Paroli system (reverse Martingale): 100,000 sessions simulated
The Paroli doubles after wins instead of losses and banks after three in a row. See what 100,000 simulated single zero roulette sessions say about its win rate and average result.
What it is and how it works
The Paroli is the Martingale turned around. You double the stake after a win and reset to the base stake after a loss, aiming to ride a short hot streak with the table money rather than your own.
In this app the streak is banked after three wins in a row, which is the most common form of the system.
A simple example at a base bet of 5
- Bet 5 on red. It wins, returning 10.
- Bet 10. It wins, returning 20.
- Bet 20. It wins, returning 40. That is three in a row, so the profit is banked.
- The next bet returns to 5. Any loss along the way also returns to 5.
What our simulation shows
We ran 100,000 sessions of this system against a fair single zero wheel, each session lasting up to 100 spins, starting with 500 virtual points and a base bet of 5. Those are the same defaults the app's Lab starts with. A session ends early if the bankroll can no longer cover the next required bet.
| Sessions simulated | 100,000 |
|---|---|
| Sessions that finished ahead | 38.4% |
| Sessions that finished level | 2.0% |
| Sessions that finished behind | 59.5% |
| Sessions that ran out of money | 0.0% |
| Average result per session | -22.9 points |
| Typical (median) result | -25 points |
| Average total staked in a session | 843.6 points |
| Loss predicted by the house edge | 22.8 points |
| Best session seen | +430 points |
| Worst session seen | -350 points |
| Average longest run of losing spins | 6.2 |
| Longest run of losing spins seen | 24 |
Read that table slowly. The share of sessions finishing ahead is often the number that sells a system, and on its own it is misleading: what matters is the average result, which includes the sessions that went badly.
Why this system cannot overcome the house edge
A single zero wheel has 37 pockets. An even money bet such as red wins on 18 of them and loses on 19, so every point you stake returns 36 of 37 points on average. That is a loss of 2.7027% of everything staked, and it applies to every single bet no matter what size it is or what order the bets come in.
Our simulation shows this directly. Across 100,000 sessions this system staked an average of 843.6 points per session. Applying the edge to that amount predicts a loss of 22.8 points. The simulation actually produced an average of -22.9 points.
The staking pattern changed how the wins and losses were spread out. It did not change the total. That is the whole story of every betting system: they move risk around, and nothing more.
Strengths and weaknesses
Strengths
- Losing runs cost only the base stake each time, so the bankroll drains slowly.
- It cannot bust from its own progression, because the stake only grows while you are winning.
- The occasional completed streak feels genuinely good without risking a large recovery bet.
Weaknesses
- Completed three win streaks are less common than players expect, so most sessions grind slowly downward.
- A streak that breaks on the third bet gives back everything it built.
Who it might suit
The Paroli suits players who want a long session with small, predictable downside and an occasional bright moment, rather than a system that tries to chase losses back.
Common questions
Is the Paroli safer than the Martingale?
It is gentler on the bankroll, because it only increases the stake with money it has just won. In our simulations it never ran the bankroll out from its own progression, but it still finished with an average loss, since the house edge applies to every bet either way.
Why bank after three wins?
Letting a streak run forever guarantees it eventually breaks and gives everything back. Banking at three is a common compromise between a meaningful return and the chance of actually completing the streak.
Test it yourself
Open the Lab in the app with Reverse Martingale, Paroli already selected, set your own budget, base bet, and number of rounds, and watch it play out spin by spin with virtual points.