Even though some different sequences spring out from a conflicting situation, most part of them are coming out from a 'streaky' propensity that cannot be wrong for long, especially whether we're assessing each deviation step class not belonging to the 1 or 2 gaps level.

It's now that a multilayered progressive plan can destroy the house as a a kind of impossible balanced symmetrical card distribution cannot act for long at one or more than one of the four roads examined (and we know there are infinite derived roads to look for).

Discount the 0 streak sequences (that is consecutive streaks happening at each road), now assess how long a streak will be silent for 1 or 2 times (or more times) at each road registration and per each 1 or 2 class considered.
Always remembering that rare events are more likely to show up clustered and then followed by a very diluted pace of apparition.


as.

Hi AsymBacGuy

I've enjoyed perusing through all your recent posting activity/though not responding daily I am indeed viewing/pondering your thoughts.

re: reply #465 above: "...Always remembering that rare events are more likely to show up clustered and then followed by a very diluted pace of apparition. .."

     I agree especially when viewed from say a specific perspective of >=4 IAR  same-side streaks.
On the same topic:

Q: Would you also agree with an almost similar inverse logic/statement: (i.e., a very diluted pace of apparition is often followed by a clustered rare event)??

Continued Success,

Hi KFB!!!

Would you also agree with an almost similar inverse logic/statement: (i.e., a very diluted pace of apparition is often followed by a clustered rare event)??

It depends about the 'rare' definition of an event or class of events.
At baccarat 'rarer' events tend to come out clustered not only for their past diluted appearance at previous shoes but as cards are not properly shuffled.

Remember the old adage stating that players have no hint about advantaged spots to bet into, nonetheless any player who have won at a given shoe will more likely return his/her money to the house at the next shoes unless a moderate or strong 'bias' keep happening.

No matter what, most of the times the 'clustering' effect will place things in a way that some spots will be more detectable than the counterpart, always accounting their general probability to happen.

For example, take the cr.
Singles are fighting vs streaks and doubles are struggling vs 3+ streaks.
If baccarat would be made by an infinite succession of 50/50 independent propositions, the number of doubles vs 3+s streaks will get sd values typical of coin flip propositions, that is unbeatable spots.

Really?

I guess that most serious baccarat players would wager toward one class of outcomes than toward the other one, providing to start and stop the betting in the proper circumstances.

More on that later

as. 

The difference between baccarat and a 50/50 independent proposition game is that at the former game some events distributions, whether properly assessed either in quality and quantity, are 'more due' than expected.

Reasons why this thing should be true is based about place selection and collectives (RVM), probability after effects (M. v. Smoluchowski) , probability in decline (Spencer-Brown) and asymmetrical BP probability (bac rules) tools, everything tends to work (or not) toward a more likely scenario after something had happened.

When reading those considerations math 'experts' will laugh at them, mainly as they do not know a fkng nothing about those important statistical tools, after all they have a zero chance to beat baccarat itlr.

Back to a 'bringing down the house' strategy.

Differently of waiting for unlikely math polarized situations favoring player (e.g. getting at black jack deck portions particularly rich of high cards) at baccarat we must confide that either the actual card distribution cannot provide back to back symmetrical situations for long and/or that streaks of a certain lenght considered as a 'class' won't happen isolated for long.

Moreover the 'results pace' will make an interesting role in that.
Take the cr.

One of our math 'id.i.ot' random walk will take care of 3+s streaks happening at cr.
Cr doubles are losses and cr 3+ streaks are winners.
Ok itlr the number of doubles is supposed to be equal to the number of 3+s streaks.

Who gives a sh.i.t?

After a 3+s streak happened at cr, the probability to get another 3+ streak vs a double within two attempts will be quite more limited than what a 50/50 independent proposition dictates.

Say that before placing a bet we want to classify such random walk in terms of WL ratios, waiting for a given negative deviation before betting.

