The Alembert progression revisited

[Arteinvivo]

For some reason, i have always liked the Alembert progression.

Here is something i did test today which gave me a very good result. No matter the bet selection, your wins/losses will oscillate around 50% unless you have a crystal ball in your sleeves or your B.S. has not been tested thoroughly which is not that rare if we look at the many claims of certain players. But let's suppose you are an average player who may have a good B.S. but nonetheless you are aware if you play long enough the distribution of W/L will oscillate around 50%.

The Alembert progression is designed in such a way that for every pair of W/L you'll get half a unit. For example, if you have this string of result : LLLWWW or LWLWLW or LLWWLLWW then you should make half a unit for each pair of L/W. -1-2-3+4+3+2 = +3 units

The problem with this progression is that your bets may escalate too fast and reach a high level or worse you can lose control of your string of bets if the table decide not to cooperate.

Let's see a small sequence of losses: LLLLLLLWLLLLLWLLWLLLLLWLLWLLWLLLLLLLLLWLLW, 34 L versus 8 W.

In terms of units we would have had these :
-1-2-3-4-5-6-7+8-7-8-9-10-11+12-11-12+13-12-13-14-15-16+17-16-17+18-17-18+19-20-21-22-23-24-25-26-27-28+29-28-29+30. See the picture ?

If you think such series of L/W is rare then welcome to the real life, it's quite common to get such a series if you visit Casinos frequently. But i admit it's good for comps. 

How can we cope with such a terrific string of losses ?

[Arteinvivo]

One thing i always keep in mind is that Baccarat as well as Roulette are binary games. Consequently, we need to think yin versus yang or 1 versus 0.

If you play long enough and use a flat bet amount...

1) how many times will you lose -1 versus winning +1 after this -1 ? around 50%, right ?
2) how many times will you lose two times -1 consecutively versus winning +1 after -1-1 ? around 50%, right ?
3) how many times will you lose three times -1 versus winning +1 after -1-1-1 ? around 50%, right ?
4) how many times will you lose four times -1 versus winning +1 after -1-1-1-1 ? around 50%, right ?
etc.

Do you begin to see a pattern here ?

More to come...

[kawa4711]

Hi, Arte, thank you for all your interesting ideas.

I like the D`Alembert, too, so I ve tried different ideas.

The last (not so bad) trials were with "Stretched D`Alembert":

par ex: 1 1 1 2 2 2 3 3 3 4 4 4 (all when there is a minus 3 times without a W) LLL LLL LLL LLL when there are 3  W s in a row you reduce the bids.
You can stretch it to 11111 22222 33333 and so on, but sometimes its a long way to come into the plus-zone.

I am curious about your ideas.

Best regards

kawa4711

[Arteinvivo]

Let's go a step further...

We have this series of wins (w) and losses (L):

w
L
w
L

we expect our bet selection (B.S.) will produce 1 win out of 2 trials

Here is another one:

L
L
w
L
L
w

at times, you can expect your B.S. will produce 1 win after having had 2 consecutive losses

Let's carry on a bit further...

L
L
L
w
L
L
L
w

at times, you can expect your B.S. will produce 1 win after having had 3 consecutive losses

Hey! last example...

L
L
L
L
w
L
L
L
L
w

Less common but... you can expect your B.S. will produce 1 win after having had 4 consecutive losses

to be continued...

[Arteinvivo]

I could keep on with these examples but i think you get the gist of it.

In a bernoulli system, you can expect to see as many runs of 2 and up as singles.

Ex.

In 1024 trials (theoretical case) you can expect to see:
runs: PPP/BB/PPPPPP/BBBB
singles: P/B/P/B/P/B

1) 512 singles vs 512 runs of 2+
2) 256 runs of exactly 2 vs 256 runs of 3+
3) 128 runs of exactly 3 vs 128 runs of 4+
4) 64 runs of exactly 4 vs 64 runs of 5+
5) 32 runs of exactly 5 vs 32 runs of 6+
6) 16 runs of exactly 6 vs 16 runs of 7+
7) 8 runs of exactly 7 vs 8 runs of 8+
8) 4 runs of exactly 8 vs 4 runs of 9+
9) 2 runs of exactly 9 vs 2 runs of 10+
10)1 runs of exactly 10 vs 1 run of 11+

This is of course a generic scale where each level has two faces.

