# The Paroli System

Doubling your bet when you win

- Type: Positive Progression

The Paroli system involves **letting your wins ride** for a predetermined number of spins.

To use the system you just need to define two things:

**Starting Unit.**This is your initial bet size.**Progression Limit.**How many spins you're going to let your winnings ride for.

Every time a bet **wins**, you wager your previous bet *and* the winnings from it on the next spin (also known as "letting it ride"). If you keep winning and hit your progression limit, you take your winnings and return to your starting unit.

If your bet **loses** at any time, you just go back to your starting unit and start over again.

## What's the logic behind the Paroli system?

The aim of the system is to **maximize the amount of money you win from winning streaks**, whilst at the same time not risking anything more than your chosen betting unit (at the start of each progression).

You'll lose more often than you win, but hopefully the big wins make up for the frequent small losses.

Note: This is known as a *positive progression system*, because you increase the size of your bet when you're winning (as opposed to a negative progression system where you increase the size of your bet when you're losing).

## Example

Let's say I've got a $500 bankroll, so I choose **$5** as my betting unit size. I also decide to use **3** consecutive wins as my progression limit.

My session could play out as follows:

- Bet $5 and lose.
- Bet $5 and lose.
- Bet $5 and win. Consecutive Wins = 1
- Bet $10 and win. Consecutive Wins = 2
- Bet $20 and win. Consecutive Wins = 3 (hit my progression limit)
- Bet $5 and lose.
- Bet $5 and win. Consecutive Wins = 1
- Bet $10 and lose.
- Bet $5 and ...

So basically every time you win, you "roll it over" or "let it ride" for a consecutive number of spins. You can choose how many times you're going to roll it over before you start, and the higher your chosen progression limit, the bigger the payout from winning streaks, but the less frequent they will be.

A common progression limit is 3, but you can choose any limit you like depending on how lucky you're feeling.

Tip: Be aware that the higher your progression limit, the more difficult it will get placing the large cumulative bets toward the end. The system will test your resolve, so choose a progression limit you know you can stick to.

## Simulator

The Paroli system results in a steady downward trend, with the occasional large win to make up for some of your losses when you successfully reach your progression limit.

Note: If you set a *high progression limit* and your unit size is large relative to the size of your bankroll, there is a chance you will not hit a winning streak at all during your session.

### Algorithm / Code

Here's some working Ruby code that shows how the Paroli system works from a programming perspective. The only clever line is `bet = unit * (2 ** wins)`

, which uses exponentiation to work out the size of the next bet based on the initial betting unit and the current number of consecutive wins.

```
# Settings
unit = 1
balance = 100
spins = 500
progression_limit = 4
# initialize the counter for number of consecutive wins
wins = 0
# Repeat for a given number of spins
spins.times do |i|
# Set the bet size based on the number of consecutive wins (doubles for every win)
bet = unit * (2 ** wins)
# Spin the roulette wheel
result = rand(0..36)
# Check if the result is a win
win = (result >= 19) # using the high numbers as the even-money wager
# Print bet size and result
print "Spin #{i}: bet=#{bet} #{win ? "(win)" : "(lose)"}, "
if win
# Update balance
balance = balance + bet
# Increment win counter
wins = wins + 1
# Reset win counter if we hit the progression limit (which will stop increasing the bet size)
if wins >= progression_limit
wins = 0
end
else
# Update balance
balance = balance - bet
# Reset win counter
wins = 0
end
# Print new balance
print "balance=#{balance}\n"
end
```

## What's the best progression limit?

A popular choice is 3, but feel free to choose a limit that is most interesting to you:

Progression Limit | Probability | Payout |
---|---|---|

1 | 48.6% | 2x |

2 | 23.7% | 4x |

3 | 11.5% | 8x |

4 | 5.6% | 16x |

5 | 2.73% | 32x |

6 | 1.33% | 64x |

7 | 0.65% | 128x |

8 | 0.31% | 256x |

9 | 0.15% | 512x |

10 | 0.074% | 1024x |

The table above shows you the **probability of hitting a number of consecutive wins** when betting on red/black (or any other even-money bet) in *European* roulette.

The cool thing about the Paroli system is that you get to **choose your own progression limit**, and there is no "perfect" number for this.

It's basically up to you to decide how lucky you're feeling at the time. If you're feeling lucky and can handle the tension of potentially massive wins, pick a high progression limit and stick to it. At the end of the day your results will balance out whether you go for the frequent small wins vs. the infrequent big wins.

## Why is the Paroli system popular?

Because it *amplifies your winnings* when you get lucky.

I like the Paroli system because it embraces the fact that roulette is a game of luck. Its goal is to maximize your wins when you get lucky, whilst at the same time giving you control over the amount you can lose from one spin to the next.

Other betting systems (e.g. martingale, fibonacci) push you in to chasing losses by increasing the size of your bets when you lose, which is a highly dangerous way to play. They're also designed with the object of trying to beat the game of roulette, which is always doomed to failure.

The Paroli system isn't designed on the premise that you can use it to beat roulette. Instead it's an honest system that gives you an alternative and exciting way to play by **compounding winning streaks**, whilst allowing you to keep control of how much you're prepared to lose.

If you're going to use any system when playing roulette, I'd recommend giving the Paroli a try.

## Does it work?

The Paroli system is like all other systems — it won't help you to beat roulette over the long run.

Your expected return is the same as if you repeatedly bet the same amount on each spin of the wheel (i.e. "flat betting"), and the structure of this particular system does nothing to change this fact.

You might hit some incredible winning streaks over the short-term if you're lucky, but over the long run you're still expected to lose slightly more than you win. To put it another way, the amount you win from your infrequent winning streaks will not make up for the amount you're expected to lose in the pursuit of the big wins.

It's a fun and exciting way to play, but it does nothing to overturn the inherent house edge in roulette.

## Where does the name "Paroli" come from?

The word "par" is Latin for "equal". Other definitions include:

comparable

corresponding in degree, proportionate, commensurate

a match for

http://www.latin-dictionary.net/search/latin/par

So that's where phrases like "on par with..." or "par for the course" (i.e. in golf) come from.

Anyway, from what I can tell the *par* in the *Par*oli system refers to the fact that you're betting an amount that's *equal* to your winnings from your last spin every time you win. So the amount you wager is always proportionate to the amount you've won.

I don't actually know where the *oli* part comes from though. If you know more about the origins of the name for this system I'd be interested in finding out.

## Conclusion

let (something) ride1. To let the winnings from a previous wager stand as a new wager.

— thefreedictionary.com

The Paroli system is my favorite betting system for roulette. It does nothing to turn the odds in your favor, but it does add an element of excitement to your sessions.

**The whole system revolves around the idea of making the most from lucky streaks**, which for me is what playing roulette is all about. Also, it doesn't have the potential to lead you in to a catastrophic loss like the martingale system can, which is something you want to avoid at all costs.

It's an honest system. It can produce big wins (if you're lucky), and at the same time it doesn't try to convince you that roulette can be beaten.

But ultimately the Paroli system embraces luck, and that's why I like it.