Say we want to build new "roads" originating by the simple B/P results succession.
For example, we classify outcomes as S (same) or O (opposite) according to a preordered pace, e.g. 4. We register our new result in relationship of what happened four hands back.
Since this new road is single paced, every outcome will be recorded but the first four results.

BBBPBPPBBPBPBPPP.. becomes

S
OOO
SS
OO
SS
O
S...

This new sequence isn't directly affected by the asymmetrical BP probability as our S/O signs distribution do not correspond to a B or P result.

Simply put, it's very hard to precisely deduce from S/O distributions what really happened on those shoes in terms of BP outcomes.
Of course the probability to be right or wrong is 50/50 and only long samples might help us to assign the proper BP results to our S/O registrations.

Now we are working into one of the simplest world of place selection.

Of course some BP patterns are going to produce (or not) homogeneous S/O situations:

BPBPBPBPBP = SSSSSS

BBPPBBPPBB = SSSSSS

BBBBPPPPBB = OOOOOO

BPBPPBPBBP = OOOOOO

Taken from the simplest definition of symmetricity, those are balanced outcomes as the number of Bs is equal to the number of Ps (except of the third pattern shortened for simplicity)

Actually it could happen that even strong unbalanced sequences as BBPBBBPBBB... (or the opposite counterpart) or long B or P streaks (longer than 9) will produce a SSSSSS pattern.

Now the question is whether this new S/O sequence alone could help us to define the features of the shoe we are playing/observing.

as.

At baccarat we can't consider any single outcome as a valid outcome in our registration unless if following normal math percentages.

For example, say the pattern is BBPP

Here we must consider first whether BB is coming from mere sym propositions, meaning that B in both cases wasn't advantaged by the rules.

Secondly we must assess whether PP didn't cross an unfavourable asym hand getting the best of it by starting underdog.

Most of the time BBPP pattern is the product of sym propositions as the asym strenght will act by the old 8.6/91.4 ratio.
Not everytime.

On the same line and more practically speaking, after a single P we should know that betting Banker means to hope that Banker will cross an asym hand more likely than not. Otherwise we're losing money.

The same after a single B apparition.

That means that there's no value to detect sym situations unless our strategy will dictate to bet Player or, reversely taken, that while wagering Banker we hadn't estimate that an asym hand is coming around shortly.

Again about key cards.

Definitely 8s and 9s will favor the side where those cards fall on. The probability those cards will fall into the first four positions is perfectly equal.
But whenever the third card is an 8 or a 9, Player side is unfavorite to get a valid point to win.
It's like 8s and 9s are symmetrically placed unless the 5th position is involved. The impact itlr is much greater about fifth positions than sixth positions as some part of 6th cards are not allowed to show up for the rules.

It could happen that Player gets some winning hands by the help of such key cards falling at 5th position (aka Player gets 0 and/or 1 initial point). But if we run infinite times this situation we'll lose.
The reversed situation is less likely to happen as some B initial points won't elicit a draw.

Therefore many seemingly equal patterns aren't equal by any means.

There's no doubt that long term results are the direct reflex of math percentages and those math percentages are the direct reflex of initial points and third card points actual situations.

Say most 7s and 8s have fallen on initial two card B side and we can't care less about actual outcomes.
Do you really expect that on the following hands the remaining 7s and 8s are more likely to fall on P side?

Same about third cards.
Third cards, while whimsically placed as they could intervene in the hand or not, are following a more or less attitude to help or not P side; in some way they constitute a supplemental random walk no matter which will be the real result.

Actually best playable shoes are those which seem to conform at most to normal math propositions and according to bac features already known here; those which aren't must be abandoned at the first opportunity.

as.

LOL

Look at the covidiot posting "Yeah, masks deprive your oxigen intake, which goes against federal regulation. Look it up"

Actually the oxigen flowing in the brain of such a covidiot is chronically low even without wearing a mask.

as.

Nevada should have taken the Hawaii "stay fkng away from our isles" line and actually it did at the very start of this pandemic (03/15).

