Our datasets show that best edge comes from a random walks registration/actual BP results ratio  set up at 0.56.
That is on average our random walks must register a slight superior amount than half of the actual BP decisions coming out.
A quite interesting percentage I don't want to discuss here, anyway now we know that the supposedly random world and/or the very slight dependent world we are compelled to face is proven to be more restricted than we think, just by getting rid of nearly half of the unnecessary BP outcomes.

Our new derived collective extracted from nearly 56% of the total BP resolved hands should follow the common probability laws but it happens it's not the case.
Some spots are more likely than others, more importantly dispersion values are well more restricted than expected, meaning that the silliest progression ever invented will get the best of it by any means.

If our aim is to get just one large (maximum limit) unit profit per every new collective formed, our edge will be so huge that we will bored to play baccarat anymore by a lack of suspence.
   
In our experiments, we've tried to raise (or reduce) the already substantial edge by discarding a larger (smaller) amount of hands but with no avail.
It's like that the 0.56% cutting hand percentage is the best number to look for.

Next I'll post real betting situations.

Sadly I fear it's more likely to beat baccarat than to destroy this fkng virus.

as. 

Winning just one unit per each shoe played

One unit win and not per every shoe dealt...it might sound as a ridiculous goal no bac player would be interested to get.
However the more we are deviating from this basic achievement, higher and faster will be the probability to lose our money.

We can't hope to win an inferior amount than one unit, that is being ahead of just one hand (before vig).
But we've seen that simple progressions may find profits on precise LW points, so transferring the problem about the probability that, besides immediate wins, after a single losing spot the next hand should more likely get a win instead of another loss.
 
The fact that we're restricting the range of one unit wins within single shoes played relies about the supposedly (ascertained) probability that the statistical irregular strenght coming up on our favor collides with the sure mathematical steady force acting all the times.
Meaning that for practical reasons, on average the statistical strenght takes its greatest value on very few spots.

Of course betting a lot of spots with a huge betting spread entices the idea we're there to gamble, in the meanwhile collecting valuable comps.
But I assure you that most bac pros I know do not give a fk about comps, thus exclusively betting the spots they'd thought to be profitable.

We know that to be really profitable itlr Banker bets must get at least a 51.3% probability to get us an edge, Player's bets need a probability equal or higher than 50.1%.
Combine those probabilities in any B/P betting range you wish, at the end you must get a proper percentage capable to invert the HE. Otherwise you're just fooling yourselves and making casinos' fortune.

Interestingly, long term random walks data show that in given spots it's way easier to find the spots where Player side will be neutral or favorite to win than to cross the opposite situation, even though general rules make Banker more favorite to win regardless.

It's like assigning certain given variable cutoff values to the probability that Banker will be more likely than Player, naturally taking into account the general 8.6% asym probability distribution and the actual BP distribution prompting different random walks.

I can't see any answer other than the actual key card distribution, knowing that when given  portions of the shoe show a strong or moderate key card balancement, outcomes will be more fkng affected by a huge "undetectable" volatility.
Sometimes the key card balancement will be so hugely represented that no valuable betting spots could arise.

Odds are that whenever key cards are strongly balanced on the initial/intermediate parts of the shoe, subsequent portions of it will be less affected by a kind of key card concentration factor that tend to come in our favor.

From casinos part are there ways to forcefully balance the key card distribution along any shoe dealt?
Who cares, we got means to take notice of that and of course I'm not talking about this here.

Next post will be about the decisive importance to discard many outcomes we're not interested to insert in our registration.

as.

Playing with an edge means that we want to falsify the theory that no matter how and when we decide to bet the dispersion values are following all the time the numbers derived from common probability.

To do that we've set up multiple betting lines within the "coin flip" A/B scheme but well knowing that the results cannot come from an independent source, moreover affected by the rules asymmetricity.
Naturally the general B/P probability varies a lot depending upon the sections of the shoe where key cards are more or less concentrated.
It's literally impossible that every single hand will follow the 50.68/49.32 probability as there are no card distributions eliciting such exact probability.

Taken from a different point of view, we could even object about the perfect random nature of the outcomes as the place selection and probability after events tools will get different values than expected, thus disproving the perfect randomness.

We could assume that along any shoe the real probability will act at various steps depending upon the key cards distribution. And not by privileging one side, just certain patterns formation.