Thus any 3-3 or 3-2-3 cr occurence will get us a win; any 3-2-2-x-x pattern will get us a loss.
Since at this plan singles are 'neutral', we'll wait that two consecutive b or r dots will show up, then wagering two times toward triples instead of doubles after a 3+ streak had come out.

Try to set up a progressive multilayered strategy after 2 or 3 fictional double attempts were unsuccessul and you'll get the idea.

The advantage of betting cr is that there's no way to arrange cards in order to get a lot of doubles interpersed with rare 3s.

For that matter, even a st.u.pid progressive plan disregarding the actual 3+ negative deviation will make the best of it by wagering toward 3s clusters and one-gap 3s clusters than rarefied isolated 3s.

as.

Card distributions at baccarat shoes

It's the constant inviariable asymmetrical card distribution that makes baccarat as the best beatable game among the gambling panorama.
Math edge cannot do anything about a 'biased' production even though each bet is somewhat taxed.
Moreover baccarat is the only game where every side bet is mathematically beatable via card counting.

Casinos had made, are making and will make a lot of profits from this game primarily because we players try to do our best to lose.

In some way playing too many hands doesn't enlarge casinos' profits for the house edge, just let the players to easily lose their control over the entire picture.
Casinos want us to 'guess' every hand dealt but the asymmetrical feature takes its full power only after a classification made by a diluted pace (sections), therefore 'every hand bettors' are forced to hope for unlikely 'human' easy detectable patterns as long streaks, steady one side predominance, long hopping spots or whatever is more likely to be caught by a human eye.

Those situations are surely coming out from a kind of asymmetrical strenght but they all belong to too few categories to be normally exploited. 

Actually nothing prevent us to take advantage of those unlikely 'univocal' situations, especially when we have reasons to think that shoes are not properly shuffled.

An asymmetrical BP succession could be splitted into infinite sub successions

Derived roads invented in the 70s are the most notorious example why a BP succession could be considered (and exploited) by different angles.
Original authors were concerned about a kind of 'univocal' situations happening at different paces of registration.

Now the BP probability is shifted toward various degrees of 'same' or 'opposite' states not belonging to an asymmetrical B/P probability.

In some way derived road inventors couldn't give a s.h.it about B>P propensity, they have just considered blue and red spots distribution.

Probably they didn't know (but Kashiwagi did and some others after him) that they have set up a decisive tool to beat this game, that is transforming a light asymmetrical succession into symmetrical sequences that do enlarge the actual asymmetrical card distribution happening along any shoe.

Mathematicians will say that subsequences derived by a 'random' original sequence will follow the same statistical features working at the original one but by far and by a degree approaching the 100% statistical confidence they are wrong.

We can take for granted that baccarat shoes, in a way or another, are affected by a kind of bias happening on the vast majority of them. It's up to us to exploit such flaw, remembering that such bias more often than not cannot last for the entire lenght of the shoe.
And of course knowing that biases are either coming out clustered at various degrees or very diluted (that is not exploitable).

as. 

Thx/Good essay AsymBacGuy

"...Math edge cannot do anything about a 'biased' production even though each bet is somewhat taxed.  ..."

     Well said/ IMO this "biased production" is also displayed in most even-chance wager games(e.g., Roul, craps line et al games). Though I do agree Bac is optimum and offers the best opportunities for exploitation(not just because of low H.E.)



"... Casinos want us to 'guess' every hand dealt but the asymmetrical feature takes its full power only after a classification made by a diluted pace (sections)..."

     Q: Do you mean after the event has "underperformed" in a prior section of that shoe?? Can you talk a little more about this diluted pace(sections)? Thank you.


Continued Success,

Hi KFB and thanks again!
I appreciate a lot your thoughts.

There is no vaccine against math edge working for one side or another, but there are strong vaccines against it once we have understood the real environment where such math edge should work at.

