D'Alembert Betting System

The D'Alembert System, named after a French mathematician, is
also used for outside, even money bets. The betting system is
relatively simple: after a win, the wager is decreased by one unit, and
after a loss, the wager is increased one unit. It is based on
D'Alembert's mathematical equilibrium theory. At least three of modern
Blackjack betting sequences use a similar technique of dropping the
wager after the first or second win. John Patrick's New York System,
George Pappadopoulos's Telephone number system, and Bill Garner's
E-Z Bet. An example of how to play D'Alembert follows:

Beginning Wager: 5 units, Win, then drop the next bet to 4 units
Next Wager:        4 units, Win, then drop the next bet to 3 units
Next Wager:        3 units, Lose, then raise the next wager to 4 units

Let me interrupt this series to point out that because the bet is being
decreased, the loss resulted in losing 3 units while the two wins were 5
and 4 units, with an average win of 4.5 units. This effect is what makes
this system work: the last win is always greater than the first loss.

To continue:
Beginning Wager: 5 units, Win, then drop the next bet to 4 units
Next Wager:        4 units, Win, then drop the next bet to 3 units
Next Wager:        3 units, Lose, then raise the next wager to 4 units
Next Wager:        4 units, Lose, then raise the next wager to 5 units

After two wins and two losses, the player is ahead by 2 units. Of
course if the losses exceed wins, the player will lose, but not as much
as if flat betting.

Note that you must start at a unit amount which will allow you to
decrease your wager. It could be four or five units, but must be
adequate because if you have a long winning streak, you will get down
to one unit and have to start over. If you get there, you will have won
14 units. This is a very safe system, and the player neither wins a lot
or loses a lot. The play is truly in equilibrium, around the starting
point, hence the name, equilibrium theory. This system doesn't allow
one to capitalize on winning streaks, so someone came up with our
next betting system: the Reverse D'Alembert.

The Reverse D'Alembert System is, as the name implies, a
system where the bets are increased after a win, and decreased after a
loss. What this amounts to is a positive betting progression when
winning, and a bet reduction when losing. If you have a long winning
streak, the bets will escalate gradually, and if you have a long losing
streak, you are losing less with each passing loss. The bets will,
however, remain near an equilibrium point, because there will be as
many losses, probably more losses, than wins. The equilibrium point
around where the bets will fluctuate may be at a higher point than
D'Alembert.

Where this system is flawed is when play is "choppy," where a win is
followed by a loss, then a win followed by another loss. This happens
often in Blackjack and occasionally in Roulette. In this case, you will
lose one more unit than you win per win/lose pair. If you have a series
of losses, you might find yourself down to a one unit bet also.

Both of these systems are safe, and you probably won't get hurt with
them, but chances are you will win very little. You will, however, play
for a long time and enjoy the game with little risk.