I am going to delete my previously posted content as I only refer to actual B&M casino reality baccarat, that I played or witnessed in person. 

Why?  Because it is the 'short run' and what is clearly being played at the table.

So, my thoughts do not fit in here, IMO.

I've canceled a couple of my recent posts because they were too intricated to be grasped.

The concept is that any result distribution move toward the right by different speeds.
Obviously more singles and the speed will be higher, more streaks and the speed will slow down in relationship of how long are such streaks.

Obviously there's an average speed as we know that every shoe dealt will end up by filling way more likely  ranges (number of columns).

"Turbo" sequences at either side of the process (very high speed, very low speed) happens but naturally they are rare to happen.
Moreover an interesting feature of baccarat subsequences is that it's quite rare to get same step speeds at two or more "derived roads".

A possible registration of the patterns could be to put a + sign anytime the side shifts (B->P or P->B) and a - sign when the same side happens again.

We are not interested to assess the +/- final number, let alone to chase a specific sign, just about their form of presentation along any shoe.

For example a shoe sequence as BPPPBBPBPBBBPPPPP is

+ - - + - + + + - - + - - - -

To cut a long story short and just to provide an example, the only overalternating +/-/+/-/+...pattern comes out when consecutive doubles come out.

In fact BBPPBBPPBB...is

- + - + - + - + -

On the other end and as already sayed above, long + or - homogeneous sequences show up at branded chopping lines (+ sign) or at long streaks (- sign).

Every other more probable pattern is entitled to form short + or - sequences getting different shapes (isolated or clustered).

The interesting part of everything is that those shapes are sensitive either of the actual lenght of the shoe they are happening and about how the previous shapes went so far.

More later

as. 

Let's consider two extremes almost never happening, it's the starting point to go down in the patterns evaluation.

a) A shoe not producing any doubles;

b) A shoe not producing any 3/3+ streaks.


a) No doubles in a shoe means that we'll never ever cross more than one singled + or - sign in a row. 
That is we'll only encounter +-- or -++ situations.

b) No 3/3+ streaks happening in a shoe means that the - sign will come out as isolated all of the time.
In fact we need at least a 3 streak to get a - - succession.
At the same time it's easy to infer that at those distributions the overalternating +/- movement is increased in probability as soon or later two or more doubles will come out in a row.

No surprises!
Those shoes are the heaven for any sensible bac player for obvious reasons: what seems to be absent should be considered as non existent, yet the optimal play would be to bet after a single + or - sign in the a) scenario (+- or -+) and to bet after the - apparition in the b) situation.
At both those situations our probability to win is 100%.

Therefore and as long as no doubles or no 3/3+ streaks happen and in the betting spots examined, our probability to win is 100%.

Unfortunately (lol) at the remaining shoe distributions, doubles and 3/3+ streaks will mix and show up whimsically by different paces and by different quantities.

It's now that we have to make an "educated guess" of what are the more likely ranges of doubles/superior streaks in terms of distribution (not quantity) per any shoe dealt.

For example there are no many overalternating situations (consecutive doubles) happening along any shoe dealt, the same about clustered + signs formed by several long chopping lines or consistent - sign clusters (long streaks).
On the same line, the + or - shape will dictate our future action.
More informations we have at our disposal at a given point of the shoe, better will be our precision in approximating what should show up next.

Anyway when strong clusters seem to come out conseutively we think that there are only two options to follow: a)waiting or b)betting until the cluster ends up.
In the latter option we need just one more hand to win, then we might (almost) freerolling or collecting the profit.
Yet only first class players are capable to get a sort of long term advantage by playing "extremes".

Next time I'll present you some real shoes played. Step by step.

as.

1- The higher two card initial points are overall strongly math favorite to win the final hand

Obviously we want our side to get a 9, 8, 7 and a 6, yet any side getting a superior two card point vs the opposite side will win a lot more hands than what a 50/50 proposition will dictate.