Then I can't understand why the hell they didn't force people to wear masks inside casinos...

I agree on many 8R9 points yet I'm feeling confident about US and especially the great State of Nevada.

as. 

It's intuitive to think that itlr chopping lines showing at most likely degrees (singles and doubles) are the direct reflex of a low imbalance of key cards.
Therefore long streaks must come out whenever a strong imbalance of key cards come out.

Nonetheless key cards are finitely placed as they are burnt from the play. Say they must be more or less concentrated along the deck.

It's true that strong points could be made by "normal" cards as a combination of 3 and 6 or 4 and 4 could do, for example. And of course many results will be dictated by "weird" situations as a 4 getting a 4 vs a standing 6 etc.
But those spots are just belonging to the short term deviations category.

Say we want that our strategy is set up in order to only bet Player side, thus trying to get a kind of advantage.
There are three steps to look for.

1- we want a higher initial point

2- we want a standing point

3- we do not want to cross an asym hand.

Anytime we get a higher initial point and regardless of the quality of the hand, we're hugely favorite to win.
Naturally key cards distribution play a great role on that. In a sense we want the shoe to get a low imbalance of key cards on the portions of shoe we chose to wager.

A standing point (6s, 7s and naturals) come out at P side with a 38% probability and of course any P standing point is favorite to win.
Such 38% probability could be more or less concentrated along the various portions of the shoe.

Finally, any P drawing situation (a close to 50/50 probability) is susceptible of crossing a 3,4,5 or 6 B point, therefore being strong unfavorite (at various degrees) to win unless the initial point is higher.

Mathematically speaking it's like playing a coin flip game, a kind of 38/62 ratio and a reversed 62/38 ratio considered at different steps.

Remember that at any 8-deck shoe symmetrical initial points will come out at those percentages:

0 = 14.74%
1 = 9.49%
2 = 9.45%
3 = 9.49%
4 = 9.45%
5 = 9.49%
6 = 9.45%
7 = 9.49%
8 = 9.45%
9 = 9.49%

as.

Say we want to transform the game into mere symmetrical successions where asymmetrical hands do not form B results, thus considering them as a bonus when betting Banker and a kind of losing zero at roulette when betting Player.

Naturally the asym hand apparition remains a bonus (+15.86%) on B bets and a same negative happening on P wagers.
Thus it's not a sure win or loss on either sides.
Surely our long term results will be affected by the number of times we crossed an asym hand when betting B, and at the same time by the number of times we met an asym situation when betting P.

Itlr and in absence of a valuable bet selection the AS/S ratio will approach more and more to the expected 8.6/91.4 ratio. Therefore we are losing.
And the EV gap between a long term betting made on B instead of P is 0.18%.

Therefore there are only two options to win or to lower/cancel the HE:

a- getting an higher asym/sym hands ratio than expected capable to invert the HE when wagering Banker;

b- wagering Player only on symmetrical situations.

Then what might help us to define the terms of the problem?

Average asym hand distribution, for example.

Players are too focused about the actual outcome, maybe in the effort to follow an unguessable succession.
When betting Banker we must hope that no matter how are consecutively placed our bets an asym hand must come out within a shorter gap than expected.
Otherwise we're losing money, a lot of money I mean, even if the actual pattern is a symmetrical  BBBBBBBBPBBBB succession (for that matter even a single asym hand happening on this sequence is a long term money loser when regularly betting banker)

Gaps between more frequent symmetrical hands and rare asymmetrical spots.

Asym-asym hand apparition hugely favors the B side and actually some shoes will present many asym hands distributed in couples (or more).
In reality. more often than not asym hands come out in single apparitions (for obvious reasons) or clustered at some portion of the shoe.
We ought to remember that natural/standing points on Player side totally deny the asym hand happening and some Player drawing points crossing an asym hand are actually favorite to win (think about a P5-B4 drawing situation).

On the other end, it's sure as hell that at least a couple of asym hands will come out per every shoe played. Meaning that sooner or later a constant Player betting virtually getting an EV not lower than zero, will cross those unfavourable spots where our P bet is worthless.

