We're deadly sure to play baccarat with an advantage but to reach this conclusion we had to dispute some common concepts made by experts denying any possible edge over the house.

a) Cards have no memory

Sure, but standing/naturals and drawing hands move around more likely ranges. The same about the important asymmetrical hands favoring the Banker. And those situations might be easily transformed into numbers.
Thus one hand means nothing, two-three hands could mean nothing, but ten hands most of the times mean more than one could imagine.
We need time to figure out how much a deviation will more likely stand up or stop. Yet basically casinos hope things will take a heterogeneous so more undetectable shape, in a word they try to take advantage of the "time" factor by two features:
- by playing a lot of hands the player has a zero probability to be more right than wrong for long;
- time dramatically increases the casinos' math edge, especially when players try to guess this or that without a solid foundation of how things really work at baccarat.
Translation: we need to understand how an "average shoe" looks like. Casinos win a lot of money not for the tiny HE, but because they get the full value of those undepictable "average" shoes where everything seems to stand too shortly to be exploited.

b) Hands are randomly distributed

This is the classic conclusion of those ignorant "I do know everything about baccarat and gambling" experts.

To say that each hand will more or less whimsically and eventually win is not the same that stating that winning/losing hands successions are forming W and L more likely (so detectable) ranges.

In fact, a baccarat random world implies sd values typical of a close coin flip game, then whether the perfect randomness should really act, every point considered of the rw succession must get the same results expected from a CF independent model. It's the simplified RVM definition of randomness.

This randomness definition can only happen at roulette where each spin is totally independent from the previous one(s) at every succession's point considered.

At baccarat each step will make a change (albeit being small) in the future probability considered by an expected long term probability and an actual probability.
It's a conditional probability acting at various levels, most of the times following the average shoe texture mentioned above.

c) Patterns are worthless

There are patterns and patterns.

Humanly perceived patterns are just constituting a minuscule part of all bac succession features.
In reality any B/P succession is the source of infinite A/B sub successions, the common displayed "roads" are just 4 or 5 different "pace/geometrical" shapes of the original sequence.

Stating that ALL patterns are worthless means to have investigated the thousands of sub succession possibilities, that is applying as a rule the same "fresh" probability to any new event coming out.
We're sure nobody investigated more than 20 or 30 different random walks before making any kind of statement.

Next time we'll see how our algos manage numbers by a fictional progressive scheme that sometimes will reach the real betting parameter.

as.

Hi Al, you answered to my questions in your last post. 

as.

Schematically we could assign a number value to any pattern happening along any shoe dealt; for some reasons we decided to cut off from the registration a fixed percentage of starting patterns considered as neutral.

Each pattern gets a given number in relationship of its lenght considered in form of isolated single/streak appearance and clustered streak/single appearance.
Numbers move within the 0-3 range, meaning that 0 is no consecutiveness, 1 is one consecutive pattern, 2 is two consecutive patterns and 3 or 3+ clustered situations are always considered as 3.

Let's make an example, three real live shoes.

First shoe presented a 1-0-1-1-1-3-2-2-(1); the final total number was 11.

Second shoe went as 2-1-2-0-1-2-0-(1), that is a 9 final number.

Third shoe produced a 2-0-0-0-2-0-0-1-1-0-1-0-3-1-0 succession, a 11 final number.

But notice what happened right after any given number at this shoe sample.

0= 1, 1, (1), 0, 0, 2, 0, 1, 1, 3.

1= 0, 1, 1, 3, 2, 2.

2= 2, (1), 1, 0, 0, 0

3= 2, 1

Despite of the strong shifted ratio (0=7 and any number different than 0=17), 0-1 clusters seem to overcome the 0-1 isolated counterpart, yet there are important features to take of about what happens next after a 2 or 3 scenario.

More live shoes:

1-1-0-2-0-0-0-1-0-1-0-2-3-1

0= 2, 0, 0, 1, 2

1= 1, 0, 0, 0

2= 0, 3

3= 1


0-1-2-0-0-0-3-2-0-2-0-0-0-0-1-0-1

0= 1, 0, 0, 3, 2, 0, 0, 0, 1, 1.