Thus any 2 point vs any zero point or any 3 point vs any 2 point will win by a percentage way superior than 50/50.
The reason is because about 30% of the shoe is "neutral", that is formed by zero value cards (third card/s) not changing the first situation.

Of course many first two card situations present the same point (especially a zero point at both sides), so the third cards impact will decide the final hand's destiny.

Moreover, some card distributions keep privileging one side (especially the Player side that is entitled to draw more third cards than Banker) so kind of disrupting a math propensity for long.

Nonetheless, the vast majority of card distributions will make more probable some greater two card initial points ranges, the reason why an average final amount of columns will be filled no matter how are whimsically distributed the cards.

Even though it's impossible to know when a high two card point (6, 7 or even an will succumb to an even greater point (at the first or after two stages), a part of those math underdog situations will come out at our favor, but this is a transitory unwanted spot that itlr will make us losers and not winners.

I mean that ranges must be assessed either from a general point of view (general distribution and average speed acting toward the right end of the display) and by actual situations that most of the times aren't showing up by symmetrical paces.

More later

as.

2- A long term successful player must be able to exploit the actual asymmetrical situations always considering that the asymmetrical world could be extrapolated by innumerable ways

For example how do you consider a BBPPBBPPBBPP succession?

Possible answers:

a) This is a perfect "balanced" situation as B=P, our registration (see above) will get a
-+-+-+-+-+- symmetrical sequence;

b) This is a perfect asymmetrical deviation as there are no singles and no 3/3+ streaks;

c) The columns speed is "neutral" so featuring a 2-step moving rate.

At the end the BBPPBBPPBBPP sequence will make as constant perfect opposite features, so we'll need to exploit just one of the three possible factors to get a homogeneous detectable succession.

But in the real world such B/P sequence won't happen so frequently, most of the times stopping after two or three BBPP patterns.

Yet the general probability teach us that doubles are the most likely occurence, anyway we do not know whether such doubles will show up consecutively or intertwined with singles.
Or of course not happening at all so far.

Now let's consider a more "mixed" pattern sequence as:

BPPPPBBPBPPPBBBPPB

B= 7 and P= 10

Our registration will get a +---+-+++--+--+-+ succession.

How many symmetrical patterns are you able to spot on?

Just one.
That is the -- patterns being clustered two times in a row (hand #12 and #15).

There are no "silent" pattern categories showing up for long and the columns speed is
+1, -1, -1, -1, +1, -1, +1, +1, +1, -1, -1, +1, -1, -1, +1, -1.

More importantly, we see that - signs will come out more clustered than isolated (3 times vs 2 times) and + signs will show up more isolated than clustered (4 times vs 1 time).

The +/- hopping situation where both + or - signs will happen alternatively either isolated or clustered for long are not happening at the vast majority of shoes.

As an asymmetrical card distribution cannot arrange results by an overalternating QUALITY factor acting at both sides for long, so quality takes a primary role over quantity.

Check your shoes and let me know how many times an overalternating +/- isolated/clustered sequence will take place at both sides and, more importantly, about how much long this possible event will happen per any shoe played.

Let baccarat experts keep stating that baccarat is a unbeatable game, it's our interest to  confirm they are right.

as.

3- Most of the times the original BP succession will make room to many "opposite" simultaneous situations happening at sub sequences

And of course those opposite situations are showing up by more likely "ranges".

Let's consider the basic (very simplified) example of the common derived roads (byb, sr and cr).

The BP shoe's fragment is BPBPBPBP

byb: r,r,r,r,r,r

sr:  r,r,r,r,r

cr: r,r,r,r

At all three d.r., just one "color" happened: the red. This is strong asymmetrical situation derived by a kind of perfect symmetrical BP original sequence.

Along with BBPPBBPPBBPP... and BBBPPPBBBPPP... (and other very unlikely superior perfect symmetrical BP sequences) those are the only spots where all d.r. present just red spots.

Then there are the infrequent long B/P streaks forming possible long red successions that anyway must start with a blue sign at all derived roads.