If any spin, roll or outcome is independent from the previous one/s, we'll have harsh (let's say impossible) times to validate our hypothesis that a given game is beatable.
Yes, even at baccarat most of the outcomes seem to be independently placed, apparently working toward a 'everything is possible' environment, yet we should remember that bac results are coming out from a finite asymmetrical card distribution acting at an already asymmetrical proposition dictated from the rules.

Q: Do you mean after the event has "underperformed" in a prior section of that shoe?? Can you talk a little more about this diluted pace(sections)? Thank you.


Definitely.

People who consistently beat this game know very well the card distribution limits, you can present them the most whimsical shoes in the universe and they'll decide the right time to bet (or not).
For the natural attitude that some players like to wager money over other peers' already placed bets, most of the times they will go unnoticed.
And btw casinos do not give a damn about those people as the vast majority of players lose and lose.
Not mentioning that unless a verified math edge works against them, they are not worried a bit.

Technical features

Probability after effects, place selection and other statistical tools applied to baccarat teach us that a baccarat card distribution will follow lines getting limiting values of relative frequency more restricted than what a 50/50 or 50.68/49.32 propositions dictate.

Therefore any shoe is affected by degrees of deviation not following a perfect independent production; after cards are shuffled and arranged into a shoe we surely know results are not belonging to a 50/50 or kind of distribution.

Depending upon which kind of pace we wish to register the results, we'll get different 'states' of distribution, either in homogeneous or heterogenous shapes.

Long B or P streaks and long B/P chopping lines will both get a univocal homogeneous red line at every derived road.

Long BBPBBPBBPBBP or PPBPPBPPBPPB sequences will get either a blue (2/3 of the times, byb an cr) constant line and a red constant line (1/3 of the times, sr).

All those scenarios imply a strong asymmetrical or kind of fake symmetrical feature that cannot last for the entire lenght of the shoe.

Let's falsify this theory, now betting toward long B or P streaks and/or long B/P chopping lines and/or long BBPBBPBBP/PPBPPBPPB sequences and you'll get the idea.

After all, the number of r/b shifts happening at every shoe dealt is well more restricted than what a kind of coin flip proposition dictates, with good peace of (losing) mathematicians.

as.

Thanks AsymBacGuy . I appreciate your reply to my Q above.

"... yet we should remember that bac results are coming out from a finite asymmetrical card distribution acting at an already asymmetrical proposition dictated from the rules..."
     Perfectly stated and its the word finite that we should always remember when at the Bac tables.

     That in my opinion is one of the main differences between Bac and many comparable games  that instead utilize dice vs cards(primarily games such as craps). Yet gaming authors and casino employees incessantly blather on "its just a fitty-fitty coin flip game", suggesting that it doesn't matter how we wager/ "no advantage to be found here".

One of several reasons there is a difference "when comparing games" : (i.e., In Bac obviously the marbles are not placed back into the jar after each drawing of balls(i mean cards).  However, if we only look at the outcomes profile of results when comparing Bac to Craps--they will indeed look similar and will indeed converge toward expectation. Yet IMO two completely different games.  Again, just my personal thoughts.


Continued Success ,

Hi KFB!!

That in my opinion is one of the main differences between Bac and many comparable games  that instead utilize dice vs cards(primarily games such as craps). Yet gaming authors and casino employees incessantly blather on "its just a fitty-fitty coin flip game", suggesting that it doesn't matter how we wager/ "no advantage to be found here".


Exactly, I agree too, such people keep thinking the game as a coin flip or 0.5068/0.4932 propositions not considering at all the source of the results taken distinctively

Of course itlr distinct ditributions will converge toward the math expected values, but a precise card distribution will get way more restricted values toward one 'status' (pseudo equilibrium) or the other one (light, moderate or strong deviation) and the final math assessment must be calculated by the root mean square.

Thus if we're going to apply a kind of 'balancement' strategy we must hope that the actual shoe is full of pseudo equilibrium spots, and not that at some point of the shoe things will change (toward deviations of some entity). That is the shoe we're playing at hopefully must contain root mean square values lower than expected.