Symmetrical spots

Sym spots hugely favor Player side for several reasons:

- first, we're playing no worse than a fair game as bets will be payed 1:1;

- secondly, as long as no asym hand will be formed, key cards will land equally on both sides;

- third, the 7/6 symmetrical standing point situation is unequally payed regarding which side we bet.

The idea is that baccarat should be considered not just in terms of patterns but in term of ranges (gaps) helping one side at various degrees or at worst not damaging the other one.
Sometimes (just for practical purposes) the most likely pattern distribution tend to correspond to those ranges. 

Knowing that most outcomes are in direct relationship of sym hands results, we should focus our attention about the actual probability and distribution to get higher initial four-card points as this is the main tool that shift the results.

A thing that we'll discuss tomorrow.

as. 

At baccarat we should play probabilities and there are general probabilities and actual probabilities.

No doubt at bac key cards are 9s, 8s and 7s.
Itlr and per every shoe dealt the side getting most of those key cards at positions #1-#3 and/or #2-#4 will get a sure advantage.
Actually 9s, 8s and 7s falling at P side will get a higher EV impact than the same cards falling at B side.

Those cards are not the cards you want to see when instructing the dealer to show "just one card" on the opposite side.

There are many other ways to form 9, 8 or 7 initial points but itlr the 9-zero value card, 8-zero value card and 7-zero value card are overwhelming the rest.

It could happen that the side getting most part of 7s, 8s and 9s will lose to the counterpart. Besides the less likely situations where those cards forming an exact 7, 8 or 9 point will lose to higher points, those cards could combine themselves with very low cards producing "worthless" points. Think about 7-3, 8-2, 9-A, 9-2, etc..
Such probability is symmetrical.

Of course per each shoe dealt those cards cannot be equally distributed on both sides. The fact that those key cards could combine with low cards getting very low points shouldn't affect the main concept that the higher the card falling on a given side, the better the probability to win.
Altogether naturally is to generally think that key cards cannot fall endlessly on one side.

It's like considering those key cards as a kind of "wild cards": they may hugely, moderately, slightly or not at all help "our" hand.

In some way, outcomes are the direct reflex of those endless (but finite as considered per every shoe dealt) propositions.
Most of the times such key cards will enhance the production of short symmetrical outcomes, it's only when the actual key card distribution tend to strongly privilege one side that B or P will take a substantial advantage over the other one.
And of course there's the rare asymmetrical impact working (or not) for B favored hands.

I mean that itlr third or fourth card happenings will affect outcomes way lesser than what initial points will do, as the initial point gap situation involves an increased 7% advantage over asymmetrical hands.

as.

Let's summarize which points we really want to get while wagering B or P side.
Remember that four card initial points on both sides are perfect equally likely.

A) When wagering Player side, of course we want to get a standing/natural point.
It doesn't matter if our P 6 point will lose to a higher point (B7 or B natural or any higher 3-card B drawing situation).
Itlr any P standing situation will make this bet EV+.

On the other end, the same standing/natural points not belonging to any asym situation falling on B side will make any B bet EV-.

Thus, regardless of the actual result, those symmetrical and specular situations will be hugely favourable when betting one side and of great detrimental when wagering the other one.

B) We bet Player and Player must draw.
Quite bad news as now we have to escape the probability that Banker gets a 3, 4 or 5 initial point.
In the remaining cases, Player can't be disadvantaged, actually it's slightly advantaged in the P5-B4 situation.
Of course in the 0-1-2 specular B/P drawing points, highest point will be favored to win itlr, but in the same long run such probability will be equally distributed.

C) We bet Banker and Player must draw.

Unless our B point is 5, 4 or 3 we're losing money itlr.
It's quite funny to watch at those players jumping in joy whenever their Banker bets are won by a natural or standing point.
Actually they are losing a lot of money.

D) Both sides must draw (no third card rule can affect the outcomes).

A perfect symmetrical scenario where the winning side is payed 0.95:1 and the other one 1:1.