In fact long BP streaks will delay the columns filling speed at all derived roads, so producing long lines of -1 spots.
Yet here the overalternating results production will be somewhat reduced. But mostly by an "isolated/clustered" statistical point of view as the +/- rhythm cannot be uniformed shaped for long.

More later

as.

The core principle is that a finite asymmetrical distribution enforced by an additional asymmetrical factor dictated by the rules will make slight more probable the formation of decent asymmetrical sequences.

By taking into account the columns filling speed we've seen that an overalternating movement (-+-+-+...) can only happen with the BBPPBBPP...sequence (or rrbbrrbb...etc). 
It's now that the "general long term findings" will help us to approximate when such kind of movement will happen, obviously without interest to know "how long" the overalternating sequences will last.

Anything different than that will 100% form a + or - cluster (++ or --) and again who cares about its lenght?

Therefore any 3/3+ streak will form at least a - - cluster, any streak ending up followed by a single is a + + sequence and any couple or more singles succession is a + + ...line.
The only possible pattern where + or - signs are coming out as isolated are whenever any 3/3+ streak will be followed by a double then another "no double" streak (BBBPPBBB ---> - - + - + - -.
In this scenario we'll get three isolated + or - signs.

Yet even in this example we could find a kind of asymmetrical distribution (+ coming out as isolated)

Now and to expand the last concept, let's build a sort of perfect asymmetrical BP succession where 
+ and - signs take an "isolated/clustered" shape at both sides.

For example a succession as BBPBBBPPBPPPBBPB
The columns filling speed (CFS) is - + + - - + - + + - - + - + +

Isolated - signs and + signs are followed by - and + clusters, yet the shifting side pace is one or two.

A more complicated example:

BBBBBB
PP
B
P
BBBB
PP
B
P
BB

CFS is - - - - - + - + + + - - - + - + + - -

Any - or + sign is followed by a different same sign quality (clustered followed by isolated and vice versa), yet isolated signs are just two in a row and the original succession is made by two consecutive streaks-two consecutive singles-two consecutive streaks-two consecutive singles...

Besides of this succession and of many correspondent situations (streaks lenght and singles lenght) any bac shoe will make quite room to + or - clusters (++ or --) and anyway distinct forms of apparition (isolated or clustered + or - signs) will be sooner or later followed by opposite shapes. The above example was extremized to present a perfect 0 step isolated/clustered delay as any isolated or clustered + and - sign (considered individually) was always followed by an opposite shape.

In any way we wish to consider result lines only those things could happen:

1- An important part of the shoe will make + or - signs being clustered at some point;

2- + or - individual signs shape will change along the shoe;

3- Itlr + and - signs move more likely by 1 or 2 steps vs superior steps (sums will be slight shifted toward the left), but this feature must be considered by a lot of caution as our primary strategy will always be directed to get clusters of something.
So by taking into account those opposite factors, only +/- double clusters will get us a two-fold propensity. Obviously once a pattern had surpassed the first (losing) 1-step, we should not be interested to chase any longer.

4- Even consecutive isolated + or - signs will constitute a pattern, but most of the times this is just a second-level strategy as generally it happens at few segments of the shoe.

See you next week.

as.

4. + and - signs move around isolated and clustered lines in relationship of the spots considered to build a given succession

That means almost nothing, whether only one succession (BP) or one sub succession is taken as the main "target" to base our wagering upon, but holding a very important role whenever we consider ALL possible sub successions as now at the vast majority of the times "extremes" cannot come out of blue for long for two or more sub sequences, either by quantity and (more importantly) by quality.

For example and again considering just the BP succession and the three common derived roads, the overalternating results pace happening simultaneously at two or more lines will be the slight less probable situation, yet the word "slight" means it'll be more than sufficient to erase and invert the HE.
Of course providing to understand that at baccarat there's a general probability to get overalternating movements (average CFS) and an actual probability to get overalternating result lines, especially when we are considering different result sequences.

In fact the bac production is asymmetrical in the past, now and in the future, our task shouldn't be oriented to "hope" that such asymmetry will particularly last for long, just approximating any card distribution by more likely "ranges".

