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.

Back to the real shoes issue.

Bellagio, HS room. $1000-$20.000 table.

The shoe went as:

B
PP
BB
PPPPP
B
PP
BB
PPPP
BB
PP
BB
PP
B
PP
B
P
BBBB
PPPP
BBBB
P
BB
P
B
P
B
PPPP
B
P
BB
PP
BBBBBB
PPP
BB

There were four players seated at this table and at the end everyone was hugely winning, despite of several bets made on opposite sides.

Big road provided long univocal patterns (think about consecutive streaks) anyway one player got almost all winnings by following derived roads.
Another player won almost every hand on the BBBBPPPPBBBB pattern.

I was quite surprised that a player wagered $10.000 (his average bet being $5000) on Banker side after the 4 Player streak (in bold) happened.
A possible explanation comes from a derived roads study.
For the record he turned up a 9 over a drawing P hand.

Ub plans:

#1 both sides: +--+-+++-++++-++-+-

#1 B side: ++++++-+-+++-

#1 P side: -++++++--

ub #2: +--+++

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

as.

For a moment let's forget all "complicated" issues regarding a profitable bet selection so focusing more about a MM.

Consider this MM plan (already invented, btw).

We split our play into endless portions of 5 resolved hands wagered by flat betting, stopping the action whenever we have reached out a +1 profit (before tax); if we didn't manage to get a profit after those five hands bet (consecutively or not) we take the loss in units then calculating the future bet working on 5 next hands by increasing the loss by one unit up to the point where we'll cover all previous losses and getting a +1 profit (minus vig).

This plan is unbeatable mathematically as the probability to win one unit per every 5-hand betting cluster is 68.75%.
Naturally the practice collides with the theory as without a proper BS plan, we need a huge bankroll to cover all the possible negative fluctuations, sooner or later surpassing the table limits.

Each 5-hand betting cluster will get 32 possible WL combinations, all specular in term of WL numbers, but since we have chosen to stop the betting after one unit profit, now we have some  combinations starting with a L working for us (namely LLWWW, LWLWW, LWWLL, LWWWL, LWWWW and LWWLW).

Therefore the probability to win one unit profit (better sayed a W>L one-step situation) per each 5-hand cluster is 22/32, that is a 68.75% winning probability.

Example.

After 5-hands bet by flat betting, the overall total would be positive right at the start 50% of the times (16 patterns start with a W) and six times over 16 whenever a L starts the pattern (the aforementioned WL patterns).
Of course the general probability to win or lose a given amount of hands is symmetrical, anyway the fact we're looking for just one unit profit tends to unbalance the ratio in some way. At the risk of the bet increase.

I've chosen to display the 5-hand clusters as I know that many bac players won't like to flat bet clusters of 7-hands, 9-hands or greater amount of odd hands.
Actually more hands we're considering for each cluster and better and more precise will be the probability to know we're working in the "right" field. Providing a proper BS is utilized.
And of course the bet increase is the decisive tool to understand whether we're randomly betting or getting the best of it by a possible edge either coming out from a bad shuffling or by bac features.

Back to the numbers.

According to this plan, the worst scenarios we are forced to face is whenever after each 5 hands bet, our total result will be -5 or -3.
That is in order to get the 68.75% edge, we must increase the future bet to 6 units or 4 units.
Naturally odds this scenario will take place are 6:32 (18.75%).

The overall remaining losing part of every 5-hand sample accounts for the other 12.5% percentage prompting just one losing hand.
Meaning that whenever we're losing, odds we'll get more than one losing hand per every 5-hands wagering are exactly 2:1.

Most experienced bac players aren't going to lose 10 hand in a row, meaning that this MM plan won't enlarge the bets by 6:1 and then 31:1 ratio standard.

That's the key point of a profitable betting.
I do not know long term winning players betting more than the double of their standard bet.
Thus restricting the bac probabilities into a 1-2 step category.

They are right, as a similar 50/50 game must be solved right at the start. Either something follows or it doesn't.

as. 

The idea I've implemented in my strategies is pretty simple in theory and quite difficult to put into practice without having mastered some notions about probability studies made in the past.

1.

At baccarat and per every shoe dealt, streaks are the direct reflex of key cards concentration or dilution that tend to produce more likely outcomes.
The key cards concentration/dilution ratio is a finite value, once a key card is either burnt or alive it must affect the probability to get more likely outcomes on either side, for now we do not know which side.

2.

Games of binomial chances work according to a probability world that no matter how dissected will form runs of certain lenght. (For now we neglect that one side is more likely than the other one).
Runs are calculated by the number of shifts from A to B.
A perfect random 50/50 game will produce the same number of runs expected mathematically.
Even though our beloved game is affected by a slight probability's asymmetricity, we can consider as a "affordable error" an actual ROI difference of 0.18% existing by the B or P wagering. 

Example: a BBBPBPPBPBBBPBPPPBB succession is formed by 11 runs, that is 11 B/P shifts.

3.

Itlr actual results surely adapt to math expected values as they mix it up.
Think about black jack. Without a spread betting procedure utilized when a positive card counting arises (I'm not talking about some sophisticated key card spotting techinques), it's impossible to beat the HE.
Even considering the best favourable deck penetrations, the best card counter in the world cannot spot in total more than 13-14% profitable decks.

4.

At bj, key cards are one-sided exploitable, meaning that some cards are favoring players and others favor the house. And of course we must bet just one side per every hand.

At baccarat we can't get a math advantage but we can serenely "wonging" at the utmost degree.
That is we can choose when and how much money we want to risk, letting the house to think that no matter how are selected our bets our EV will be always negative.

5.

