D’Alembert

Risk · Medium Negative Progression
In one paragraph

Add one unit after a loss, subtract one after a win. Far gentler than Martingale — drawdowns grow linearly, not exponentially — but recovery is also much slower.

How the ladder moves

9 published steps · one unit = the base bet
1 lost 2 lost 3 lost 4 won 3 lost 4 lost 5 won 4 won 3  

Win and loss are not recorded anywhere — they are read off the sequence. On a negative progression a bigger next bet means the one before it lost, and a smaller one means it won. The last step has nothing after it, so it carries no mark.

Works because

  • Much gentler bankroll growth than Martingale — losses scale linearly
  • Ideal for players who want a 'system feel' with manageable risk
  • Works well in medium-session rakeback-farming alongside the grind strategy
  • Low hidden-max-bet risk since bet sizes stay small

Breaks because

  • Recovery is slow: needs one more win than loss to return to baseline
  • Still negative EV on any game without compensating rakeback
  • Long losing runs still create meaningful drawdowns — not 'safe'
  • Requires discipline to track the current step without automation

Run the numbers

live · no calculate button
Recomputes on every keystroke progression 1, 2, 3, 4, 3, 4, 5, 4, 3… · max safe steps 15 · bankroll 200x base bet
Martingale calculatorPayout ×2.0000 · edge 1.00%

01Casino

02Your numbers

Steps survivable 6
Last-step bet 32

Ladder stopped by your bankroll after 6 steps.

Balance utilization 63.0%
Insurance coverage 63.0%
Critical event (1-in-N) 1 in 60

Pace at these settings

Sequence odds (1h) 100.0%
Profit / day -864
Profit / month -25,920
Doubling time

Best casinos for D’Alembert

the ranked set that carries this system
All casinos compared →
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Duelbits Anjouan (Union of Comoros) 8.9 dice rating
Best for D’Alembert

Turning over $1,000 costs $7.43 here: $9.90 of edge, minus $2.47 handed back. The published ladder reaches 5× the unit: run from this casino’s own $0.10 minimum that step is $0.50, against a $50,000 table max.

Rakeback
25% of edge
Net cost / $1,000
$7.43
Min bet
$0.10
Table max
$50,000
Stake Curacao Gaming Authority · OGL/2024/1451/0918 9.2 dice rating
Runner-up

Turning over $1,000 costs $10.00 here: $10.00 of edge, minus $0.00 handed back. The published ladder reaches 5× the unit: run from this casino’s own $0.0001 minimum that step is $0.0005, against a $25M table max.

Rakeback
3.5% of edge
Net cost / $1,000
$10.00
Min bet
$0.0001
Table max
$25M
Rakeback pays nothing below $10,000 of lifetime wagering — the first sessions run at the full edge.
Roobet Curacao · OGL/2024/687/0427 8.4 dice rating
Third

No rakeback rate is published here, so $10.00 per $1,000 wagered is the gross edge — the real cost can only be lower, and we cannot say by how much. The published ladder reaches 5× the unit: run from this casino’s own $0.01 minimum that step is $0.05, against a $100,000 table max.

Rakeback
Not published
Edge cost / $1,000
$10.00
Min bet
$0.01
Table max
$100,000
The loyalty rate is not published, so the net cost above is unverified.

Illustrative equity curve

one seeded session · 12 sampled points
$118 $114 $109 $105 $100
Illustrative only — not a profit guarantee.
1 6 12

One seeded session, sampled at 12 points — the shape this system makes, not a forecast. It is not an average and not a projection: the dashed line is the $100 it started from, and the same settings run again land somewhere else entirely.

Variants

The Reverse D'Alembert (add after a win, subtract after a loss) is a positive-progression variant that captures winning streaks rather than chasing losing ones, at the cost of slower recovery and a very different risk profile.

Problems & limits

The flat linear progression buys survival time against losing streaks, not a mathematical edge. Net EV is still house edge × turnover; rakeback of ≥1% on a 1% house-edge game breaks even.

−$7.43 … −$10.00 expected cost per $1,000 wagered, across the casinos above

FAQ

3 questions
Why doesn't D'Alembert actually balance wins and losses?
It assumes wins and losses naturally equalise, but in a short session they don't. You can lose 15 in a row far more often than the strategy's "safety" implies.
What is a good RTP for this strategy?
Target dice games with ≥99% RTP and ≥5% instant rakeback. At those numbers the negative EV from the house edge is largely offset and the flat-ish bet sizing keeps turnover reasonable.
Can I automate D'Alembert?
Yes — most crypto dice autobets support +N on loss / -N on win modes. Set the step to your unit size and cap maximum bet at ≈15× unit to stay within the safe-steps range.