Conversely, a kind of 'deviation' strategy must hope that the root mean square tool will get its expected value at different degrees and we just need a number different to zero to get a sort of advantage.

Again let's consider how many times a given A or B (or W and L) opposing scenario will get long 'hopping' sequences vs homogeneous sequences and we know that the latter case is well more likely.

Raise the general probability to succeed and we see that such 'hopping' balanced scenario will be more and more unlikely.
After all, the root mean square value (and values acting toward it) must happen at some point for three diifferent reasons:

- it's a normal situation happening even at pure independent propositions;

- the game is produced by a sure asymmetrical card distribution;

- the A/B or whatever taken x/y propositions are asymmetrical by definition.

In some sense any single fkng shoe dealt is affected by a number of 'pseudo equilibrium' spots and 'deviation' spots where the latter tool tends to be more prominent (or not quite balanced by the opposite situation) than the other one.

Say that cards are voluntarily arranged toward a strong balanced status, meaning that 'trend following players' (constituting the vast majority of bac bettors) will get no hint to bet this or that.

Really?

Card distributions making strong balanced distributions (that is not reaching the mean square value) for long cannot happen at all four common registrations (BR, byb, sr and cr), let alone about other random walk registrations.

The number of -1/0, 0/-1 and +1/0 and 0/+1 spots cannot last for long as they MUST jump to -1/-2 and +1/+2 spots. And so on.
If the 0 value would be reached several times in short sequences, baccarat wouldn't exist.
And btw it would be a strong falsification of the sure fact (not hypothesis) that cards are asymmetrically distributed per each shoe.

Whenever a shoe is forming at a given subsuccession a higher than expected number of 'pseudo equilibrium' spots (huge number of very low deviations going around a 0 point), odds are that subsequent shoes will approach more and more the root mean square (RMS) value, meaning that the same succession will get more deviations than 'pseudo equilibrium' spots, and it's now that we'll get an edge over the house.

Globally, our edge is estimated to be 3% over the house AFTER VIG, a huge edge I mean.

This edge comes from a simple RMS natural happening:

- from 7 to 12 hands played the RMS is 3
- from 13 to 20 hands played the RMS is 4
- from 21 to 30 hands played the RMS is 5
- from 31 to 42 hands played the RMS is 6
- from 43 to 56 hand played the RMS is 7

and so on...

Even though a strict flat betting scheme will get the best of it, we can easily set up a kind of 'bringing down the house' strategy by adopting a progression that cannot be wrong by any means as the probability to lose the entire bankroll is almost not existent.

We'll see it in a couple of days.

as.

Natural deviations at any shoe dealt

If you toss a fair coin for long, sooner or later you'll encounter 20 or more heads or tails in a row and/or every other strong predominance following the expected sd values.
For example a streak of 20 at either side will come out, on average, two times over more than 1 million trials.
It's a normal happening everyone knows here.

The same could happen at baccarat, long streaks happen of course more probably at B side.

What it's interesting is that all intermediate situations are taking a univocal expected distribution at a coin flip proposition but slight different lines at baccarat.

Due to the asymmetrical card distribution typical of baccarat shoes, you can take for grant that most part of our bets will be either hugely right or hugely wrong as two-card initial situations will mathematically dictate the final result by a very strong edge.
A thing completely different than a coin flip proposition where each bet made will get a symmetrical probability to be right or wrong.

No matter the strategy employed, this feature endorses the probability that things will tend to come out wrong or right more in clusters than in isolated fashions. Shoe per shoe.

It's a sure fact that casinos will make tons of money from baccarat tables as players cannot realize how many bets are placed into the 'negative territory' (almost always by improperly increasing the wagers) and how many bets are placed into the 'positive territory' by low or too low amounts.

The math edge is just a 'booster' for casinos and not the main cause for they are collecting millions from baccarat.

From a technical point of view, we can summarize and simplifying the issue by expecting more W clusters and L clusters than long WL or LW spots as the root mean square deviation must happen shortly (especially when strong WL and/or LW states seem to negate this natural appearance).