1= 2, 0

2= 0, 0, 0

3= 2


2-2-2-0-1-1-0-2-1-0-0-(2)

0= 1, 2, 0, (2)

1= 1, 0, 0

2= 2, 2, 0, 1

3= not applicable

2-0-3-0-3-3-0-1

0= 3, 3, 1

1= NA

2= 0

3= 0, 3, 0

0-1-2-0-0-0-1-1-2-0-0-0-0-2-1

0= 1, 0, 0, 1, 0, 0, 0, 2

1= 2, 1, 2

2= 0, 0, 1

3= NA

1-2-0-3-0-1-3-0-(1)

0= 3, 1, (1)

1= 2, 3

2= 0

3= 0, 0

0-1-2-3-1-3-3

0= 1

1= 2, 3

2= 3

3= 1,3

3-0-0-1-0-1-1-0-2-2-3-0-0

0= 0, 1, 1, 2, 0

1= 0, 1, 0

2= 2, 3

3= 0

3-0-1-0-0-3-0-3-1-(2)

0= 1, 0, 3, 3

1= 0, (2)

2= na

3= 0, 0, 1

0-0-2-0-1-0-1-0-1-0-0-0-1-0-0-0-0-0-0-0-2

0= 0, 2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2

1= 0, 0, 0, 0

2= 0

3= NA

0-1-1-0-2-0-0-0-2-0-3-(1)

0= 1, 2, 0, 0, 2, 3

1= 1, 0

2= 0, 0

3= (1)

3-3-0-0-0-0-2-3-2-(1)

0= 0, 0, 0, 2

1= NA

2= 3-(1)

3= 3, 2

3-0-0-2-0-1-1-2-0-0-0-0-1

0= 0, 2, 1, 0, 0, 0, 1.

1= 1, 2

2= 0, 0

3= NA

3-0-0-2-2-0-1-1-2-1-2-(1)

0= 0, 2, 1

1= 1, 2, 2

2= 2, 0, 1, (1)

3= 0

1-1-0-0-0-0-0-3-0-1-1-1-1-0-0-0-(2)

0= 0, 0, 0, 0, 3, 1, 0, 0, (2)

1= 1, 0, 1, 1, 1, 0

2= NA

3= 0

0-0-3-1-0-1-3-1-0-1-0-0-1-3-0-(2)

0= 0, 3, 1, 1, 0, 1, (2)

1= 0, 3, 0, 0, 3

2= NA

3= 1, 1, 0

0-0-0-0-3-0-0-0-0-0-3-0-2-3

0= 0, 0, 0, 3, 0, 0, 0, 0, 3, 2

1= NA

2= 3

3= 0, 0

2-0-0-0-0-0-0-0-0-0-3-0-0-0-0-0-3-1-0-1-(1)

0= 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 1

1= O, (1)

2= NA

3= 0, 1

0-1-0-1-1-0-0-0-1-0-1-0-0-1-3-0-0-0-0

0= 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0

1= 0, 1, 0, 0, 0, 3

2= NA

3= 0

0-1-1-0-0-2-0-3-0-2-0

0=1, 0, 2, 3, 2

1= 1, 0

2= 0, 0

3= 0

1-0-1-0-1-2-0-0-3-1-0-0-0-0-0-0-(2)

0= 1, 1, 0, 3, 0, 0, 0, 0, 0, (2)

1= 0, 0, 2, 0

2= 0

3= 1

1-2-2-0-3-0-1-3-1-1

0= 3, 1

1= 2, 3, 1

2= 2,0

3= 0, 1

0-0-0-3-0-2-1-0-3-2-3

0= 0, 0, 3, 2, 3

1= 0

2= 1, 3

3= 0, 2

1-0-1-3-0-0-0-0-3-1-0-0-0-0-0-(1)

0= 1, 0, 0, 0, 3, 0, 0, 0, 0,(1)

1= 0, 3, 0

2= NA

3= 0, 1

1-0-3-2-0-3-1-0-3-0

0= 3, 3, 3

1= 0, 0

2= 0

3= 2, 1, 0

0-3-0-0-0-1-1-2-3

0= 3, 0, 0, 1

1= 1, 2

2= 3

3= 0

1-2-3-1-1-0-0-1-0-2-0-(1)

