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.

The absolute certainty to play baccarat with an edge is by knowing precisely on which side a key card will fall. We know that and we know that this thing isn't possible.

Next it comes the more intricate field of "statistical approximations", that is how things could more likely develop according to both general specific guidelines and actual observations.
It's true that without any math edge we are generally going to nowhere, but it is altogether true that when a given method itlr is getting lower sd values than expected we are at least taking a less worse approach.
More deeply we want to go in the process, higher will be the probability to win up to the point where the negative HE will be inverted to our favor.
Meaning that no "unfortunate" back to back sequences could destroy our plan if we have carefully assessed what I name the "asym factor" (ASF) working for each shoe dealt.
Higher is the ASF value, higher is our probability of success.

Bac outcomes are the direct product of:

- asym hands apparition favoring B side mathematically, getting a finite frequency over a single shoe;

- key cards finite distribution falling here and there;

- very slight propensity to get the opposite result just happened;

- actual result of asym hands;

- actual result of sym hands;

- third card impact on outcomes.

Say each one of those factors are more or less unbalanced in the shoe we're playing at.
Of course most strenght should be assigned to the asym hand apparition as any B4 or B5 (and at a lesser degree any B3) facing a P drawing situation is hugely favorite to win.

Next comes the key cards falling, nobody wants to face a first card 8 or 9 when wagering Banker and vice versa.

Then the old very slight propensity to get streaks ending up.
It's a sure fkng statistical finding that at baccarat streaks are shorter than at any other same probability independent propositions results (try to compare REAL bac shoes with 50.68/49.32 mere probability decisions)

The actual result of asym hands is an issue understimated by many.
Once a math situation went wrong for the favorite side, betting Banker next means to hope that another asym hand will come out.
I'm not suggesting that when an asym hand produced a Player result, the best bet is wagering Player. Just that the possible asym math force was quite consumed.

The actual result of sym hands is probably one of the most important factors to be examined.
Itlr and no matter what is the actual result, we are way less disadvantaged whether each same class of selective bets are made upon hands getting sym decisions when betting P than B. Obviously.

Finally there's third card nature, more or less unbalanced to produce favourable or not situations to Player side.
Surely 4s are the best cards to be dealt to a drawing P side, then 5s and so on.
Notice that there's a subtle line between a third card 8 or 9 being more detrimental than not to P side, but at the same time hugely beneficial when Banker shows a natural point negating P to draw and getting those key cards as first card.

To simplify a lot, best random walk to follow is that one that had shown a huge degree of asymmetricity whatever intended, either from a mere quantity point of view and, more importantly, from a quality point of view.

Our goal should be oriented to get ALL winning situations at the shoe we're playing at and naturally we can't win every hand when wagering each hand dealt or most hands dealt.

Therefore we must find the best random walks getting such feature in the shoe we're playing at and, of course, to get all winnings we must start with a win.

as.

Actually in the vast majority of the times, strong Player shoes feature many asym hands that went "wrong" for B side.
It's like betting a less likely situation knowing that events favoring the opposite B side are not coming out as the shifting power was somewhat over.

as.

Neglecting ties for simplicity, any possible hand will get those true percentages for the player:

Betting B at any asym hand: +0.95 x 57.93% - 1 x 42.07 = + 12.96%

Betting P at any asym hand 1 x 42.07 - 1 x 57.93% = - 15.86%


Betting B at any sym hand: +0.95 x 50% - 1 x 50% = - 2.5%

Betting P at any sym hand +1 x 50% - 1 x 50% = 0%

Therefore itlr we can only hope to be ahead by catching a higher percentage of asym hands than expected when betting Banker and a higher than expected amount of sym hands when betting Player. The remaining events are just belonging to strong or very strong negative propositions.

Obviously there's no one method in the world that could hope to be long term winner whenever the cumulative sums of those four situations will produce the expected negative amount.

It's just a work about detecting when an asym hand will show up more likely within a restricted range of hands, at the same time trying to get rid of those sym hands going to B side as itlr the number of sym B hands will be equal to the number of P sym hands but very differently payed.

For example, say we bet Banker and a simple BBBB pattern shows up with no asym hands coming out.
Itlr we are losing more money than if we were wagering Player side thus losing all four bets.
An apparent "good" situation just becomes a strong losing event.

Conversely a Banker steady wagering on the same BBBB pattern including just one asym hand will get us a long term profit.

Back to your question.

The asym Banker advantage is an average long term value made by all possible standing/drawing situations after a third card is dealt to the Player and Banker can decide what to do in relation of its point (3,4,5 and 6 initial points).
We know that most edge comes from standing 5s, then standing 4s, then standing 3s.
6s drawing after a 6 or 7 is dealt to the Player just lower the disadvantage, it's not a true advantage.
I mean that the asym power on asym hands could be more or less concentrated, always depending upon how is the card distribution on the actual shoe.
Thinking this way we may assign a specific role to any asym hand occurred, not only in the form of initial point but in terms of actual result.

