Alembert"):
Starting with $1 base bet, after 15 consecutive losses:
15th bet size: $16
Total lost: $120
To break even: Need 15 consecutive wins
D'Alembert's equilibrium theory assumes that wins and losses will balance out in the short term. In reality, this "balance" only occurs over extremely long periods, and the house edge ensures you'll have slightly more losses than wins.
D'Alembert can seem successful in short sessions because the slow progression means you're less likely to hit extreme bet sizes. However, this also means slower recovery from losses.
Like all betting systems, D'Alembert doesn't change your expected value. You'll still lose about 2.7% of your total wagered amount on European roulette over time.
We ran D'Alembert through 10,000 simulated sessions on a European wheel: $1,000 bankroll, $5 base unit, stopping at $1,500 (win), $500 (loss), or 500 spins.
Methodology: results are generated by our open simulation engine with a fixed random seed, using the same default settings as the interactive simulator below — so you can reproduce and vary them yourself. The average result is negative because no betting progression changes the house edge; these numbers show how D'Alembert shapes the way you win or lose, not whether you win long-term.
Run your own D'Alembert simulation with different settings →Change the bankroll, base unit, and stop rules, run thousands of sessions, and sweep parameters to see how the numbers above shift.
Open the D'Alembert simulatorD'Alembert is a conservative progressive system with lower risk than most alternatives. While it's based on flawed logic, the slow progression makes it much safer than Martingale or Fibonacci for players who insist on using a progressive system.
Try the D'Alembert strategy in our simulator and compare it with other betting systems.
Test D'Alembert Strategy