0= 0, 1, 2, (1)

1= 2, 1, 0, 0

2= 3, 0

3= 1

0-0-2-1-1-0-0-3-0-3

0= 0, 2, 0, 3, 3

1= 1, 0

2= 1

3= 0

1-3-0-1-2-0-0-1-0-1-(2)

0= 1, 0, 1, 1

1= 3, 2, 0, (2)

2= 0

3= 0

0-1-0-0-0-0-1-1-3-0-0-2-0-0-1

0= 1, 0, 0, 0, 1, 0, 2

1= 0, 1, 3

2= 0

3= 0

There are several ways to exploit such sub successions, think about how many "NA" spots happened, meaning that at an interesting part of shoes dealt one pattern hasn't the room to be properly assessed by a back-to-back scenario. As it simply didn't happen.

as.

Utilizing an approximated approach doesn't mean to navigate in the uncertainty ocean, everyday we approximate things outside of the gambling field and fortunately most choices we'll make are right. Or at least not being so bad.

Hoping for the best but expecting the worst is our mantra while playing baccarat, so the primary goal we should aim for remains to preserve our bankroll, trying to spot the situations when something should be "more due" by reasons unfortunately not strictly belonging to mathematics.

In the effort of trying to constantly beat this game, the average (entire) shoe composition represents what we should look for first.

"Extremes" rarely happening make the fortune of recreational players or of those very rare acute players capable to ride those unlikely situations; everything different than that will make the casinos' fortune or creating the basis where professionals will make money.

oOoOo

We know that long chopping shoes will eventually fill a huge number of shoe columns ignoring the 2nd row, yet at derived roads such columns filling is slow paced.
 
On the other end, streaky shoes will fill more rows than columns, ok it's a banal assumption.
Yet, derived roads are asymmetrically affected by either the SHAPE and DISTRIBUTION of such streaks. Meaning that some derived roads will stall on many columns and others will quickly abandon those columns.

And remember that we can build infinite derived roads besides the common byb, sr and cr.

More later

as.

Good read indeed.

I have some questions, see you tomorrow.

as.

Thanks KFB.

Any comment about your favorite players club/s?

Thanks

as.

In our opinion baccarat can be "solved" by assigning a number to the more likely patterns, so at the end by adding the various patterns' number happening along any shoe dealt, we'll get more probable final number ranges.

Of course for the natural permutation issue, we can't know precisely when low, moderate or huge numbers will show up, yet the final totals must fit within more probable ranges.
Good news is that back-to-back low or huge values must concede room to the opposite situations as the final value must be someway limited.

To provide a banal example, at a horizontal classic registration we know that a decent number of columns will be filled, but if we'd restrict the actual row's impact we either find situations when a row will fill a new column or when a column tend to negate a new column apparition.

Consecutive filled columns and chopping shoes tend to increase the final patterns number up to a point.

Casinos hope that players, in  a way or another, like to force such total ranges especially when players do not assign a cutoff value to the long univocal situations happening at both side of operations (shortening or prolonging the columns lenght), thus giving a lesser damn to what a final shoe will show up.

More in a couple of days.

as.

QuoteThx Asym for your prompt reply to my Q above.

re:Your addendum comment in same post above:

 "...You could argue that a BBB sequence should be even more shifted toward an A, so enticing to prolong the A betting at the same pattern.
Our data do not suggest to keep betting and for practical reasons waiting the BBB trigger to show up before wagering is a waste of time...."

Q--What does your data suggest for a BBBB_ sequence ??
 
For example
PBBBB_ or
PPBBBB_ or
PPPBBBB_ or
PPPPBBBB_ 

? all the same or do u treat them differently?


Thank You,

Hi KFB!!!

B (0.25) fights againts A (0.75) pattern.

as.

 

Hi KFB and thanks!!

Say we have an A/B succession, pA=0.75 and pB=0.25.

For example AABABAAAAABABB(?)

