Hi Asym.
I like the way you state that:

"...There are several ways to classify an asymmetrical or symmetrical pattern, just to make things simpler say that every streak followed by a single or every single followed by a streak is a first step asymmetrical pattern.
Whenever a homogeneous pattern happens as a single/single or a streak/streak situation, we'll wait  until a new different pattern will happen. ..."


More on this later,

Hi KFB, thanks!!

Before thinking to play baccarat with an advantage, let's see the main reasons why we aren't supposed to accomplish that task.

1) Per each bet placed, we'll wager 1 unit to get an inferior than 1 economical return being in form of many kind of commissions at winning B bets and a general underdog probability at P bets.
It's the old math HE, obviously working whether the result distributions are really randomly arranged.

2) The vast majority of players think that a kind of progressive plan will make the job, in reality such "ploy" will increase the casinos' profits as those players are relying upon the mere LW patterns (in any permutation) coming out along the way.
Actually if they would know when things start to change, they should just wait for such spots without consuming money at previous worthless losing situations.

3) More hands are wagered and less precise will be the winning targets as most of the times anything can happen anytime.

Summarizing the worst baccarat player in the universe is anyone thinking that results are randomly distributed, making some fancy "progressive" betting plans and wagering a lot of hands.
Such player will get a 0 probability to win itlr.

Conversely, a possible long term winner must rely upon the partial "unrandomness" of the results, wagering by a strict flat betting scheme and betting very few hands.

What the baccarat literature "teaches" us:

a) Best bet to make is always the Banker bet (rattlesnake.stuff)

b) Any new hand is a completely independent hand from the previous one(s) (bighorn.stuff)

c) No matter when we'll decide to bet, each resolved bet (no tie) will get an average 50.68% or 49.32% probability to show up (strongest desert tortoise sh.i.t)

Actually the game cannot be perfect randomly distributed by definition, as for any hand dealt key cards and game rules cannot form a complete independence in forming patterns.
We're deadly sure about that, meaning that after some conditions are met some patterns are way more likely than others and that's where our edge comes from.

We have already seen that a single result "going wrong" can shift more likely short patterns into a longer one, that's the unlikely situations where amateurs look for.
Of course it happens that many patterns "naturally" evolving in long patterns are getting an opposite and math unlikely help toward short patterns, yet itlr short univocal patterns will overwhelm the longest ones.

Casinos prosper about our intrinsic inability to know what should happen about columns patterns and not about row patterns as most players rely upon rows lenght and not about columns quality.

No matter how's the specific random walk considered, any pattern is more likely to move around a 1 or 2 step.

as.

Single/few hands vs the whole picture

Suppose we want to consider patterns by the number of resolved hands (no ties) forming them.

Let's start with two-hand (A or B) patterns:

AA, BB, AB and BA.

Here the probability to cross a homogeneous pattern (AA and BB) vs a heteregeneous pattern (AB and BA) is 50%.

Three-hands patterns:

AAA, AAB, ABA, ABB, BBB, BBA, BAB, BAA.

Now homogeneous results (AAA and BBB) constitute 2/8 (25%) of the possible outcomes.


Four hands patterns:

AAAA, AAAB, AABA, AABB, ABAB, ABAA, ABBB, ABBA
BBBB, BBBA, BBAB, BBAA, BABA, BABB, BAAA, BAAB.

Now there are only two homogeneous patterns (AAAA and BBBB) vs 14 heterogeneous patterns. It's a 12.5% probability.

And so on.

Sooner or later every pattern will more or less coming out by the expected probability, yet per each shoe dealt such probability will be somewhat "biased", meaning that homogeneous and heterogeneous patterns will be more probably distributed by a kind of clustering effect.

Whenever such clustering effect acts at heterogeneous patterns, we'll get an easy job as an opposite side must come out at different levels: we might let some hands go before betting (for example privileging the exact value patterns already happened) or trying to "force" the model by betting two or three times in a row to get the searched outcome.

On the other end, homogeneous patterns being the less probable situation to face tend to consume "space", meaning that they somewhat decrease the probability to get the heterogeneous counterpart.

Cutting to the chase this complicated issue and knowing that cards are asymmetrically distributed along any shoe dealt, say that homogeneous patterns are surely (but slightly) more probable to be followed by a heterogeneous pattern, yet the process consume "space".
At the end and since we are forced to "approximate" at best the more probable patterns, say that a  homogeneous pattern showing up somewhat reduces the probability to cross multiple heterogeneous situations.

This thing could be better ascertained whenever we'll consider the common derived roads. Only very long (and unlikely) BP streaks will deny the heterogeneous patterns formation.

Another way of considering shoes is by assigning a progressive number to every consecutive same pattern (singles or streaks): itlr final total values will be restricted into well defined ranges and, more importantly, we'll see how's the probability an intermediate value will fit the average value or not.

Baccarat shoes are not a balanced mix of something, something is biased at the start.

as.

Hi AsymBacGuy. Thx for another great essay.

re:"...2) The vast majority of players think that a kind of progressive plan will make the job, in reality such "ploy" will increase the casinos' profits as those players are relying upon the mere LW patterns (in any permutation) coming out along the way.
Actually if they would know when things start to change, they should just wait for such spots without consuming money at previous worthless losing situations...."

    My opinion differs on the progression part(Posprogression is the path mi amigo). HOWEVER, the pos progression must be applied against "An increasing improbability", then set aside, then reinserted again later on. In other words, not inserted with the expectation for a single event to continuously repeat in perpetuum. Many players have unrealistic expectations for "same-event streaks". that's my opinion.

"...3) More hands are wagered and less precise will be the winning targets as most of the times anything can happen anytime.  ..."

    I concur 100%.



Continued Success To All.

"...3) More hands are wagered and less precise will be the winning targets as most of the times anything can happen anytime.  ..."

However, if you do not wager, you cannot win.  Of course you cannot lose as well.  A vicious Catch-22 big time.

I have seen people continuously wager for the same triggers and continuously lose and then those same people continuously win.  Likewise I have seen people not wager and talk about each hand while waiting out-would have won continuously.  Then when they attempt to jump in and wager, they can't win anything. 

IMO, of course.