Efforts made in the past by eminent researchers were oriented to find spots where one side would have been more probable than the other one adopting a "black jack style" approach. Fruitless efforts we know.

In reality baccarat must be solved statistically, that is by taking advantage of the many intricate issues only very few players know.
It can be done, believe me.

In the endless process of studying deeply this game I have to thank:

- Richard Von Mises works, an eminent mathematician who publicized, imho, the strongest definition of randomness.

- Marian Smoluchowski works, a physics professor.

- Semyon Dukach inspiring ideas, one of the most famous member of the black jack MIT team that destroyed Vegas and many other casinos.

- Akio Kashiwagi, probably the best baccarat player in the world of all times.

- Glen "Alrelax", the only one person in the world besides my team colleagues I would risk my money with.

As long as outcomes are not coming out from either a perfect independent and/or a perfect random source, we know we'll get an edge.

as.

Since at baccarat we can't use mathematics directly (besides side bets card counting ), we must use statistics to extract hidden informations from large datasets.

Thus we are not interested to estimate what could happen most by considering common BP values, instead we should focus our attention on multiple different random walks that tell us what's really more probable after a given outcome or series of outcomes had come out.
A/B spots I mean.

Simply put, we should consider a baccarat shoe in the same way bj counters approach the decks.
At bac we can't get the luxury to know that high cards and aces favor the players and low cards favor the dealer, but here (along with many other advantages) we have the advantage to estimate the probability to get several states of key card concentration/dilution acting at various degrees by some finite values.
This feature fully reflects the patterns formation, hence we are not compelled to track key cards as patterns formation will make the job we're looking for.

Summarizing, to be deadly sure we'll get the right side of the proposition (EV+ play) itlr we must get at least a 51.3% winning percentage on our Banker bets and at least a 50.1% winning percentage on our Player bets.
Every bac player knows that such values tend to be quickly disregarded. Unless a proper bet selection is working.

as.

Al, your answer could be a reasonable one, anyway long term data suggest that deck portions particularly poor of key cards seem to endorse the volatility of the outcomes as more cards are employed in the construction of a hand higher will be the probability to fall into an "undetectable" world.
A partial proof comes from the fact that ties are well more likely whenever six cards are employed to form a hand.
And of course the probability that a hand will be resolved by six cards will be higher when the deck is poor of key cards.

as. 

What would you think after facing this shoe fragment?

BBBB
PPPPPP
BBB
PPPP
BBB
PPPPP
BBBBBBB

There's only a sensible answer: Here probabilities are that key cards were hugely concentrated alternatively on either side.
This sequence is very very unlikely to happen and, of course, is one of the rare situations recreational players like to cross: betting the last outcome, that's it.

Now let's consider the three derived roads:

Big eye boy:

AAA
B
A
B
AA
B
AA
BB
AA
B
AA
B
A
B
AAAA
B
A

Small road:

AA
B
AAA
B
AAAAAA
BB
AA
B
AAA

Cockroach road:

AAAAAA
B
AA
B
A
B
AAA
B
AA

Things seem to change a lot as the cumulative singles/streaks ratio appearing on d.r's  is very different than the big road original sequence.
Nonetheless, from a strict mathematical point of view, such sequence is among the most likely ones whenever key cards are hugely concentrated on a given shoe portion.

Just to complete the picture about the most simple strategy options anybody is aware of, I'll add the OBL random walk:

AA
BB
AAAA
BB
A
BB
AA
BB
A
BB
AAA
BB
AAAAA

Again, we can see huge differences between this OBL r.w. and the original big road sequence.

In some way we could think that the above big road sequence is well predictable by either recreational players and by pro players. Of course by taking advantage of different features (BP steps considered by different lenghts).

And we may conclude that shoe portions particularly rich of key cards are more detectable than the common supposedly random world we're entitled to face.

Naturally when we have seen that key cards are more concentrated on some portions, odds are that we'll expect to get more dispersed key card falling on subsequent parts of the shoe, meaning we'll get a more volatile (then undetectable) world.
Mathematically speaking, the probability to detect a two-card higher point falling on either side will be lower whenever the deck is poor of key cards.
And we must know that to get a long winning plan we'll have to get a larger amount of two-card higher initial points than expected as this is the only long term tool to realize we're really getting an edge over the house.