Of course taking B and P as the main registration to base our strategy upon and under normal circumstances is among the silliest things to do that casinos particularly like.
'Smart strategies' as betting B after PPP or PPPP are just a waste of time and an insult to common intelligence that were tested and demonstrated to be as totally worthless.
(Those who are disputing this assumption are invited to confirm their hypothesis by betting B after three or four random hands are dealt regardless of the BP outcome, and results will get the same negative EV).

Our progression, part 1

There are no other ways around to confirm that baccarat is beatable by adopting a strategy different than a flat betting scheme. Maybe a well calibrated progression could dilute the risk of ruin but sooner or later this ruin will happen.
If not, it means that along with a careful MM, a strong valid bet selection is in order.
And if this is true, why not concentrate our betting by wagering very few spots supposedly getting a kind of EV+ by large sums?

Back to the progression.

Bankroll is formed by 224 bets splitted into eight and four multilayered betting levels.
Minimum bet is 1 unit and highest bet is 10 units.

So we can safely join a Vegas HS table by setting up a $2000 minimum bet, knowing at the worst scenario we'll wager $20.000. Bankroll is $448.000.

Actually it's very very rare to wager more than 4x standard units, meaning we'll get yet 24 bets behind (see later).

The progression is able to endure a 43 negative WL gap, meaning we need to meet a 44 L/W gap to lose the entire bankroll.

Naturally vig will erode winning spot amounts, but progressive bets stay low no matter what.

The progression is so solid that most peers stressed us to accelerate it but getting a firm 'no' from our part as we know that s.h.it could happen.

Progression basis concept

If things tend to come out more clustered than isolated and taking into account the root mean square value, we better bet progressively toward winning clusters than isolated clusters at the same time fearing most losing clusters that represent the same opposite side of the medal.
If our effort is restricted to the least when losing and slightly enlarged when winning, we should get an edge as the W and L situations are specular itlr (before vig).

Therefore our scheme is splitted into 10 different bet unit levels (totaling 44 betting spots) by wagering a two-step positive progression. That is after a win we let the entire amount to run for one time more. 

First eight levels stay at 1 unit betting level until a higher than 8 unit loss come out, now we'll step forward a 2 unit bet.

From the 2 unit bet, each level will stay four times instead of eight and so on.

The amount of the actual bet is dictated by the total number of units lost:

from 1 to 8 unit lost = bet 1 unit

from 10 to 16 unit lost = bet  2 units

from 19 to 28 unit lost = bet 3 units

from 32 to 44 unit lost = bet 4 units

from 40 to 64 unit lost = bet 5 units

from 70 to 88 unit lost = bet 6 units

from 95 to 116 unit lost = bet 7 units

from 124 to 148 unit lost = bet 8 units

from 157 to 184 unit lost = bet 9 units

from 194 to 214 unit lost = bet 10 units

There are additional 'rules' we'll see in the second part, the important thing to see is that each every losing bet (regardless of the first or second step result) remains at the same level (and set up by the current total losing unit amount) whereas every winning bet must be always 'parlayed' one time even if we're in the positive or neutral field.

So if we are working at the 1 unit level we'll get:

LL  = -1, -1 = -2
LW = -1, +1 = 0 (before vig)
WL = +1, -2 = -1 (before vig)
WW = +1, +2 = +3 (before vig)

Itlr such totals will be equal so getting us a loss for the vig, but the slow progression betting will make more and more probable the easiest winning situations we are really looking for, that is any WW sequence that tend to neutralize (many times slowly) many previous losing spots.

Acting in this way we are deadly sure to play a perfect symmetrical winning/losing proposition not giving a fk about the urge to break even shortly and at the same time capable to get the best of it when things come in our favor for long (think about a WWWWWWWW sequence getting us a +12 unit profit before vig)

After years of reading gambling forums, you should not find yourselves in the position to be behind 44 bets, it's a kind of impossible task.

as.