As you can see it is a binary thing. The Alembert progression is geared to exploit this aspect or handle the regression to the mean or regression to a state of equilibrium between these opposites forces.

The Alembert progression i want to show tries to exploit the return to a state of balance at each level of this scale. But, you don't need to reach a state of balance at every level to be in profit. When you are in profit, it's best to play safe and reset your numbers.

If your risk to tolerance is not high then you might want to confine the Alembert progression to some levels only, levels which begin at step 3 and up.

[Arteinvivo]

Here is how it works:

Track 8 to 10 levels in our scales.

If you decide to confine the Alembert to some levels greater than 2 then fine, here is how to proceed:

When you lose 3 times in a row, like this, then at the fourth trial try to recover these 3 units

-1
-1
-1
+3

If you lose then you will need to wait for the next opportunity :

-1
-1
-1
-3

Then write where you stand in your scale
(n/a = non applicable)
1:n/a, 2:n/a, 3:2, 4:1, 5: 1, 6:1, 7:1, 8:1 etc.

next opportunity...

-1
-1
-1
+6

We update our  scale:
1:n/a, 2:n/a, 3:1, 4:1, 5: 1, 6:1, 7:1, 8:1 etc.

[Arteinvivo]

In this example, i have confined the progression to levels greater than 1.

[Arteinvivo]

At any point, you can balance your chart if you find a lower level gets to high. For example, if level 2 reaches 4 while all other levels are low then you can transfer part of level 2 to some other levels. You want to keep your chart as normalised as possible.

As you can see, it's very flexible. The Alembert is played independantly at each level of the scale and not in a linear way as we were used to do with the original concept.

[Arteinvivo]

Now, let's see another variation where i only play scale level 1, all other scale levels are disabled:

[Worm]

I dont get it...i feel like a retard 

[Arteinvivo]

Again, in the last example (second variation) you can transfer or normalise your chart if your bets get too high at level I. Add new levels as necessary. This is certainly one of the most flexible way to up your bets.

Here is a side-by-side comparaison with flat-betting using a very tough sequence:

[Arteinvivo]

I dont get it...i feel like a retard 

LOL. Look at the scale which enumerates the distribution of runs vs singles. I just try to capture the return to equlibrium at each level. But i can use the help of the most performing levels or less solicited levels to help other less effective levels during a session or multiple sessions.

[Worm]

Think i got it now, atlest some of it..man where do you get all your ideas from? 

[Arteinvivo]

Think i got it now, atlest some of it..man where do you get all your ideas from? 

I have plenty in store and many i would never discuss as i would find them toooooooooo complicated to explain though easy to understand once the Eureka moment has come 

[Arteinvivo]

Here is another test, always betting on Bank: 371 bets placed consecutively.