I'd suggest to consider a baccarat shoe in the same way bj players think about a playable or unplayable shoe.
At baccarat we do not get unidirectional player's card distributions, just probabilities to get A or B and we know that A or B must considered in terms of gaps.
This AB feature is in direct relationship of the key cards concentration/dilution ratio acting at different degrees along any shoe.
Differently than bj, we are absolutely certain that some betting lines will get all winnings per every shoe dealt at a degree well higher than what expected values dictate.

Btw, there's no fkng way in the universe to beat any EV- game by strategies capable to be effective other than by adopting a strict flat betting method.
People claiming otherwise are just pure fkng clowns.

as.

Best bac players in the world play a A/B game.
More specifically they play baccarat by taking advantage of runs and gaps.
They do not follow anything, they don't like Banker as being more favorite to win.
They bet very few hands.
And, of course, they bet rarely but wagering huge amounts.

Probability world is made upon runs and gaps, I mean the number of BP shifts. Ouch, AB shifts.
Everything depends about how we want to consider opposite results.

Consider this 18-hand shoe portion:

B
PPPP
BB
PPP
B
PPPPP
BB

7 runs, 2 singles, 1 double, 3 3+s  singles/streaks ratio 2:5

Big eye boy road:

A
BB
A
B
A
B
AAA
BBB
A
B

10 runs, 7 singles, 1 double, 2 3+s  singles/streaks ratio 6:3

Small road:

AA
BB
AA
BB
A
B
AA

7 runs, 2 singles, 4 doubles, zero 3+s. singles/streaks ratio 2:5
Cockroach road:

A
B
AA
B
A
BB
A
B

8 runs, 5 singles, 2 doubles, zero 3+s. singles/streaks ratio 5.2


In summary the overall singles/streaks ratio is 15:15

The overall doubles/3+s ratio is 11:5


Now this second 18-hand shoe portion:

B
P
BB
P
B
P
B
P
BBB
P
BBBBB

11 runs, 8 singles, 1 double and 2 3+s.  singles/streaks ratio 8:3

Big eye boy road:

A
BBB
AAAA
B
A
BBB
AAA

7 runs,  3 singles, zero doubles, 4 3+s.  singles/streaks ratio 3:4

Small Road

BB
A
B
AAA
B
A
B
AAA
B
A

10 runs, 6 singles, 1 double, 2 3+s. singles/streaks ratio 6:3

Cockroach road

AA
B
AA
B
A
B
A
B
AAA

9 runs, 6 singles, 2 doubles and 1 3+s. singles/streaks ratio 6:3

Overall the singles/streaks ratio is 23:13.

The doubles/3+s ratio is 16:12

Both shoes portions came from a moderate/strong key card concentration, even though they formed quite different BP results.

Of course I've posted the most common derived roads any bac player is familiar of and the fact that some AB patterns are cumulatively superior than counterparts was just a coincidence.
Moreover any B or P result could form opposite patterns on different roads (a single from one part and a streak from another one, etc).

We can put in action more random walks, for example OBL, A=same, B=opposite:

first shoe

A
BB
AAAA
B
A
B
A
BBB
AA

second shoe

B
AA
BBBBB
A
B
A
B
A
BBB

As long as long streaks are not coming in short intervals and as long as "symmetrical patterns" are not coming out consecutively any betting plan has its merit. And odds are that they do not itlr.
Btw, those are the precise situations recreational players are looking for. And I do not know a single recreational player being ahead of the game.

as.

Although baccarat provides innumerable card situations, math advantaged spots falling here and there are surely going to win itlr (now "itlr" is way more widely intended as commonly considered).
By far the largest impact cards will make over the actual results are coming from 7s, 8s and 9s.

There are many card combinations forming final winning hands not involving those cards (or working partially), nevertheless whenever we are going to peak at our cards we better aim to get one of those cards, instead of hoping that our 4 will be followed by another 4 or a 5. 
This card class constitutes 23% of total cards dealt and it's more or less concentrated along the shoe with a "memory" as key cards are burnt from the play.

Differently to black jack where the final count of "good" or "bad" cards must be zero (penetration considered), meaning that only few portions of the shoe might be favourable for the player ('good card' concentration after a strong 'good card' dilution), at baccarat there are no good or bad cards for the player, just probabilities to get key cards concentrated or diluted along various portions of the shoe.
Naturally at baccarat we have the advantage to bet any side we wish anytime we want and the disadvantage to not know which side will be kissed by such a possible key cards impact.

