Key facts
- The d'Alembert betting system adds one unit to your bet after a loss and takes one off after a win, never going below one unit.
- With equal wins and losses (and no drop to the floor) you finish ahead by one unit per win. Over 100 spins you stay ahead unless losses beat wins by 10 or more.
- On a single zero wheel losses outnumber wins by 10 or more in 26.5% of 100-spin runs, in our calculation.
- In our simulation a $5 d'Alembert with a $500 bankroll goes bust within 100 spins 30.6% of the time, and within 500 spins 83.1% of the time.
- Its average loss is still 2.70% of the total bet. Spread over many spins, that total gets large: about $2,316 bet in a typical 100-spin session at $5 units.
How the d'Alembert betting system works
The d'Alembert betting system is a slow, steady loss-chasing method. You bet a fixed unit on an even-money chance (red, black, odd, even, 1 to 18 or 19 to 36), raise the next bet by one unit after a loss, and lower it by one unit after a win. The bet never goes below one unit.
It rests on the hope that wins and losses even out. Unlike the Martingale there is no doubling, and unlike the Labouchere there is no line to finish. You just ride the ladder up and down.
A worked d'Alembert sequence at $5
Eight spins, four wins and four losses, in the order L, L, W, L, W, W, L, W:
| Spin | Bet | Result | Running total | Next bet |
|---|---|---|---|---|
| 1 | $5 | Loss | -$5 | $10 |
| 2 | $10 | Loss | -$15 | $15 |
| 3 | $15 | Win | $0 | $10 |
| 4 | $10 | Loss | -$10 | $15 |
| 5 | $15 | Win | +$5 | $10 |
| 6 | $10 | Win | +$15 | $5 |
| 7 | $5 | Loss | +$10 | $10 |
| 8 | $10 | Win | +$20 | $5 |
Even split, and you are $20 ahead: four wins, four units. That is the whole selling point of the d'Alembert strategy, and the arithmetic is correct.
The formula behind it
If your bet never touches the one-unit floor, your profit after n spins depends only on the gap between losses and wins at the end. Call that gap d (losses minus wins). In our derivation:
profit in units = (n minus d x (d + 2)) / 2
For 100 spins:
| Losses minus wins | Wins / losses | Profit (units) | At $5 a unit |
|---|---|---|---|
| 0 | 50 / 50 | +50 | +$250 |
| 4 | 48 / 52 | +38 | +$190 |
| 8 | 46 / 54 | +10 | +$50 |
| 10 | 45 / 55 | -10 | -$50 |
| 12 | 44 / 56 | -34 | -$170 |
| 14 | 43 / 57 | -62 | -$310 |
The profit falls with the square of the gap. A small gap still leaves you ahead; a gap of 10 or more flips you into a loss that grows fast. On a single zero wheel an even-money bet loses 19 spins in 37, and in our calculation the chance that losses beat wins by 10 or more over 100 spins is 26.5%.
The order also matters once the floor kicks in. Five wins then five losses leaves you 10 units down, because the wins were all placed at one unit and the losses climbed to five. Five losses then five wins leaves you 5 units up. Same results, opposite outcome.
A d'Alembert session, simulated
The formula ignores the floor and your bankroll, so we simulated 200,000 sessions of $5 units with a $500 bankroll (100 units), stopping when the next bet could not be covered:
| Spins | Bust | Finished ahead | Average result | Middle result | Worst 5% |
|---|---|---|---|---|---|
| 100 | 30.6% | 54.5% | -$64.60 | +$50 | -$485 or worse |
| 500 | 83.1% | 16.3% | -$224.34 | -$445 | -$495 or worse |
| 1,000 | 93.9% | 6.0% | -$310.06 | -$450 | -$495 or worse |
The middle result for a 100-spin session is a $50 profit, which is exactly why the system has fans. But almost a third of those sessions run out of money, and over longer play bust becomes the normal ending.
Why the gentle ladder still costs 2.70%
The d'Alembert never changes the edge on a single bet; it just keeps you betting more than one unit most of the time. In our simulation the average 100-spin session put $2,316 through the wheel at $5 units, and the average result was close to 2.70% of that, the same rate a flat $5 bettor pays. The longer you play, the more you bet and the more the edge collects. The VGCCC's plain summary applies: all table games provide a significant house edge to the casino.
Pundit tip: the d'Alembert's real danger is that it feels calm. Bets creep up by $5 at a time, so a $70 bet arrives without any sense of alarm. Set a maximum bet before you start and stop when you hit it.
Dalembert strategy compared with the others
| System | After a loss | After a win | Shape of results |
|---|---|---|---|
| D'Alembert | +1 unit | -1 unit | Steady small wins, slow-building large losses |
| Martingale strategy | Double | Back to 1 | One unit per run, rare huge loss |
| Fibonacci betting system | Next number | Back two numbers | Mostly break-even sequences, rare bust |
| Labouchere betting system | Add bet to line | Cross off two numbers | Line usually finishes, rare large loss |
| Paroli betting system | Back to 1 | Double | Small frequent losses, rare big win |
| Oscar's Grind | Same bet | +1 unit, capped | One unit per series, long losing series |
Every row costs the same 2.70% of the total bet on a single zero wheel. You can see the doubling version's numbers in our Martingale calculator.
Before you try it anywhere
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Frequently asked questions
How does the d'Alembert betting system work?
You choose a unit, say $5, and bet one unit on an even-money chance. After every loss you add one unit to the next bet; after every win you take one unit off, with one unit as the minimum. There is no target or end point; you simply stop when you choose to.
Is the d'Alembert strategy profitable?
No. It profits when wins and losses come out close to even, but losses outnumber wins slightly on a roulette wheel. In our simulation a $5 d'Alembert finished 100 spins ahead 54.5% of the time and lost $64.60 on average.
Why does the d'Alembert win when wins and losses are equal?
Because each win is placed at a higher stake than the loss it follows. Four wins and four losses in the order L, L, W, L, W, W, L, W at $5 units leave you $20 ahead, one unit per win.
What is the biggest risk with the d'Alembert?
A choppy run where losses edge ahead of wins by 10 or more. Your bet climbs a unit at a time and every loss is placed at the higher stake, so the losses grow with the square of the gap. A gap of 14 over 100 spins costs 62 units.
Is the reverse d'Alembert better?
No system changes the house edge. Raising after wins instead of losses swaps many small wins and rare large losses for many small losses and rare large wins, at the same 2.70% average cost.
Related reading
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