Long term baccarat results are just the cumulative sum of mathematical propositions.
There are no ways to humanly guess a fkng nothing unless we take care of the above math situations.

Hence when wagering Player or Banker side we ought to estimate the actual probability to get: 

- a standing/natural point on P side when wagering Player;

- the exact situation to cross a Player drawing hand facing a Banker 5, 4 or 3 point when betting Banker.

Since the former scenario is affected by huge volatility and of course not involving a math edge, mostly we should focus our attention about the latter scenario, being profitable by ranges and not by precise situations.

It's a sure fact that people making a living by playing baccarat are those capable to catch the situations when their P bets are crossing more standing/natural points on Player side than expected and/or when their B bets are getting a higher ratio of P drawing/B 3,4 or 5 points than  expected.

The rest  belongs to the Imagination song:  "Just an illusion"

as. 

Hi Rickk!

1) Most Banker asymmetrical strenght comes from standing 4s and 5s (and at a way lesser degree from standing 3s). In those instances when Banker must draw after knowing the third card dealt to Player, the hand becomes symmetrical.
Banker initial 6s are, along with pure sym situations, the points you really do not want to get when betting Banker as the hand becomes asymmetrical only when a third card 6 or 7 is dealt to the Player. And in this instance the B disadvantage is just lowered.
If itlr you'll know for sure that one side will get a 6 initial point (symmetrical probability) but you don't know which side gets this point, would you prefer to wager P or B?

2) Nope.
First four cards I'm referring to are extracted from every new hand situation.
Say we want to build up two simple random walks according to the actual shoe distribution in terms of initial four card points.
Itlr the side kissed by a higher 4-card initial point will be favored to win.
Of course there's no debate that a 6 or 7 (or natural) P initial point will get the best of it itlr. As the same equally probable counterpart is not going to get the same edge for obvious reasons.

The problem arises when Player is forced to draw (0-5 points) and Banker shows a 3,4 or 5 initial point that makes the above assumption worthless.
But we know the general probability that such thing will happen.

There are times when Player crosses situations where the higher initial point will belong to asymmetrical propositions and others when the asym B force is denied at the start.

Moreover a kind of third random walk could be put in action anytime higher initial points will win or lose depending upon the actual nature of third (or fourth) card.
This being the natural reflex (at various degrees) of the actual card distribution that must deny a perfect balanced distribution.

3) By any means any standing/natural situation (being equally probable) will favor Player side wagering.
For that matter, try to observe how happy are casinos' acute floormen working at HS tables when clueless players are jumping in joy after winning a Banker bet by a natural. Those players do not know that they are losing a huge amount of money itlr. 

4) Overall any 2 card Player point vs 3-card Banker point is hugely favorite to win itlr.

as.

At this point it should be clear that our long term results are in direct relationship between the different EVs working on those two very diverse situations.

Many craps players like to place odds at pass lines or don't pass lines after the point is established. Normally the HE is never zero, say very close to zero but never zero.
At baccarat we've seen that as long as no asym hands will be formed, wagering Player side is a way better option than betting Banker as the payment is 1:1 and not 0.95:1.
That means that on symmetrical hands virtually no card distributions could alter significantly the Banker negative EV.

Reasoning in this way we could build a result plan just on the very first four cards dealt.
As long as Player draws and Banker do not show a 5, 4 or a 3, we are really in good shape when betting Player.
Conversely, this is the exact situation we want to look for when wagering Banker.

Going to less likely situations, we see that any standing/natural situation can only advantage Player side itlr, even if in that shoe any Player 7 point will lose everytime to a Banker natural.

No asym hand = no Banker party!

What's the real probability to get the Player drawing/ Banker 5,4 or 3 initial point situation?

It's 7.72%

Meaning that 87.05% of the times our Banker bets are long term losers.
And of course that 12.95% of the times are huge long term winners.

It could happen that some shoes are so badly shuffled that the asym formation would be more or less likely in many portions of the shoe, we can take into account the consecutiveness of the asym apparition, the quality of asym situations etc.