Notice that I haven't mentioned "how much we want" as a long term winning plan must win by flat betting.

Anyway if we are here is because we are trying to prove that a key card concentration/dilution approximation acting along any shoe will play a huge role over our winning probability as many times some actual patterns will be more detectable than others.

It's natural to think that conditions not fitting a perfect random world are more likely to produce winning situations (when properly considered), as "perfect" key cards distributions can easily produce too many undetectable patterns.
If the key card distribution would be always close to the expected 23% ratio, well no betting plan could get the best of it.
Fortunately no one single live shoe dealt in the universe will get such constant ratio.

It's interesting to say that some very unlikely BP patterns will get no hint to be attacked, but certain derived AB situation will at some point.

Obviously we'd prefer to place bets when a derived AB situation MUST come out clustered, thus lowering the probability to catch a losing spot.

Math speaking experts say that every bet will make is EV- no matter what.
That's our fortune.

Tomorrow more AB hints. 

as. 

At baccarat we have endless options to consider binomial propositions, Big Road is by far the most commonly used for wagering, then there are the four derived roads (BP, BEB, SR and CR).

No matter how deep we want to dissect outcomes, math experts teach us that after considering the slight asymmetricity, A=B forever and ever.

In reality A=B with all related statistical implications if the propositions are randomly placed at any shoe dealt.
More precisely, if we bet A at any given stage of the shoe, itlr A or B must follow the old 0.5068/0.4932 ratio. An unbeatable ratio, btw.

This kind of thought is failed by several reasons.

- we can't mix results coming from different shoes as the random postulate cannot be working at any shoe dealt. Actually randomness doesn't work for most shoes dealt. 

- at baccarat there's no one single hand getting the 0.5068/0.4932 probability to appear (ties considered neutral).

- pc simulated shoes differ from real live shoes.

- players must rely upon successions of short term situations, the long run apply to very large long term data that easily confuse unrandomness with pseudo randomness, that last one more likely approaching the "expected" values.

- at baccarat place selection feature totally denies the perfect randomness of the outcomes.

- at baccarat probability after events feature totally denies the perfect randomness of the outcomes.

- the number and lenght of "runs" (a run is the number of the shifting attitude of changing the winning side) is quite different than what 50/50 or a 0.5068/0.4932 ratios dictate, thus proving the unrandomness of the outcomes.

Actually I can't swear that the partial and unconstant unrandomness will play the decisive role on that, maybe baccarat is vulnerable by its own characteristics, but I'd tend to be very cautious to state this last assumption.

Next time I'll post some ideas about how to build up a winning random walk.

as.   

The plans applied to the above shoes show that in the long run the final total of bets (units) won or lost will be almost always approaching the zero value, burdened by the vig.
We can't disrupt the math action, we can only take advantage of statistical features happening or not at different degrees shoe after shoe.

Of course we do not know when and how long things might come in our favor, yet some card distributions are more likely than others, meaning that certain patterns are more likely than others.
In other words, patterns may be so hugely card endorsed that we could win 8 or more bets for the entire lenght of the shoe without having a single loss and by a probability way greater than math expected.

Notice that getting an aim to win 8-12 bets in a row without a single loss needs to reduce the actual results by a 1:10 ratio. In reality less than that as many hands are formed by "neutral" ties.

Considering for simplicity BP outcomes as mere 50/50 propositions, math will teach us that we'll win 8 bets in a row by a 1/64 probability (1.56%).
If a method applied to a large sample data provides ratios higher than that we are in very good shape. (Of course the same reasoning applies to lower classes of WL probability values).

From a strict probability point of view that means that baccarat must be solved by disproving a perfect random shoe formation acting here and there with all the related falsifications of the hypothesis.

Certain shoes are more well shuffled than others, anyway it's not how deep or how light shoes are shuffled (unless consecutively dealt), what it counts is about how key cards are more concentrated or diluted along a given shoe. Better sayed, the portions where such features will more likely take place.

Biased shoe.

In the 80s some black jack scholars raised the issue that not everytime a positive count will get the player a math edge over the house, thus enlarging a possible "card clumping" problem.
Simply put, not everytime a shoe supposedly rich of high cards will get the player an edge as those favourable high cards might remain silent in the unplayable portion of the shoe.
Recent studies tried to disprove scientifically this suspicion, nonetheless and knowing the actual bj rules adopted by casinos, the original theory seems to take a more sensible impact.