Now it's time to bet toward A as itlr BBA>BBB by a ratio superior than the expected 0.75/0.25 (3:1). We know we have to bet two times in the sense that we need to catch just one win within a two betting range.
If both bets will fail we let the BBB pattern go, so waiting for another fresh BB to show up. And so on.

You could argue that a BBB sequence should be even more shifted toward an A, so enticing to prolong the A betting at the same pattern.
Our data do not suggest to keep betting and for practical reasons waiting the BBB trigger to show up before wagering is a waste of time.

There's a statistical reason beyond that.
Gambling and baccarat in particular is a game of streaks; some streaks are more likely than others to show up clustered or to break UP TO A POINT, once this is surpassed we're navigating in the more undetectable ocean.

It's obvious that baccarat streaks are the by product of the higher two-card initial points, first. Such probability moves around more likely ranges.
Then there's the third(s) card impact making a more decisive role at Player bets as sometimes Banker doesn't need to draw so standing as math favorite. Anyway those situations constitute a minuscule part of the total outcomes (asym hands).

Thanks to one of Alrelax's post we have investigated deeply how many times and how much a third card could continuously favor (or not) the Player side and this is another range to take care of.

Naturally it's impossible to guess when a math advantaged hand will show up, yet it's possible to estimate the math advantaged more likely ranges, this is a good start.

On the other end, third card(s) make an important role. Most of the times being ininfluent, other times completely altering a math propensity.
Again ranges of intervention might help us.
I guess that a B7 or B6 vs a Pzero sooner or later will succumb to a 8 or 9 third card draw. And vice versa.

Unfortunately and despite of knowing very well that to get a long term edge we need a kind of math  advantage whatever taken, even a part of unsound unlikely spots must be won in order to collect an interesting profit. Otherwise the edge will be too diluted to be profitably exploited.

More later.

as.

Let casinos think that everything can happen anytime, let casinos think that everytime we'll place a bet a perfect opposite situation could easily happen for long.

This is a complete fkng ignorant statement endorsed by losing mathematicians.

Actually they are right whether we play every fkng hand dealt as randomness can't be controlled by mechanical plans or by human guesses.
Well, randomness can't be controlled anyway, that's why bac shoes can be beaten by exploiting unrandom features.

In our opinion, unrandomness can be exploited by a proper assessment of positive and negative lenght sequences, most of the times being the by product of a general greater probability but very often shifting too much from expected values to get an advantage from as one or two hands not forming a math more likely final outcome could easily change a more likely flow into a strong unwanted deviated situation.

Say (p)A = 0.75 and (p)B = 0.25  (p)= general probability considered in two betting steps.

Once A do not show up after two expected attempts, B event must be considered in its average consecutive apparition.
Obviously probability to get A after B will be 3:1 placed, so itlr the situations to get BA vs BB are 3:1 placed.
No shifted events to rely upon, the model seems to be randomly distributed.

Naturally, the only obstacle to overcome this "balanced" situation by a kind of progressive multilayered betting plan will be the "permutation" issue, meaning that long negative B sequences coming out in a row must not put in jeopardy our bankroll.

Anyway, let's display the four more likely A/B situations:

1) AA > AB

2) ABA > ABB

3) BA > BB

4) BBA > BBB

Notice that despite of the asymmetrical A/B probability, the first element is symmetrically placed (A or B).

There's no fkng possibility in the world that itlr AA < AB, in a word that A won't come out clustered for long or at the very least coming out more times clustered than isolated.

The second scenario (B coming as isolated as opposed as clustered) is more debatable as long more likely A sequences must be somewhat balanced by either a B short-gapped or consecutive B situations.
The same about the third situation.

Then the BBA vs BBB scenario will make things so polarized that baccarat becomes the best game to get an edge from as there's no way that the BBB sequence will overcome the BBA sequence.

To summarize:

a) betting A after an A is a break even option

b) betting toward A after a single B is a break even option

c) betting toward A after a single B is a break even option

d) betting toward A after a couple of BB is a strong EV+ move.

