The Paroli betting system is based all around streaks, it’s very simple to use however it is lacking in a little mathematical logic. It works like so...
As you can see the Paroli system is very much based on streaks and while streaks do of course exist this system does fail to take a few things into account. Nevertheless it is a fun system to use, many people do use it and it can earn you a profit over a short period of time. However like most systems, when used over a long period of time it will not beat the inherent house edge in any casino game.
The Paroli system will not work over a long period of time because of the fact that a win does not make another win more likely, nor does it make a loss more likely. All events, just like a coin flip are totally independent of each other, and what happened previously has no bearing on what will happen next. A coin flip may not be the best example in this case, as over a long period of time, the coin will land on heads and tails 50% of the time, meaning that if you bet on heads constantly you would not win any money, however you would not lose any either. Perhaps a better example is in an actual casino game such as roulette where red and black pay even.
Red and black do in fact pay even money, however the house edge in roulette on even money bets is created by the 0 or the 00 in the game, and when the ball drops into those pockets, both red and black will of course lose. The zero in the game of roulette is how the house advantage is created and the Paroli system cannot take that away.
Some people use the Paroli system simply because it makes their wagering time more enjoyable, and it is indeed a bit of fun. You find that should you try it it does actually work from time to time and you will get 3 wins on even money in a row. However, as stated, it will not give you a profit over a period of time and just like all betting systems just be used for a little entertainment.