d´Alembert: A question of BALANCE?

In the late 18th Century, at time of many discoveries in mathematics and physics, the Italian-French scientist Joseph Louis Langrange, and later the French mathematician Jean le Rond d´Alembert, worked on a statement of the fundamental Laws of motion. They concluded that "the sum of the external forces acting on a body and the inertial forces are a system in equlibrium. This is a generaization of Newton´s Second Law and is called the d´Alembert Principle.
When this law of equilibrium is applied to games of chance, it leads to the belief that future outcomes will be more likely to balance unlikely variations of the past. This means that, for instance, after a long streak of black, red becomes a more likely outcome. As such it is simply what now is known as THE GAMBLERS FALLACY AND NOT TRUE. However, it means that the socalled progression d´Alembert is based on the player winning as often as he or she loses.

AT FIRST SIGHT THIS SEEMS TO BE TRUE in our balanced heads filled with balanced ideas from The Age of Enlightenment. If we still have heads, however, we should be able to think: We lose three times and win three times: -1-2-3+4+3+2.
And now we win three times and lose three times: +1+1+1-1-2-3. NEXT BET IS FOUR UNITS. WHERE IS THE BALANCE IN THAT?

We are unable to reduce our bet each time we win just one unit. This simple fact MUST disturb the balance.

"THERE´S ONLY ONE STEP DOWN FROM HERE, BABY
IT´S CALLAD THE LAND OF PERMANENT BLISS"
(Bob Dylan)

What's your point ? That the "Gamblers Fallacy" is indeed a fallacy ? This news is quite old.

Quote: Dane

In the late 18th Century, at time of many discoveries in mathematics and physics, the Italian-French scientist Joseph Louis Langrange, and later the French mathematician Jean le Rond d´Alembert, worked on a statement of the fundamental Laws of motion. They concluded that "the sum of the external forces acting on a body and the inertial forces are a system in equlibrium. This is a generaization of Newton´s Second Law and is called the d´Alembert Principle.
When this law of equilibrium is applied to games of chance, it leads to the belief that future outcomes will be more likely to balance unlikely variations of the past. This means that, for instance, after a long streak of black, red becomes a more likely outcome. As such it is simply what now is known as THE GAMBLERS FALLACY AND NOT TRUE. However, it means that the socalled progression d´Alembert is based on the player winning as often as he or she loses.

AT FIRST SIGHT THIS SEEMS TO BE TRUE in our balanced heads filled with balanced ideas from The Age of Enlightenment. If we still have heads, however, we should be able to think: We lose three times and win three times: -1-2-3+4+3+2.
And now we win three times and lose three times: +1+1+1-1-2-3. NEXT BET IS FOUR UNITS. WHERE IS THE BALANCE IN THAT?

We are unable to reduce our bet each time we win just one unit. This simple fact MUST disturb the balance.

"THERE´S ONLY ONE STEP DOWN FROM HERE, BABY
IT´S CALLAD THE LAND OF PERMANENT BLISS"
(Bob Dylan)

heck of a post

First the Rules of that progression from SN Ethier book
The Doctrine of Chances
Probabilistic Aspects of Gambling
page 289

The first bet is one unit.
After a loss, the bet size is
increased by one unit,
and after a win, the bet size is decreased by one unit.
***The system terminates after an initial win. *** <<< this is the part you got wrong

After an initial loss, the system
terminates as soon as the number of wins equals the number of losses or,
equivalently, as soon as the system calls for a bet of one unit.

The idea underlying this system is that a win followed by a loss, or a loss
followed by a win, leaves the bet size unchanged and increases the gambler’s
cumulative profit by one unit.
Thus, the order of wins and losses is not
important (except to the extent that it affects the time at which betting
stops), and if the number of wins ever equals the number of losses, the goal is
achieved and the gambler’s cumulative profit will equal the number of wins.

Quote: Dane

d´Alembert is based on the player winning as often as he or she loses.

AT FIRST SIGHT THIS SEEMS TO BE TRUE in our balanced heads filled with balanced ideas from The Age of Enlightenment. If we still have heads, however, we should be able to think: We lose three times and win three times: -1-2-3+4+3+2.

agree and the cumulative gain to the bankroll is 3 units because you have 3 wins

Quote: Dane

And now we win three times and lose three times: +1+1+1-1-2-3. NEXT BET IS FOUR UNITS. WHERE IS THE BALANCE IN THAT?

There is your error!
The system terminates after that first initial win
up 1 unit
+1

The system terminates after that next initial win +1+1-1-2-3
up 1 unit
+1

The system terminates after that next initial win +1-1-2-3
up 1 unit
+1
up 6 units with your examples

we continue our play
-1-2-3 the system has yet to terminate as we do not have equal win/loss (0/3)

Some just terminate the system after a net gain and start over but the original version looks to be when wins=losses

So, it looks like you did not understand how the system terminates.
1) after the first initial win
2) when the initial result = a loss, when wins = losses

Sally

When I use the D'Alembert at Baccarat, I usually start at one or two units above table minimum. That way you absorb the correct guesses you may make at the start. So long term, if you guess at 50% correct decisions, you make money. The gr8 one, at 53%, should own a casino or two.

Quote: mustangsally

First the Rules of that progression from SN Ethier book
The Doctrine of Chances
Probabilistic Aspects of Gambling
page 289

The first bet is one unit.
After a loss, the bet size is
increased by one unit,
and after a win, the bet size is decreased by one unit.
***The system terminates after an initial win. *** <<< this is the part you got wrong

After an initial loss, the system
terminates as soon as the number of wins equals the number of losses or,
equivalently, as soon as the system calls for a bet of one unit.

The idea underlying this system is that a win followed by a loss, or a loss
followed by a win, leaves the bet size unchanged and increases the gambler’s
cumulative profit by one unit.
Thus, the order of wins and losses is not
important (except to the extent that it affects the time at which betting
stops), and if the number of wins ever equals the number of losses, the goal is
achieved and the gambler’s cumulative profit will equal the number of wins.
agree and the cumulative gain to the bankroll is 3 units because you have 3 wins
There is your error!
The system terminates after that first initial win
up 1 unit
+1

The system terminates after that next initial win +1+1-1-2-3
up 1 unit
+1

The system terminates after that next initial win +1-1-2-3
up 1 unit
+1
up 6 units with your examples

we continue our play
-1-2-3 the system has yet to terminate as we do not have equal win/loss (0/3)

Some just terminate the system after a net gain and start over but the original version looks to be when wins=losses

So, it looks like you did not understand how the system terminates.
1) after the first initial win
2) when the initial result = a loss, when wins = losses

Sally

With this fascinating progression and one unit as a starting point the BALANCE is seriously disturbed. This is what I wanted to point out.
For some reason or other I now had this dream:
TERMINATOR ate Camembert with d´Alembert! But back to reality:

+1. STOP!
"And so I face the final curtain".
New session Next day: +1. STOP!
"And so I face the final curtain"
New session Next day: +1. STOP!
"And so I face the final curtain".
Next day´s SESSION starts with three losses: -1-2-3= -6.
Our "terminal" decisions, curtains, and coffee breaks do not EXTERMINATE the Laws of probability.
What at first sight seemed to be BALANCE (winning three times and losing three times) is not reflected in our wallets or in our Enlightened heads.