More later

as.

Good comments Asym. Thx for your essays.

Asym above:
"...Moreover, some card distributions keep privileging one side (especially the Player side that is entitled to draw more third cards than Banker) so kind of disrupting a math propensity for long.

Nonetheless, the vast majority of card distributions will make more probable some greater two card initial points ranges, the reason why an average final amount of columns will be filled no matter how are whimsically distributed the cards..."



Continued Success,

Thanks KFB, I appreciate a lot your comments here!!

Before continuing to present our "technical" findings and ideas, let's consider again what casinos are instructed to think about baccarat:

a) The game is randomly distributed, so no strategy will work itlr;

b) No matter what, casinos are mathematically favorite to win per every single bet placed or, more precisely, the sum of placed bets will be EV-;

c) All gambling experts have denied a possible bac vulnerability (besides the side bets card counting).

After several years of studying this wonderful game by many statistical and math aspects we got those possible answers:

a) Outcomes are randomly distributed? It's a total bighorn.sh.it.

b) Yes, any bet is "supposed" to be EV-, but there are more probable ranges where the EV is at least 0 (think about those hands not forming an asymmetrical hand favoring the Banker side) or where a "normal" flow is slightly more entitled to go toward the right side (CFS) at some points of the infinite shoe sub successions we can build up.

c) Gambling experts do not know a fkng nothing about how the randomness will work at baccarat.
Mainly as they haven't properly considered the RVM and M.V. Smoluchowski "theories" applied to slight dependent and asymmetrical finite successions.
Conclusion is that bac successions aren't randomly distributed. Period.

Even at perfect "coin flip" independent sequences, there are studies which have shown that certain patterns are more probable to be encountered FIRST than others (think about the "waiting time", etc).

OoOoO

If the baccarat world (in any possible sub sequence derived by the original BP succession) would present homogeneous + and - signs for long (e.g. +++-----+++++---), the game would be easily beatable.
On the other end, more likely sequences happen as ++-+--+++-+---+ or -+-+---+-+--+.

The common denominator is that a kind of overalternating line (+-+-+...) happens just at the original BP succession or at one derived r/b succession, as CFS will get a way different speed at many possible sub sequences, thus making plenty of room to clustered lines.

Nonetheless, clustered consecutive + and - signs equal or greater than 3 are not coming out around the corner, for sure the vast majority of the times they'll happen just at one of the possible main road and at one of the three derived roads.

In fact, when a given line will present a unlikely univocal 3/3+ clustered situation for long, most remaining derived roads or main road will be more probable distributed by a 1-2 step.

In a couple of days some real examples.

as.

Consider this quite deviated shoe fragment as

BBBBBBB/P/B/P/BBBBB/P/B/P/B/P/B/P

That is a - - - - - + + + + - - - - + + + + + + + CFS sequence

A hell of a shoe's portion, meaning we do not want to set up sophisticated strategies to try to "guess" the actual + and - distribution. We simply follow through (3, 3, 3, 3..), that's it.

Yet the same BP sequence form those derived roads:

Byb:

b/rr/b/rrr/bb/rrrrr (CFS= + - + + - - + - + - - - -) --->  1, 1, 2, 2, 1, 1, 1, 3

Sr:

b/r/b/rrr/b/r/b/rrrr (CFS= + + + - - + + + + - - -) ----> 3, 2, 3, 3

Cr:

bb/rrr/b/rr/b/rrr (CFS= - + - - + + - + + - -) ---> 1, 1, 2, 2, 1, 2, (2)

We see that just one out of the three d.r. (sr) seems to "mirror" the original BP succession.
The other two d.r. have formed a lot of 1-2 successions where now the "3" becomes the only enemy (appearing just once at the end of the byb line).

Obviously even the sr could become a possible "target" as no 1s and just one 2 happened)

Now another quite deviated and different shoe's fragment.