P   -1   
P   -2   
P   -1   
B   1   
B   1   
B   1   
P   -1   
P   -3   4
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
B   4   3
B   1   
B   1   
P   -1   
B   3   2
P   -1   
P   -2   3
B   1   
P   -1   
P   -3   4
B   1   
P   -1   
B   4   3
P   -1   
B   3   2
B   1   
P   -1   
B   2   
B   1   
B   1   
B   1   
P   -1   
P   -2   3
B   1   
P   -1   
P   -3   4
B   1   
B   1   
P   -1   
B   4   3
P   -1   
B   3   2
P   -1   
P   -2   3
P   -1   
P   -1   
P   -1   
P   -1   
B   1   
B   1   
P   -1   
P   -3   4
P   -1   
P   -1   
B   1   
P   -1   
P   -4   5
B   1   
B   1   
B   1   
B   1   
P   -1   
B   5   4
P   -1   
P   -4   5
B   1   
B   1   
P   -1   
P   -5   6
P   -1   
P   -1   
B   1   
P   -1   
B   6   5
P   -1   
B   5   4
B   1   
P   -1   
P   -4   5
P   -1   
B   1   
P   -1   
P   -5   6
B   1   
P   -1   
B   6   5
P   -1   
P   -5   6
B   1   
P   -1   
B   6   5
P   -1   
B   5   4
P   -1   
B   4   3
B   1   
P   -1   
P   -3   4
B   1   
P   -1   
P   -4   5
B   1   
B   1   
P   -1   
B   5   4
B   1   
P   -1   
P   -4   5
P   -1   
P   -1   
B   1   
B   1   
B   1   
B   1   
P   -1   
B   5   4
P   1   
P   -4   5
P   -1   
P   -1   
P   -1   
P   -1   
B   1   
P   -1   
B   5   4
P   -1   
P   -4   5
B   1   
P   -1   
B   5   4
P   -1   
B   4   3
B   1   
B   1   
B   1   
B   1   
P   -1   
P   -3   4
P   -1   
P   -1   
B   1   
P   -1   
B   4   3
P   -1   
B   3   2
B   1   
P   -1   
B   2   
P   -1   
P   -2   3
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
B   3   2
B   1   
B   1   
B   1   
P   -1   
P   -2   3
P   -1   
P   -1   
B   1   
B   1   
P   -1   
B   3   2
P   -1   
P   -2   3
B   1   
P   -1   
P   -3   4
B   1   
B   1   
B   1   
P   -1   
B   4   3
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
P   -3   4
P   -1   
B   1   
P   -1   
P   -4   5
B   1   
B   1   
P   -1   
B   5   4
P   -1   
P   -4   5
B   1   
P   -1   
P   -5   6
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
P   -6   7
B   1   
P   -1   
P   -7   8
B   1   
P   -1   
B   8   7
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
P   -7   8
P   -1   
B   1   
B   1   
P   -1   
B   8   7
P   -1   
P   -7   8
P   -1   
P   -1   
P   -1   
P   -1   
B   1   
P   -1   
P   -8   9
B   1   
P   -1   
B   9   8
P   -1   
P   -8   9
B   1   
P   -1   
B   9   8
B   1   
B   1   
P   -1   
B   8   7
P   -1   
P   -7   8
B   1   
B   1   
P   -1   
B   8   7
B   1   
B   1   
P   -1   
B   7   6
P   -1   
P   -6   7
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
B   7   6
P   -1   
P   -6   7
B   1   
P   -1   
P   -7   8
P   -1   
B   1   
B   1   
P   -1   
P   -8   9
B   1   
P   -1   
P   -9   10
P   -1   
B   1   
B   1   
B   1   
P   -1   
P   -10   11
P   -1   
P   -1   
P   -1   
P   -1   
P   -1   
B   1   
B   1   
B   1   
B   1   
B   1   
B   1   
P   -1   
B   11   10
P   -1   
B   10   9
B   1   
P   -1   
B   9   8
B   1   
P   -1   
B   8   7
P   -1   
P   -7   8
B   1   
B   1   
B   1   
B   1   
P   -1   
P   -8   9
P   -1   
P   -1   
B   1   
P   -1   
P   -9   10
P   -1   
P   -1   
B   1   
P   -1   
P   -10   11
P   -1   
P   -1   
P   -1   
P   -1   
P   -1   
P   -1   
B   1   
P   -1   
B   11   10
P   -1   
B   10   9
B   1   
B   1   
P   -1   
B   9   8
B   1   
B   1   
B   1   
P   -1   
B   8   7
P   -1   
P   -7   8
B   1   
P   -1   
B   8   7
B   1   
P   -1   
B   7   

Total : +49 units, minus commission +28.5 units, flat-betting : +16 units minus commission +5.4 units.

[Arteinvivo]

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