Since we know that the casinos' aim is to provide the most astounding heterogenous quality for every shoe dealt, we think to be in a wonderful shape to exploit a low deviation level of the a, b and c features, at the same time taking the best of it by exploiting the d) propensity that no one voluntarily card distribution can't disappoint.

as. 

Is this a real losing hand? LOL

Hi KFB and thanks for your posts.

I think that regardless of the random walk utilized (even though some r.w.'s are way better than others), the best approach to take is to know how much ON AVERAGE the different patterns will impact over the shoes. In some way it's an approximation of the card distribution probabilities and to do that we have to assign a specific number to the several pattern categories (and we know they are only three).

On the other end, to get a long term advantage we have to find solid proofs that (++) vs (+-) sequences must get a better than 0.75/0.25 expected ratio or other intricate and more unlikely +/-
strings.

As already sayed here, if a positive streak will reach the 24-30 value but the negative streak counterpart will be 6 or 7 long (18 or 21 unit losses), we know to play with a (diluted) edge.

By far the best situation to make a huge bet is whenever a given random walk will get a couple of consecutive losing spots (a thing quite rare to happen), then wagering toward a + (in two consecutive times).
If this two layered wager is lost we have to wait for another opportunity.

More later

as.

The statistical isolating/clustered feature already taken in consideration to condense the original outcomes in + and - signs could be applied even at those short sub successions.

Thus if we bet toward + after a first + appearance or toward + after a single -, only a sequence as +-- or --+- will get us losers two times in a row; and of course longer than this successions will prolong such losing streak as +--+- or --+--.

Given the shortness of derived patterns, it's obvious that a single pair of - signs happening in a shoe means that the shoe won't be a final winning shoe.
Since winning shoes are more frequent than losing ones, in some sense is like that the actual card distribution must be particularly full of + signs at the very start of it to get an advantage. 

So let's see how many signs of the sub succession we'll get in the first position of every shoe dealt:
The answer is that we'll collect 44 units (before vig), always considering W as +1 and L as -3.
The longest consecutive losing spot happening at the very first sub sequence was four in a row, the longest winning sequences were 20, 17 and 13 in a row.

as. 

In the above 183 shoes examined, it's interesting to notice that before vig (ignored for simplicity) we got 91 winning shoes, 73 losing shoes and 19 shoes were a push.

At the end and by accounting only the + and - impact we collected a small profit but considering that "push" shoes are anyway losing shoes (for the vig), basically everything broke even.

From another point of view, we might consider the most catastrophic W/L shoes succession, that is all losing shoes coming in a row, a thing impossible to happen but that cannot be discarded.

In reality the most long losing shoe sequence was six in a row and two times 4 losing shoes in a row.

On the other end, the longest winning shoe sequence was seven and six in a row.

We know very well that such W/L consecutive streaks do not mean nothing, it's just a permutation issue.
For example, after the first 70 shoes dealt, we got a +78 unit peak that slowly balanced towards the losing side.
That's why we need a quality factor to be utilized tending to give the most limited fluctuations.

More later

as.

Hi KFB, very good points!

My guess is that by introducing those side bets, casinos have transformed a kind of coin flip low edge game into a more appealing constant chase right on those "unlikely" bets that could guarantee huge returns.
Especially when players are losing, so mathematically aggravating the losses.

It's not a coincidence that Vegas HS rooms do not offer EZ tables where the vast majority of bets is payed 1:1, probably knowing that it'll be very unlikely that tourists are willing to bet the F-7 wager as being too rare to happen.
In any instance at EZ tables the HE is 1.01%/1.24% and 7.6%, whereas at Tiger/Lucky 6 tables (very common at HS rooms) HE is 1.46%/1.24% and 14% plus.
 
So no commission tables somewhat lure the Banker action backed up by some kind of side bet action, but in both cases (EZ and T/L6) what remains the best side to wager (generally speaking) now becomes the most burdened betting option, surely worse than the unchanged Player 1.24% HE.

It has to be sayed that differently to F-7 bets, Tiger bets are easily controllable by card counting, moreover featuring a decent average distribution among the shoes dealt.

Anyway we think that the best tables to risk our money at are normal commission games, even knowing to concede a 0.05% worse edge at B bets.

as.