Now let's compare the general probability with the actual probability: 8.6% asym occurence getting a 15.86% B advantage with what really happen at the shoe we're playing at.

Former value is more stable than second one as it's more likely to get P drawing situations as opposed to 3,4,5,6 B points. Actually almost no one single shoe will form no asym hands.
Yet the average 15.86% B edge on those asym hands is more whimsically placed, being the reflex of which B point is dealt when P draws. Not mentioning that the main destiny of asym hands is focused about just one card, that is the third card.

as.

If baccarat is a constant asymmetrical game, first we should focus our attention about real symmetrical probabilities.
More specifically about the lenght of those sym probabilities.

A perfect world dictates that whether a baccarat shoe won't produce asym B favored hands, a constant Player wagering will get at least a zero negative edge against the house.
Oppositely, ONLY a higher than 8.6:91.4 asym/sym hands ratio will lower, erase or invert the house edge on B wagers.

On average, an asym hand will come out about one time over 11.62 hands. To simplify say we'll get one asym hand out of 12 hands and some of them are producing a tie hand.
We also know that a 8.6% probability, differently to other gambling games, cannot be silent per every shoe dealt (that is within a 75-80 hands sample).
Therefore we might imply that no matter how whimsically is the actual card distribution, sooner or later probabilities will change from 0.5/0.5 to 0.5793/0.4203.

In a sense, now we are not interested about how things seem to develop but about will be the probability to cross either 0.5/0.5 or 0.5793/0.4203 events.
That is how much and how many times those two different probabilities change in our actual shoe.

But there's a third important factor to be examined.
That is how asym hands went as more than four out of ten times a shifted math probability favoring B side will be "disregarded".

Now we could consider any shoe as a finite world made by many subsequences of sym/asym hands; on their part asym hands will form further sequences of W/L patterns.

as. 

Hi Rickk!

The principal aim of this plan is to win just one hand getting a general P 0.75 winning probability. If we are betting toward singles and doubles, we must hope that the third unwanted "3" won't come out after the other two different states (singles and doubles) had come out at least once each.
For example a P 1-1-1-1-1-1-3-1-1-1-1 sequence, despite being so attractive doesn't elicit any betting.
If in the same sequence the 3 would be replaced by a 2 (1-1-1-1-1-1-2-1-1-1-1) we'll get four wins when betting "infinitely" and just one win after the 1 that follows the 2.

The 1-2 unit progression was just an example; actually we generally use a softer 1-1.3 or 1-1.5 progression, meaning that the main effort is focused about singles as doubles are considered just a back-up plan.

Of course the 0.75 P winning probability is extracted from a perfect 50/50 proposition but we know that bac B/P probabilities jump from 0.5/0.5 (sym hands) to 0.5793/0.4207 (asym hands), therefore in no way we could think to really wager each hand by a real 0.5068/0.4932 probability ratio.
Especially when we are restricting at most our range of intervention by quantity and quality factors.

as.

"Points" of interest

What is the long term distribution of Banker and Player final points?

Contrary to what many could think, only two categories of points will get the same probability to appear on both sides.
And of course those two are natural 8s and natural 9s. Every other point category will feature a different probability whether we are considering Banker or Player.
Another form to think about asymmetricity.

Hence the only situations where final points get a real symmetrical probability occur with naturals. Not even 6s and 7s will get a symmetrical probability (for obvious reasons).

That's why the Dragon bonus side bet involves a quite different house edge depending upon the side we choose to bet (by far the house edge is a lot lower on P side bets).

The slightest difference between same point B and P probabilities comes with "3" and "7" points. Then about non natural 8s and 9s, 0, 1 and 2 points.
Then "6" points.
Greatest gap in probability exists with 4s and 5s. (Obviously)

On average a deck will form around 19% of naturals on either side, thus around 4/5 of the total hands dealt are following a more or less pronounced asymmetricity.
Naturally we are not talking about more likely B or P outcomes, just about long term final points probability.

Of course the higher the point the better is the probability to win, yet itlr those point gaps are constantly moving around fixed probabilities, each point fighting with a general and an actual shoe probability.

Taken from another point of view, we should see that if 4s and 5s are the more gapped final points (5.4%) then a kind of Banker advantage is more concentrated right on those exact B final points. And we know this being absolutely correct as most asym B edge comes from standing 4s and 5s.

Well, standing. And not all 4s and 5s stand after Player draws.
Not mentioning that some 4s must stand when a third card ace id dealt to the Player, a slight negative edge situation.
And 4s and 5s cannot come infinitely.

The third more pronounced gap situation between same points is about point 6, now favoring Player side and accounting to around 1.1%.
That is that we'll get more P 6 final points than B 6 final points and of course a 6 point is long term favorite to win.

Cumulatively and regarding final points distribution, B 4s, B 5s and P 6s get a nearly 6.6% general asymmetrical probability to appear that we should compare to the actual shoe situations.


as.