At baccarat this "clumping card" theory is well more interesting for several reasons and by different points of views:

- besides Montecarlo casino where more than two decks are discarded from the play (8-deck shoes), almost every live casino in the world will deal the shoe for the most entirety of it.
Actually whenever the first card is not a picture or zero value card, most part of the shoe is dealt at different degrees by cutting off very few cards.

- at baccarat we can bet any side we wish at any moment we wish and by any amount we wish.

- at baccarat previous patterns belonging to certain random walks are decisive to know whether the future outcomes will get a more or less key card dilution/concentration as some numbers must follow finite sequences having a given probability to show up.

- at baccarat the key card concentration/dilution problem could be assessed by the times (gaps) some favorite precise two-card points will get a real win or a loss, meaning that favorite two-card points distribution must be registered up to given cutoff points. After those cutoff points are surpassed, we ought to consider that cards are shuffled to get too whimsical results to be properly exploited.

Every baccarat shoe dealt is an endless proposition of two-step math oriented results getting certain gaps of appearance.
First step involves the higher two-card point, this is the main step.
Say the third card impact will be just an accident.

If the third card won't intervene, the probability to get a higher point will be symmetrical, but a finite card distribution will put some limits on it. Depending about how much cards were properly shuffled.
I mean that without the third card intervention and baccarat rules, only an idi.o.t couldn't find a way to beat the game.

Especially if we want to disprove a perfect "so called" ndependent random source of outcomes.

as.   

Palms casino, $25-$5000.

PPPP
B
P
BBBBBBB
P
BB
P
BBBB
P
B
PPPP
B
P
BBB
P
BBB
PP
B
PP
B
PPP
B
PPPP
BBBB
PPPPPPP
BB
PP
B
P
BBBBBBBB
PPPPP

ub plan #1 both sides: +++-+-+++++++-++-++++-+-+

ub plan #1 B side: -+++++++--

ub plan #1 P side: ++++++-+-+

ub plan #2: ++

actual random walk: --++++++++++--

as.

Gold Coast casino.

BBB
PPP
B
PP
BB
PP
BBBB
P
BBBBBB
PPP
B
PP
BBB
PP
B
P
BBBB
PP
BBB
PP
BB
P
B
PP
BBBB
P
BB
PP
B
P
B
PPP
B
P
B
P
B

ub plan #1 both sides: -++-+++--+--++--++++-+++++

ub plan #1 B side: --++++---++++

ub plan #1 P side: --+++++++-++

ub plan #2: +++

actual random walk: +++++++--++++++--

as. 

Another MGM HS room shoe:

P
B
P
BBB
P
BBB
PP
B
P
BB
P
B
PP
B
P
BB
PP
BB
PP
BB
PP
BBBB
PP
BB
PPPP
B
P
BBBBB
PPPPP
B
PPP
BB
P
B
P
BB
PPPP
BBB

ub plan #1 both sides: ++-++++++++++++++-+++++-+++-

ub plan #1 B side: ++-+++++---++-

ub plan #1 P side: ++++++++-+++++

ub plan #2: +--++++

actual random walk: ++++++--++++++++++

as.

Bellagio, HS room. $100-$20.000

P
B
P
B
BBBB
PPPP
BB
PP
BB
P
BB
P
BBBBB
P
B
P
BB
PPPPPPPP
B
P
B
PPPPPPPPP
BBBBB
PPPPPP
BB
B
P
B
PP
BBB

ub plan #1 both sides: +-++-+++-+++++-+++-

ub plan #1 B side: -+--++--+-

ub plan #1 P side: -+++-++++-

ub plan #2: --+++

actual random walk: ++++++----+++++

as.

Another shoe, now from MGM HS room.

B
PP
B
PP
B
PP
B
PPP
BB
B
P
BB
PPPP
BBB
P
BB
B
P
B
P
BBB
PP
BBB
P
BBB
PP
B
P
B
PPPPPP
BB
PPPP
BBB
PP
BB
P
PP
B
P

ub #1 plan both sides: +++++-++--+++--+-++--+++

ub #1 plan B side: ++--+-++++--

ub #1 plan P side: +++++--+++-+

ub #2 plan: +++++

actual random walk: ++---+++--++

as.