Paroli Calculator — Reverse Martingale
Paroli — also sold as reverse martingale or anti-martingale — raises your bet after a win and resets after a loss. This calculator prices the win-streak against a real casino: the odds of completing your cap, the banked profit, the give-back when a streak dies one rung short — and whether your casino’s autobet can even run a capped Paroli at all.
01Casino
02Your numbers
Break-even win chance at ×2.0000 payout is 50%. This generic 1%-edge dice gives you 49.5% — short by exactly the house edge, at every chance and every cap.
The cycle
| Win # | Stake | Odds of reaching it | Net if you lose here | Net if you bank here |
|---|---|---|---|---|
| 1 | $1 | 49.50% | -$1 | +$1 |
| 2 | $2 | 24.50% | -$1 | +$3 |
| 3 | $4 | 12.13% | -$1 | +$7 |
| 1 | $1 | 49.50% | -$1 | +$1 |
| 2 | $2 | 24.50% | -$1 | +$3 |
| 3 | $4 | 12.13% | -$1 | +$7 |
Where a cycle dies
Worst-case cycle loss: -$1 (at even money a loss on any rung costs exactly one base bet — this number changes with your payout).
EV: -$0.0297 per cycle (every bet donates exactly the 1% edge × its stake) ≈ -$61.45 per hour at these settings.
Rakeback 0% — set a percent to see the wager-rakeback offset. Only wager-based programs (Duelbits Ace’s, Stake’s VIP rakeback, Shuffle’s instant/daily rakeback, Roobet’s Instant Rakeback) pay on Paroli volume; lossback programs don’t.
Illustrative math, not advice: Paroli reshuffles WHEN you lose, not WHETHER — the EV line above is negative at every setting. Preset limits and edges load live from the same audited data as our dice simulator.
Watch the streak on a live dice session
The calculator says how often a streak completes — the simulator shows it happening, seed by seed, including the cycle that dies on the last rung.
Casino
Stake
No session yet
- Final balance where the session ended
- Net profit against your starting bankroll
- Total wagered what the edge is charged on
- Max drawdown deepest peak-to-trough dip
- Longest streaks best win · loss run
Session detail
- Expected edge cost
- Net incl. rakeback
- Rakeback earned
- Win rate
- ROI (net / wagered)
- Session outcome
Illustrative RNG simulation — every run is a fresh random session, not a prediction or a profit guarantee. Payout multipliers are rounded the way each casino’s own panel displays them: that is a model of what the panel shows, measured in-account, and not a rounding we have confirmed against a settled bet.
How to use the Paroli calculator
- Pick your casino. The limits and house edge load from the same audited data our dice simulator uses.
- Set your win chance. The payout multiplier derives from the casino’s edge, exactly like the game itself prices it.
- Set the escalation percent. 100% — doubling the bet after every win — is what every casino’s autobet actually ships; the purist “let-it-ride” version, betting the whole balance forward, works out to (m−1)×100%.
- Set the cap. The field follows what your selected casino’s autobet can really enforce, not what the textbook rule allows.
- Read the ladder’s two net columns before you play: what a loss on that rung costs you, and what banking there actually pays.
The formulas, in the open
The stake at rung i is base·f^(i−1), where f is 1 plus your escalation percent — so at 100% escalation, f = 2 and the bet doubles every rung, exactly like a martingale ladder running upward instead of down.
Banked profit after k straight wins is (m−1)×total staked, where m is the payout multiplier — the same parity identity the martingale and D’Alembert calculators use, just paid out on a win streak instead of a loss recovery.
The net on a rung-i loss is m×C(i−1) − C(i), where C(i) is the cumulative stake through rung i — and at even money that identity collapses to exactly −1 base bet at even money on EVERY rung, win-streak length included.
That −1 base bet only holds at m = 2. Below it, a rung-i loss can cost more than one base bet, because the prior wins never banked enough to fully cover the next rung’s stake — the calculator’s net-on-loss column is what actually prices that top-up, not the shorthand identity.
The odds of reaching rung k — k wins in a row — are P(k wins) = chance^k, the same compounding-streak math behind every progression’s survival table, just counting up instead of down.
EV per cycle is −edge × expected stake: every bet donates exactly the edge — the progression only chooses when. Escalating the bet on wins doesn’t change what any single bet donates to the house; it only changes which bets are large and which are small.
Paroli ≠ Delayed Martingale
They get confused because both wait for a streak before doing anything drastic — but they escalate on opposite outcomes. Paroli raises the bet after WINS and resets on the first loss, a positive progression: the worst a cycle costs you is capped near one base bet. Delayed Martingale still doubles after LOSSES — it just waits out a trigger streak first — which makes it a negative progression with the same exploding-ladder risk as classic martingale. Our dice simulator runs Delayed Martingale as its own strategy so you can see the difference on a real session instead of just the name.
FAQ
Is Paroli safer than Martingale?
Different risk shape, same expected loss. Martingale risks an exploding ladder to chase one base unit; Paroli risks roughly one base unit per cycle chasing a streak payout. At even money a failed Paroli cycle costs exactly one base bet — but the EV line is negative in both systems, because every bet still donates the house edge times its stake.
Are Paroli, Reverse Martingale and Anti-Martingale the same system?
Yes — three names for one rule: raise your bet after a win, reset to base after a loss. “Paroli” is the classic casino name, “reverse martingale” and “anti-martingale” describe the same positive progression. This calculator answers for all three.
Is Paroli the same as Delayed Martingale?
No — they are opposite families. Delayed Martingale still doubles after LOSSES (it just waits out a trigger streak first), which makes it a negative progression like classic Martingale. Paroli escalates after WINS. Our dice simulator ships both as separate strategies.
What win-cap should I set — and what do casinos actually ship?
Classic Paroli banks after 3 straight wins; Stake’s shipped Paroli preset resets after the 4th. Only Stake’s strategy editor and BC.Game’s builder can enforce a cap automatically — on Shuffle, Roobet, Duelbits and DuckDice the autobet can only escalate-and-reset, so any cap is a manual banking decision (or a Stop-on-Profit threshold). The calculator’s cap field follows what your selected casino can really do.
Can Paroli beat the house edge?
No. The break-even win chance at any dice payout is 100 divided by the multiplier, and the casino always grants a chance short of that by exactly the house edge — at every chance, every escalation and every cap. Wager-based rakeback (like Duelbits Ace’s Rewards) can offset part of the cost because it pays on volume; loss-based cashback cannot be farmed the same way.
Looking for the mirror system — doubling after losses instead of wins? The Martingale Calculator prices that one. Sizing a slower ladder instead? The D’Alembert Calculator covers Classic and Contra. And if your casino pays wager-based rakeback on this volume, the Rakeback Calculator is built for pricing Duelbits’ wager-based Ace’s Rewards properly.