Say you want to split the shoe into 6-hands betting portions (bet for real or fictionally). At a 8-deck shoe you'll get around 12 situations (ties ignored).
It's impossible that every situation will be symmetrically placed, thus some portions must involve a B advantage (asym apparition).
Nevertheless most portions are symmetrically placed getting a very different EV depending upon which side we like to bet.
It could happen that one or more asym hands will show up within every single portion of this shoe (thus making profitable a B wagering), but I guess it's more likely we'll hit a slot jackpot.

More likely and knowing that the asym hand apparition probability is around 8%, some portions will be asym hands free.
The average probability is that a slight lesser amount of such portions will be symmetrically placed. Actually a balanced occurence of asym hands cannot get a steady pace for obvious reasons, so we could infer that more than one asym hands might show up in one or more portions. Therefore lowering (or increasing) the probability on subsequent portions.

Not giving a damn about the actual results, we know that the shoe is producing an average amount of pure sym or asym/sym portions.
Portions formed by all sym hands cannot elicit other than a Player betting. On the contrary, portions containing one or possibly more asym hands will elicit a Banker wagering.

Combined with the very slight propensity to get the opposite result, asym hand quality and actual outcome, general asymmetricity of card distributions and some other features regarding specific random walks, it's not that difficult to spot the situations where our EV will be neutral or hugely shifted toward one side or another.

as.

Hi Rickk!

We can't hope to be long term winners without getting a positive EV, no matter how is taken.

Globally we know that our EV is negative, being slight negative (0.18 is the difference) by constantly wagering Banker side.

Math speaking, there are only two situations to bet favourably itlr:

- catching more asym hands than expected while wagering B side;

- NOT catching asym hands while wagering P side.

Example.
An infinite run of six hands are dealt (consecutively or not, it doesn't matter) and we want to see what's our EV depending upon which side we would like to bet.
If all those six hands are symmetrical, we know that itlr we'll win half of them regardless of the side we choose to bet.
Thus the EV is:

Banker bets: (0.95 x 0.5) x 3 - (1 x 0.5) x 3 = 1.425 - 1.5 = -0.075

Player bets: (1 x 0.5) x 3 - (1 x 0.5) x 3 = 0

That means that betting a $100 unit we'll get on average a $296.25 return on our money when betting Banker and a $300 return while wagering Player side.
Same proportions could be extracted regarding eight hands or ten hands or about hands of any lenght.

When a single asym hand comes out, things abruptly shift toward Banker side, altering hugely the normal EV flow just for that very hand.

Now the asym hand EV on Banker bets is 0.95 x 0.5793 - 1 x 0.4207 = 0.1296

Do the math and you'll see that itlr an invincible betting plan could be oriented to spot the situations when an asym hand apparition is more likely within a more restricted than expected range or, at a way lesser degree, that a given shoe sequence is more likely to produce more natural sym events. In the former case we will of course privilege B side, in the latter the P choice.

Naturally the 0.5 (sym) and 0.5793 (B/P asym) probability values are just general values, yet the payment remains the same (B=0.95:1 and P=1:1), that is hugely shifted toward one side.

And we know that not all asym hands will get the 0.5793 probability, it's just a cumulative math situation.
Most asym hands power comes from Banker 5 points facing a P drawing hand, then Banker 4 points facing a P drawing hand and at a way lesser degree B 3 points facing a P drawing hand.
6 B points dealing a 6 or a 7 third card to P side are just lowering the negative egde.

Of course all standing-natural/standing-natural situations (belonging to the sym spots category) itlr will advantage Player side as first they are payed 1:1 instead of 0.95:1, then any Banker 6 point facing any standing Player situation must stand prompting a sure negative math proposition.

Tomorrow we'll see how to consider outcomes in terms of asym/sym actual distribution.

as.

Think about math percentages first.

If we would bet Banker side five hands long then getting at least one asym hand, we're getting a long term advantage.
If by taking advantage of other bac features we want to wager Player side, we want all sym hands to be formed, meaning we're not losijg a dime itlr.

