Paroli or Parlay, is an amazing system for the even chances (red-black, high-low, odd-even). It is the absolute “go with the flow” approach and the fundamental “up as you win” progression. It is extremely simple to describe: “after a win double your bet, after a loss start over with 1 unit”.
No confusing calculations, no adding and subtracting, no nothing. Just bet your initial bet plus your winnings again and again. With Paroli you can expect many losing sequences that will cost you each 1 unit and you hope for that super successful sequence with many consecutive wins that will make you rich. Or something like that. As you understand, from the simple description of the system there is a very important question one should answer: “When I win how long do I keep doubling up my bets? When do I stop, take my winnings and start over? Because if I keep doubling up indefinitely, at some point a loss will come and it will wipe out all my winnings.” That’s the million dollar question. And it is the reverse question of the Martingale player who asks “how long should I keep increasing my bet hopping for a win”? The decision how long (how many steps long) you keep the progression is yours and there are no right or wrong answers, just trade-offs.
In the following table you can see the probabilities and statistics of even chances as well as the possible winnings of the Paroli progression, so you are fully aware of the possibilities, their risk and their reward.
Two things are obvious from the above table: With each consecutive win your profits are increasing exponentially, but at the same time your chances to win the next bet decrease exponentially too. Paroli progression is very aggressive. This is an all or nothing progression, because every loss wipes out all your previous profits.
Paroli vs Martingale
Paroli is the reverse strategy than Martingale, that’s why it is also referred to as Anti-Martingale or Reverse Martingale. As totally opposites Martingale and Paroli share many similarities. They are the Yin and Yang of roulette betting strategies: same system from opposite directions. Martingale hopes that consecutive losses can’t last too long, while Paroli hopes for a long continuous win sequence. However there is one important (perceived or psychological or actual) difference. Paroli is perceived as less risky. That is because even though you do make large bets, it’s with “casino money”. This is both true and false. True because yes, the amount you bet is indeed the profits you made from your previous consecutive wins. There is no case to “run out of money for your next bet” as can be the case with Martingale. On the other hand, money won is your money now, not casino’s and by betting it you risk the chance to lose it. No matter what the mind games of naming profits “casino money”, you just lost money that could still be yours.
There are three main approaches to the Paroli progression.
Keep it aggressive
We already showed the benefits and dangers of keep doubling your bets. So yes, it is a risky approach, but the possible benefits are well worth it. We keep doubling up our bets till forever or more practically till we reach table limits and cannot increase our bet. This method is the absolute all or nothing approach. Its proponents have the following argument: if one says that the Martingale is a bad progression because you will eventually face the sequence from hell and lose your shirt, then it is almost equally possible to face the extraordinary favorable sequence and win thousands of units. All we need are just 8 or 9 consecutive wins (probabilities: 0,38% and 0,19%! After that you reach the table limit in a casino anyway, so you take your 25600% or 51200% profit and go home. This relies on the same principle, but even more aggressive, as the reverse Labouchere, used by Beresford and Leigh.
A more conservative and manageable approach is to limit the Paroli progression to 3 or 4 or 5 steps only. This is the opposite as the 4-step Martingale. I suggest the 3-step Paroli. This approach does very well if there are enough 3-consecutive-win-sequences, but fails miserably if there are not enough of them. Normally such a sequence should appear every 7 winning sequences (4 of them are 1 spin long, 2 are 2-spin and 1 sequence should be 3 and above spins long). Let’s see two examples.
Instead of the aggressive double up progression (1-2-4-8-16-32 etc.) we could use a less aggressive progression (like Fibonacci: 1-2-3-5-8-13 etc.). These mild progressions have the disadvantage that in a favorable run, they do not increase our profits as fast. But the advantage is that after a few wins even if we eventually lose we have amassed a profit already and don’t lose everything. This is an extremely interesting approach and I have done extensive studies in this kind of Paroli variations which I will hopefully present in a future article.