You said:

" It's a sure fact that casinos will make tons of money from baccarat tables as players cannot realize how many bets are placed into the 'negative territory' (almost always by improperly increasing the wagers) and how many bets are placed into the 'positive territory' by low or too low amounts.

The math edge is just a 'booster' for casinos and not the main cause for they are collecting millions from baccarat"

Which a whole lot and I do mean a whole lot of casino patrons have no real clue as to what the real odds or house advantages are at any given table at the time they buy in and begin their play. 

Also, I don't care what at any math nut claims, those numbers do not apply to me because I am only going to play 20 or 30 or 40 hands out of 2 or 3 or even more shoes. 

A second also is, those numbers come from (if done correctly) millions of hands.  Not 25 or 100 or 200 and so on.

So if I sit down and lose my buy in within 20 hands, I did not lose 1.06% on the Banker or whatever's being claimed these days, I lost 100%.  As well, if I lost  I never had a 99% chance to win.  I had a 100% chance to lose.  There, fuel for the math nuts to talk how stupid we are here.

The sad story comes on as patrons choose so often to believe those math nut's numbers.

Good Job on reply #474 above AsymBacGuy. A lot of solid thoughts/examples. We may have to nominate it for Post-Of-The-Year.
I will comment(and ask a couple Q) in a day or so as it is a lot to digest.

as:

"...It's a sure fact that casinos will make tons of money from baccarat tables as players cannot realize how many bets are placed into the 'negative territory' (almost always by improperly increasing the wagers) and how many bets are placed into the 'positive territory' by low or too low amounts.

The math edge is just a 'booster' for casinos and not the main cause for they are collecting millions from baccarat..."


alrelax:

"...Which a whole lot and I do mean a whole lot of casino patrons have no real clue as to what the real odds or house advantages are at any given table at the time they buy in and begin their play.

"... A second also is, those numbers come from (if done correctly) millions of hands.  Not 25 or 100 or 200 and so on.

So if I sit down and lose my buy in within 20 hands, I did not lose 1.06% on the Banker or whatever's being claimed these days, I lost 100%.  As well, if I lost  I never had a 99% chance to win.  I had a 100% chance to lose.  There, fuel for the math nuts to talk how stupid we are here.
  .."


     Well stated/ I agree 100%.  Variance will always be our number one nemesis (not H.E.)


     Continued Success,

Thanks a lot for your replies Al and KFB!!

Back to the progression

Say we are splitting our strategic plan into four infinite WL situations by adopting the 1-2 positive limited progression (anytime we win we'll leave the original bet plus the bet won; any bet lost at either two-step stage remains at the same level without any betting increase). For simplicity we do not take into account the vig.
Further progression rules will be posted later.

No matter how concentrated or diluted our wagers are, 4 hands bet can produce just 16 WL situations:

1) WWWW (+1, +2, +1, +2) = +6

2) WWWL (+1, +2, +1, -2) = +2

3) WWLW (+1, +2, -1, +1) = +3

4) WWLL (+1, +2, -1, -1) = +1

5) WLLL (+1, -2, -1, -1) = -3

6) WLLW (+1, -2, -1, +1) = -1

7) WLWW (+1, -2, +1, +2) = +2

WLWL (+1, -2, +1, -2) = -2

Specular 'losing' counterparts are:

9) LLLL (-1, -1, -1, -1) = -4

10) LLLW (-1, -1, -1, +1) = -2

11) LLWL (-1, -1, +1, -2) = -3

12) LLWW (-1, -1, +1, +2) = +1

13) LWWW (-1, +1, +2, +1) = +3

14) LWWL (-1, +1, +2, -1) = +1

15) LWLL (-1, +1, -2, -1) = -3

16) LWLW (-1, +1, -2, +1) = -1

Of course the total final amount of hands #1-#8 is +8 and at hands #9-#16 is -8.
For that matter 1-8 hands range provides 5/3 W/L cumulative ratio and the same is oppositely true about 9-16 hands range (5/3 L/W cumulative ratio).

