Paroli betting system wikipedia

With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet. With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued. Thus, the total expected value for each application of the betting system is 0. In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of Eventually he either goes bust or reaches his target.

This strategy gives him a probability of Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll. In reality, the odds of a streak of 6 losses in a row are much higher than many people intuitively believe.

Psychological studies have shown that since people know that the odds of losing 6 times in a row out of 6 plays are low, they incorrectly assume that in a longer string of plays the odds are also very low. In fact, while the chance of losing 6 times in a row in 6 plays is a relatively low 1.

The wager will result in either a net loss of one unit or a profit of seven units and a new progression begins. Although each Paroli progression must end on either a loss or the successful completion of three wins in a row, it is useful to think of the wagering in groups of three bets in order to understand the possible outcomes. These are summarized in the table below.

Note that for any three consecutive bets, there are eight possible patterns of wins and losses, only one of which results in the 7-unit profit: What is the logic behind the Paroli betting system? This strategy rests on the premise that wins and losses tend to come in streaks.

A player can maximize profits by betting more during winning streaks and less during streaks of losses. Larger bets are made possible by units won from the House, and each time a succession of three wins occurs, the profit is seven units, which should cover the accumulated small losses. Adherents say the Paroli system is much more stable and consistent than negative betting progressions.

When losses occur, they are gradual and unspectacular. Also, table limits are never a barrier to successful completion of the progression. Why is the Paroli betting system flawed? The risk of playing the Paroli betting system exclusively is that the accumulation of one unit losses can far too easily exceed the 7-unit wins required to pay for them.

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