## Progressive-2 Blackjack Strategy

The two-level progressive system instructs the player to set two wagering levels—typically one and three units—and to risk the higher wager after each win and the lower after each loss. In theory as well as in practice, this will maximize the player’s profits on winning streaks and minimize it on losing streaks, and the player will come out ahead of a consistent-wagering player who bets two units on each hand:

WAGER | 1 | 3 | 1 | 1 | 3 | 3 | 3 |
---|---|---|---|---|---|---|---|

RESULT | W | L | L | W | W | W | L |

BALANCE | +1 | -2 | -3 | -2 | +1 | +4 | +7 |

However, during periods when the pattern is win-loss, the player will always place the higher wager on the losing hands, and the player will be worse off than the consistent-wagering player who bets two units on each hand:

WAGER | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 3 |
---|---|---|---|---|---|---|---|---|

RESULT | W | L | W | L | W | L | W | L |

BALANCE | +1 | -2 | -1 | -4 | -3 | -6 | -5 | -8 |

In the end, the outcome a 90-hand session played by the progressive-2 wagering system will depend on how the cards came out. If winning streaks occur reasonably often, and win-loss patterns occur infrequently, the player will, in fact, come out ahead. However, the belief that streaks occur with any regularity is purely superstition.

This does not mean that the two-level progressive system will produce consistent losses: only that the outcome of a given session will vary unpredicatably, depending on the “happenstance” of the way that the win-loss pattern emerges.

## Progressive-5 Blackjack Stratgey

The five-level progressive system instructs the player to begin with one wagering unit, adding an additional wagering unit after each win, and returning to a single unit after a loss or a streak of five consecutive wins. As is the case with the two-level progressive system, this will in fact maximize the player’s profits on winning streaks and minimize it on losing streaks:

WAGER | 1 | 2 | 3 | 1 | 1 | 1 | 1 | 2 | 3 | 4 | 5 | 1 | 1 | 1 | 1 | 1 | 1 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RESULT | W | W | W | L | L | L | L | W | W | W | W | W | L | L | L | L | L |

BALANCE | +1 | +3 | +6 | +5 | +4 | +3 | +2 | +4 | +5 | +9 | +14 | +15 | +14 | +13 | +12 | +11 | +10 |

However, also like the two-level progressive system, the player’s net losses when a sequence of hands is mixed:

WAGER | 1 | 2 | 3 | 1 | 2 | 1 | 2 | 1 | 2 |
---|---|---|---|---|---|---|---|---|---|

RESULT | W | W | L | W | L | W | L | W | L |

BALANCE | +1 | +3 | 0 | +1 | -1 | 0 | -1 | 0 | -2 |

A lengthy winning streak, or a number of brief ones, will build up a “cushion” that will require a lengthier win-loss pattern (or losing streak) to consume. For example, two wins will leave the player at +3, so it would take six hands in a win-loss cycle (or three losses in a row) to negate this lead; three wins will leave the player at +6, requiring twelve win-loss cycles or six consecutive losses to balance the total.

Over the course of many hands, the five-level progressive system is no less likely to result in losses than its two-level version, but the losses will whittle away the player’s bankroll more slowly.

In the end, it is also a system by which the outcome of any given session will vary unpredictably—sometimes a net profit, sometimes a net loss—depending on the way the hands happen to conclude.

## Fibonacci Blackjack Stratgey

The Finbonacci series is a sequence of numbers, each of which is the sum of the previous two: 1, 2, 3, 4, 8, 13, 21, 34, 55, 89, etc. that is suggested (but not recommended) as an alternative for the Martingale system. Fibonacci seems a less risky alternative because the value of the wager does not increase as rapidly. For the same reason, a win recaptures only the previous two losses—and after the third loss, the player will not recover the full amount he has lost to that point:

LOSSES | MARTINGALE | FIBONACCI | ||
---|---|---|---|---|

1 | 1 | +1 | 1 | +1 |

2 | 2 | +1 | 2 | +1 |

3 | 4 | +1 | 3 | 0 |

4 | 8 | +1 | 5 | -1 |

5 | 16 | +1 | 8 | -3 |

6 | 32 | +1 | 13 | -6 |

7 | 64 | +1 | 21 | -11 |

8 | 128 | +1 | 34 | -19 |

The likelihood of a run of eight losses is slightly less than 1%, but it is 65.7% likely this will occur in a 90-hand session. Meanwhile it is abysmally unlikely that the player will have a run of nineteen sequences in which he wins the first or second hand to recover those losses. All things considered, this is a losing system.

## D’Alembert Blackjack Stratgey

Jean D’Alembert suggested the probable outcome of an event in a sequence will be influenced by the known outcomes preceding it. In more concrete terms: if a tossed coin lands face-up three times in a row, there is an increased likelihood of the next toss landing face-down, as it must to effect the statistical average in the long run.

This gives rise to a wagering system that instructs the player to increase his wager after a loss (assuming a win is more likely afterward to balance the equation) and decrease it after a win. Mathematically, this will produce a zero sum is the number of wins and losses are equal and the increases and decreases balance out:

WAGER | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 3 | 4 | 3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

RESULT | L | W | W | W | W | L | W | L | L | L | W | L |

BALANCE | -1 | +1 | +2 | +3 | +4 | +3 | +5 | +4 | +3 | -1 | +3 | 0 |

Statistically, basic strategy will produce a sequence of hands in which losses and wins are roughly equal in the long run, so D’Alembert’s strategy would seem to be effective regardless of the pattern in which these wins and losses will occur. However, to balance the equation perfectly in all situations, the player would need to be able to place a negative wager on his own hand (or bet on the dealer’s hand to beat his own), which is not an available option. Moreover, since the win-loss ratio is slightly less than 50:50, the total outcome will also be slightly less than zero.

## Reversing Martingale, Labouchere, and D’Alembert

If a player assumes a system is guaranteed to fail, it would seem logical that doing the exact opposite will produce a system that is guaranteed to win. This gives rise to the “Reverse” (also called “Contra” or “Anti-“) wagering systems. Mathematically, the assumption is sound—but if a player reverses a system that’s guaranteed to win, the result will be a sure loser.

**Reverse Martingale** is played by doubling the wager after each win (instead of after each loss) in order to capitalize on winning streaks. In the long run, this will never be successful because the player will inevitably lose a hand—and that single loss will capture all the player’s previous winnings, plus one more unit.

**Reverse Labouchere** works the same way: if losing wagers decreased the array from which the wager is tabulated and winning ones increase it, the result of a series of hands played to its conclusion will inevitably be failure.

**Reverse D’Alembert**, meanwhile, is no better or worse than the original. Since the ultimate end of the D’Alembert strategy is a zero, inverting the equation will still produce zero. Moreover, since the chances of winning are somewhat less than zero (and the player still cannot wager a negative sum), the outcome will still be slightly less.

These strategies are presented largely for informational purposes—so that a player can avoid bad advice. Seeing how these systems consistently fail to producethe intended result, it may be easier to understand the perspective of those who are categorically opposed to wagering systems. However, as the section on effective systems demonstrates, this generalization, like most, is false.