Without a possible bet selection advantage, the probability to get each of those different outcomes is fkng symmetrical but there are some differences even in this perfect balanced scenario:

a) any pattern starting with a W will get an average final total amount of +14 at W spots and an average final total amount of -6 at L spots (+14 - 6 = +8)
On the other end, any pattern starting with a L will get an average final total amount of -13 at L spots and an average final total amount of +5 at W spots (-13 +5 = -8).

b) whenever a specular extreme pattern as WWWW or LLLL comes out (getting the same probability to appear), we'll get different final results, in fact:

WWWW = +6
LLLL = -4

the same about the back to back appearance of those 'extreme' results, so:

WWWW/WWWW = +12

LLLL/LLLL = -8

and so on.

In other words, whenever our first bet of our 4-step wagering 'unlimited' strategy is a W, we'll get 5/3 odds to end up with a final win ranging from +6 to +1 and a final loss ranging from -1 to -3.

Conversely, whenever our first bet is a L, we'll get 5/3 odds to conclude the 4-step wagering with a cumulative loss ranging from -4 to -1 and a final win from +1 to +3.

If we'd symmetrically put the same W/L opposite eight scenarios together, we'll see that cumulatively we are going to get just two situations having a +2 global result, one getting a -1 result and another one getting a -3 result. The remaining four situations are going to get a 'break even' spot.

Hence itlr we know we must face half of the outcomes to be W/L 'balanced' and the rest to be deviated in a way or another.

Back to the WL scenarios getting a transitory strong 'balancement' (temporarily denying a root mean square normal value):

WLLW = -1

WLWL = -2

LWWL = +1

LWLW = -1

WWLL = +1

LLWW = +1

Cumulatively those 'perfect balanced' W/L spots are going to get us a -1 global result perfoming a 6/16 probability to happen (p=0.375).

That means that the remaining part of results (p=0.625) are affected by a kind of normal 'bias' toward either side of the bell curve.
Naturally a perfect independent proposition cannot get us any valuable hint to bet this or that, therefore these assumptions cannot apply at roulette, for example.

But since at baccarat it's highly improbable (say impossible) to arrange key cards proportionally along any shoe dealt and by different paces both being insensitive of the place selection and probability after effects statistical tools (those ones confirming or not the real random nature of the shoe), we know that sooner or later the root mean square value will get its rights to happen.

For that matter I do not know a single long term winning player capable to quit a session as a winner unless he/she is able to catch the spots where W is more followed by another W than by trying to stop a L spot.

Later about the progression topic.

as.

In essence and no matter the strategy employed, per each shoe dealt we'll get a number of pseudo equlibrium spots and a number of deviations going toward the natural RMS value.
Obviously it's highly preferable to play toward the latter scenario not because we have in mind a kind of 'sky's the limit' attitude but simply as baccarat is a word of multiple asymmetrical propositions.

Adopting a mini positive (multilayered) progression will help us to define if our bets are falling into the 'pseudo equilibrium' territory or a more hopeful mild, moderate or strong deviation.

Naturally if WW is the searched scenario and LL is not that terrible (proportionally speaking), our enemies are isolated Ws and, at a different extent, isolated Ls.

Example.
The succession is WLLLWLLLLWLLLLLLLLWLLL (W/L ratio 4/18)
The RMS value is abundantly passed (3.7-sigma), but we were betting the opposite situations.
Our progression (assuming to stay at the same first level) applied to this sequence is:
+1, -2, -1, -1, +1, -2, -1, -1, -1, +1, -2, -1, -1, -1, -1, -1, -1, -1, +1, -2, -1, -1. total = -18 units (plus vig).

The specular natural counterpart is LWWWLWWWWLWWWWWWWWLWWW (W/L ratio 18/4)
Now we'll get: -1, +1, +2, +1, -2, +1, +2, +1, +2, -1, +1, +2, +1, +2, +1, +2, +1, +2, -1, +1, +2, +1.
total = + 21 units (minus vig)

It's evident that this 22-hand succession from a statistical point of view is perfectly balanced but from an economic point of view is asymmetrical to our favor.