Asym hands that went "wrong" for B side just endorse the probability to get sym hands on the very next outcome as the probability to get back to back asym hands is distant. We surely do not want to wager a side being payed 0.95:1 than 1:1.

By the same way of thinking, a B natural is going to produce a way lesser impact than the same P natural.

Next time we'll consider naturals.

as.

Mathematically our long term EV is in direct relationship between asym and sym betting ranges.

For example, say a portion of the shoe presents eight straight sym hands and the actual outcomes of those sym hands are producing an eight Banker streak.
If we were betting Banker each hand belonging to this streak we may think to be lucky or geniuses. Actually we are severely losing money.
On the other hand, the same sym 8-hand pattern could form a Player streak of the same lenght and now a steady Player betting cannot get us other than a zero negative edge at least.

Since the probability to get one of the possible 256 different BP patterns on those sym situations remains the same, it's quite obvious that there's no point to bet Banker at any of those eight sym hands.

Thus the Banker side should be wagered just about the probability to form or not an asym hand among a very restricted range of hands.
This one is the only wise math approach working itlr as the math advantage must overcome the negative HE.

We should remember again that most asym hands edge comes from 5s and 4s Banker initial points and, at a lesser degree. from 3s.

Think that many Banker 5s and 4s initial points will cross standing/natural Player situations, therefore transforming potential shifted events (that is asym hands) into mere symmetrical circumstances.

In some way we could infer that the probability to form a 4 or 5 Banker initial point is somewhat dependent about the previous situations and we should always be focused about the mere asym/sym probability.
Let's say that as long as no 4 or 5 (and, at a lesser degree a 3 point) Banker initial point will be formed, we are betting a close to zero negative edge game when wagering P side.

In any case, we want to add a further parameter, that is how asym hands went in our shoe.

Say we know for sure that the actual shoe is presenting such sequence (S= symmetrical hands and N= non symmetrical hands):

S-S-S-S-N-S-N-S-S-S-S-N-N-S-S-S-S-S-S-N-S-S-S-S-S-S-S-N-S-S-S-S-S-S-S-S-S-S-S-S-S-N-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-S-N-S-S-S-S-S-S-S-S-S-S-S-S

The are no other perfect plays than wagering Banker at hands #5, #7, #12, #13, #20, #28, #42, #64.
For now we cannot care less about the real BP outcomes, after all the winning probability of such sequence is a long math proposition of 0.5 (S) and 0.5793 (N) events.
Quite likely not every N spot will form a Banker hand, not mentioning that at S spots everything will be possible.

Now let's compare the same deck N or S situations with the new distribution.
Of course the probability to get the exact N or S distribution will be zero and, by an obvious higher degree, the same results.

Nonetheless, the clustering N or S effect will seem to remain the same as cards tend not to be properly shuffled.

It's like playing a game where we might be very very slight favored or hugely favored at various degrees, totally getting rid of the potential situation to find ourselves facing the exact counterparts.

as. 

My bad.
Thanks Al and sorry Rickk and everyone.
After posting the shoe everything appeared correct on my screen.

Let's try again with a simpler form:

B
P
BB
PP
BB
PP
B
P
B
P
B
P
BB
PPPPPPPPP
B
P
B
P
B
PP
BB
PP
BBB
PPP
BB
P
B
P
B
PP
B
P
B
PPPPP
B
P
BB
P
BBBBBB
PPP


as.

Look at this shoe (ties ignored).

BPBPBPBPBPBPBPBPBPBPBPBPBPBPBPBPBPBPBPBP
     BPBP           BP            PBPBPB  B     P   P      B  BP
                            P                BP                 P           B    P
                            P                                      P           B
                            P                                      P           B
                            P                                                    B   
                            P
                            P
                            P 

In this shoe there were 12 asym hands (well above average) whom one produced a tie.
Quite curiously Banker got more naturals than Player.

This shoe produced ALL winning hands in the five hands played (for that matter we didn't bet a single hand on the Player nine-hand streak and on the Banker six-hand streak).

as.