PPPPPP/BBBB/PPPPPPPPPPP/BBBBBB/PPP/B

CFS: - - - - - + - - - + - - - - - - - - - - + - - - - - + - - + (3, 1, 3, 1, 3, 1, 3, 1, 2)

Derived roads:

byb:

rrr/b/rrr/b/rrrrrr/b/rrrrr/b/rr/b (- - + + - - + + - - - - - + + - - - - + + - +)

CFS= 2, 2, 2, 2, 3, 2, 3, 2, 1)

sr:

rrrrr/b/rrrr/b/rrr/b/r/b/rr/b (- - - - + + - - - + + - - + + + + - +)

CFS= 3, 2, 3, 2, 2, 3, 1)

cr:

rrrrrrrr/b  (- - - - - - - +)  CFS= 3

Ok, you'll tell me that only an id.i.ot could lose at this shoe fragment (BTW a real shoe) but that's not the point.
Instead, notice for example how long some values remained "absent" per every succession (2s at BP road, 1s at byb and sr; actually cr line didn't get the room to provide other than one (long) 3 outcome.
In reality there are several ways to find out asymmetrical spots (e.g. 'b' isolated signs at byb and sr, etc)

Unfortunately (actually it's our luck as casinos rely upon less deviated shoes) such two deviated shoes' portions won't happen so frequently, yet there are some considerations to be made.

For example the first shoe's fragment is a lot more probable than the second one, so in some sense we should be more inclined to rely upon a kind of "inverse" probability whenever we want to take into account simultaneously several random walks.

More later

as.

One of the interesting property of BP doubles is that they remain the most probable patterns, yet they are more likely to show up clustered (consecutive) by quite "detectable" distributions.
That means that their sd values of clustered (back to back) apparition is quite restricted, especially when we take into account the many possible sub sequences deriving from the original BP succession.

Obviously a "consecutive double" could be "prevented" by betting toward a single after any double or toward a 3/3+ streak after a following two streak (AAB bet A or AABB bet B and vice versa).

Along any shoe there are no many consecutive double clusters superior than 2 (minimum cluster) happening at all common derived roads as the CFS sooner or later must get a more specific speed negating a kind of overalternating movement (+ - + - + - etc).
When the 2 value is surpassed, we do not want to chase anything, just letting 'em go without further betting.

Naturally even "isolated" doubles present many situations to be attacked but exposing ourselves to bet too many hands that is always detrimental to our plan.   

More later

as. 

First player numbers ranges are interesting.

For example to get a number 0 homogeneous sequence (no absent doubles sequences as explained above) we need to cross this exact succession:

1) AABAABAAB...(0, 0, 0) or

2) AABBB...AABBB...AA...BBB (0, 0, 0)

3) Any mix of the two above situations (AABAABBB...AABAABBB..etc) ---> 0, 0, 0, 0.

Arrange the cards into a shoe as whimisically as you wish and you'll notice that an overalternating 0/any different number distribution will be the less probable "movement".

In practical terms and without a proper training is quite difficult to spot such triggers and making the future bet (that's why algos should make the work for us), anyway the first player always relies upon doubles (or other specific patterns) being absent for given frames transformed into numbers.

as.   

Asym:

"...Arrange the cards into a shoe as whimisically as you wish and you'll notice that an overalternating 0/any different number distribution will be the less probable "movement".

In practical terms and without a proper training is quite difficult to spot such triggers and making the future bet (that's why algos should make the work for us), anyway the first player always relies upon doubles (or other specific patterns) being absent for given frames transformed into numbers...."

that's interesting.

QuoteAsym:

"...Arrange the cards into a shoe as whimisically as you wish and you'll notice that an overalternating 0/any different number distribution will be the less probable "movement".

In practical terms and without a proper training is quite difficult to spot such triggers and making the future bet (that's why algos should make the work for us), anyway the first player always relies upon doubles (or other specific patterns) being absent for given frames transformed into numbers...."

that's interesting.

Thanks KFB!

I guess you, Alrelax and me would constitute a formidable team. 
Hope to play together very soon!

as.