Someone could argue that in the first heavy losing sequence we might wait for a W to come out before betting without immolating money on those long L series (so losing less than 18 units). And the same about the second sequence by betting more than a mechanical 1-2 progression on that strong winning succession (so winning more than 21 units).
But this kind of reasonment is failed by an obvious post hoc thought.
Winning and losing both belong to the same process, we know sooner or later things will take a more natural flow but we do not know when (partial imperfect information) and how much (true imperfect information).

Of course a steady pseudo equilibrium status will more likely elicit a deviation of some kind, after all the original succession could be splitted into infinite ways where the equilibrium is the exception and the deviation is the rule.

Progression steps

Our initial betting unit is 1 (there are reasons to set up this initial bet at 5, we'll talk about this issue in the future).
We'll always parlay a first win just one time forever and ever, no matter whether we win the first step (WL) or the second step (WW) our bet will be 1 until a deficit of 8 units will be reached.
If we are in the positive territory we'll stop the betting until the RMS value is reached, waiting if the RMS value is erased then starting to bet again.
We'll bet 1 unit whenever our losing amount is included into the 1-8 units range.

When we are behind of 8 units we'll pass to the 2nd betting level made of four stages, that is betting 2 units with the same parlay rules.
We stay at this 2 level if our deficit is reduced to 7 units, now we take back the first 1 unit betting level step.

If our deficit raises to 16 units, we'll start to bet 3 units made of four steps, again with the same parlay rules.
If we are able to come back at a 14 unit deficit we'll go back to the second step (that is betting a 2 unit); if we're unfortunate to further increase our loss (28 unit loss) we'll step forward the 4-unit level (again made of four steps) and so on by increasing one unit for four times long up to the final 10-unit betting level. Up to the point where we'll get one unit profit.

Step one and two follow the same rules, but next step levels (3,4,5,6,7,8,9 and 10) must stay at the same level after a parlay win.
After two consecutive parlay wins made at levels 3-10, we'll go back to the immediate inferior betting level; for example after having won two times a parlay bet of 4 (4+8 and 4+8 = 24 units) we'll step back to 3 level.

I'll provide a scheme about what to do in relation of the actual deficit, but it's quite simple to understand that to go back to the inferior betting level we need to end up as winners at a given betting level.

Technically this progression 'challenges' the results not to give at least a RMS value for long and, frankly, this situation it's almost impossible to happen even if we're voluntarily playing to lose.

But let's falsify such hypothesis by setting up a strategy oriented to get more pseudo equilibrium spots than deviated spots those ones reaching at some time a normal natural deviation. The progression utilized remains the same.
In other words we're hoping that WL and LW spots are more likely to happen than WW or LL spots.
A paraphrase of D'Alambert progression that was proven to be a sure recipe for disaster.

Instead of 4-hand propositions let's take just 3-hand ways to consider outcomes:

WWW = +1, +2, +1 (+4)
WWL = +1, +2, -1  (+2)
WLW = +1, -2, +1  (0)
WLL = +1, -2, -1  (-2)

LLL = -1, -1, -1  (-3)
LLW = -1, -1, +1 (-1)
LWL = -1, +1, -2  (-2)
LWW = -1, +1, +2 (+2)

In eight 3-hand attempts, odds to break even are 1:8.
In eight 3-hand attempts, odds dictate that the maximum win (1: is +4 and the maximum loss (1: is -3.
In eight 3-hand attempts, half of the time we'll get either 2 units won or 2 units loss.

Just in one scenario we'll be behind of 1 unit.

Therefore we know that after three hands played, our bankroll movement is 6:2 favorite to get either an increase or a decrease superior than 1.
Not a good thing to know when applying a kind of constant 'balancement' play.

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Here the progression scheme

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