The Paroli Betting Strategy

The Paroli betting system is a variation of the Martingale system. It is different in that it modifies how much to bet on an individual game. The limit is set by the size of your bankroll, and ties are allowed (limiting loss to winning bets).

Paroli betting systems are popular among professional poker players because they makes placing large bets more manageable, especially with high-risk hands where there is a better chance for winning more than just one round.

Each round consists of making one bet and collecting back the whole bankroll, adjusting bet size based on score and final round results. If you want to collect more than your bankroll while keeping your “expectation” for winning above 0, you must make a tie.

The beauty of paroli betting is that if everyone plays it correctly (which is not realistic), there’s no edge over the human brain (or computer) and anyone appearing to win will actually win.

First, the bankroll is divided into 5 or 10 parts. All starting bets are made on the first round. The difference between the bankroll and the final round balance is accounted for as “expectation”.

If everyone plays accordingly, on average there will be at least two ties (limits) per game (one in each of the first 4 rounds). If you make 3 ties, it’s like having won 5 times. If you make 4, it’s like having won 9 times; etc. with the difference being your “expectation”. You can also tie on round 8, or round 10 even.

The expectation is the key to this bet, because if you start with $100 and end up with $51 you lose -51, but if instead you end up with $49 then you lost -2. The key is that you made two ties (rounds) that added 2 to the total game won. You ended up losing money but that’s irrelevant (you tied).

In order to beat the system, you have to “beat” it with a BET of at least -4. So the formula is:

Expectation of losing less than 2 money units on round “I” of bet 1.

Expectation of losing 2 money units on round “I+1”, available betting on round “I+2” is +$4, on round “I+3” is +$8 and on round “I+4” is overall +$16.

Expectation of losing 2 money units on round “II”, available betting on round “III” is +$4, on round “IV” is overall +$16.

Expectation of losing 2 money units on round “III… IV”; so expect an overall loss of more than 4 money units and you can bet lower than -4, otherwise it’s a tie and you lose the original bet.

The problem with paroli is that the expectation is not always easy to calculate.

For example, if you have a bankroll of $100 and drop to $50, then you lost -50. Your expectation is that someday in the future you will win -$46. At which point, your overall expectation will be zero because you have lost all of your money and have nothing left to bet with even if you could do so now.

You could argue that you have a small chance of winning the next round, but you have to consider that if you won the next two rounds with a total bet of $100, your expectation would still be -46. So it doesn’t really help to add in the probability of winning more than one round.

If you do not tie when you drop from $100 to $50 then when your bankroll is supposed to hit zero, it will be at about $51 instead. That is a +10 expectation. However, you will have already lost around $20 from playing the system within the first four rounds. If you were betting that you would win 2 or 3 rounds, then your expected loss would be around -4.

In other words, the only way to beat paroli is to win more than 1 round while it corrects your expectation from -$46 to +0. That can only be done by winning more than 1 round.

This paroli system has been around for a long time, but it is pretty much impossible to play perfectly. You have to bet the same every round, because if you are winning or losing, your expectations are either +$4 or +$16 rather than zero.

That’s why the best way to beat paroli is to find an advantage in the expected value of certain events that aren’t included in the examples above. An example would be to bet less than -$2 on the “last round”.

Another example would be to bet more than you have available. You do this by multiplying your available money by the expectation of the game. Suppose you have $10 and the expectation is -$4. You first take $8 and bet that, then you bet your last two dollars and see what happens.

There is a 2/3 chance that this will tie, and if it doesn’t then you will be up $8 for your next round (plus your original $10). If it ties, then you lose 2 dollars (your original bet). That would give you a positive expectation of -2 rounded off to -1. The next round would be a tie.

How is this paroli? It’s using your expectation that the game will be lost to improve your game. You won -1 because you hovered around that number. However, if you bet less than what is expected of you, then you will win more than expected.

The problem with paroli is that it requires your bankroll to be more consistent than your high-risk double downs. Because you are betting more, often on the last round, you can’t afford to go all in too early. You have to bet big enough to make the round go long enough for you to make a tie.

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