Every shoe dealt in the universe must get a more or less key cards concentration or dilution along the way.
Say we want to classify as key cards all 7s, 8s and 9s. It's a 96/416 percentage, that is a 23% dynamic probabiity.
Zero value cards add up to a 30.76% dynamic probability, but there are no other card combinations prompting more likely events for long.
 
Greater is key cards concentration within small portions of the shoe, better will be the probability to get shifting outcomes (runs). Meaning that whenever many key cards are concentrated within strict terms, higher will be the probability to get shorter univocal streaks, hence a larger amount of runs.

For the same reasons, a deck's portion  particularly poor of key cards will form longer streaks, say a more undetectable world.

6.

The final strategy should be shaped about the probability to get, per every shoe dealt, a key card distribution strongly or moderate concentrated into some portions of it. Thus favoring a greater amount of runs of certain lenght.
And do not forget that at any EV- game,  player's edge comes very diluted and not constantly placed. The comparison with bj is straightforwardon on that.

7.

No matter how we want to register outcomes, itlr there's a strict relationship about key cards falling and actual results, that is about the number of runs acting per every shoe dealt.

After all in order to win itlr we have to falsify the hypothesis that every single result is randomly placed and that our actual results are not following dispersion values dictated by mathematics.

Simply put, that the average key cards distribution won't get those dispersion values belonging to an unbeatable bell curve.

as.

Quote from: RickK on November 07, 2020, 12:52:35 PM
as....you mention in another thread that some of your best baccarat ideas came from roulette aficionados. Any chance you could share some of those strategies or possibly compare the two games, if you think that would maybe help us understand your baccarat methodology ? Just looking for a way to help us understand your writings a little (maybe more than a little) better.

Hi Rickk! Yep thanks to answering Garfield question, ub=my plans #1 (splitted in three categories) and #2.

Some roulette researchers seem to have an edge over most pure baccarat scholars, they want to fight independent successions trying to spot any possible randomness defect.
Of course this thing is very difficult, say almost impossible both theorically and practically. Nonetheless some ideas are quite interesting and sometimes may be applied even to baccarat productions, now not being independently formed. 

Personally I think the best simplest and only way to attack modern wheels is by approaching certain IB automated roulettes where the software production seem to be decently predictable, especially if we can place the bets after having assessed the rotor velocity of each spin.
Cons are that the HE at those roulettes is too high (2.7%/5.26%) to overcome and, more importantly, that you can wager relatively small amounts of money. Then there are further considerations I do not want to discuss here.

The common idea, imo, is that both roulette and baccarat productions are affected by a fair transitory asymmetricity, lasting for given periods of time. But at baccarat we can find way better conditions to state and prove that the asymmetricity belongs to a more limited (hence predictable) world than expected for many reasons.

Finiteness of the shoe and key cards distribution with all shuffling implications make a huge and decisive role on that, again two simple examples:

- at baccarat symmetrical streaks are shorter than at roulette, meaning that whenever the third card rule doesn't intervene on the hand's outcome, we'll expect a way lesser amount of long streaks than at other 50/50 independent sources.
For example, at baccarat we need a larger amount of hands dealt to cross a pure symmetrical 7-hand streak that at roulette shows up with a 2/128 odds proposition (zero/s ignored).

- at baccarat probabilities are calculated only by considering math combinations working into a perfect random distribution.
A statement surely true in the long run by mixing everything regardless and naturally taking for grant all perfet random productions coming up from a software.

Really? No way.
Let's take the math asymmetrical probability favoring Banker, it's 8.6%.
And now take the single zero roulette probability to get a series of three given numbers showing up after a 75-80 spins run. It's 8.1%, so almost correspondent.
Are those "almost same probability" dispersion values equally placed?
They should, but they don't.

Good news.

Now we know that a given percentage of hands math favoring Banker will feature lower dispersion values than what any other pure independent game will do.
Even though we'd want to admit that every baccarat production we have to face is perfect randomly formed.

Ok, there's always the whimsical card fall favoring one side or the other one at the start (two initial cards).
Good, at which point the most likely situation can come out consecutively? And what if we want to consider results at different paces and quantities? And is hands quality an important factor before betting?

as.

Quoting Ben Mezrich on his "Busting Vega$" book: "Sometimes you had to close your eyes, forget the appearances, and just trust the numbers".

I'd meekly suggest to change the word "sometimes" with an "always" word.

Even though at baccarat numbers are not so precisely depicted than at bj, we know that after a given number appeared within certain terms, the future probability will be affected in some way.
As the probability to get the "more expected" calculated by our tools will be proportionally lowered or raised.
Say that while playing bj the low/high cards ratio will be negative or neutral for the player after half of the deck was dealt, what's the probability to get a profitable positive count on the remaining portion of the shoe?

At baccarat we have some choices to know that per every shoe dealt, negative cannot be always followed by a proportional amount of positive, but that in some situations positive can last for the entire shoe.
Thus positive at the start could build a whole positive situation and negative can only hope to recoup some losses along the way but at a proportional lower degree then what the former event had done in the past. And vice versa but we shouldn't forget that every bet we'll place will be math unfavorite.

Casinos make their huge profits hoping that either players won't properly exploit all winning shoes and at the same time knowing that players experiencing harsh losing situations won't get immediate positive situations at the same shoe played.
The math advantage doens't hurt casinos for sure, but at HS rooms whenever a shoe is dealt casinos like to front players that want to guess hands no matter what.

as. 

We can beat this game itlr if we have the strict scientifical proof made by rigid measurements that this thing is possible.
We can't rely upon "elastic" methods or, even worse, about raising the bets because we had lost a given amount of bets.
If any fkng method can't win by flat betting, well it only means we're playing an EV- game.

If a given MM approach would be able to beat this game, it means that along the way some bets are more likely than others, therefore why not to wait to cross this situation before wagering?

In a word, every silly bet we want to place on the felt MUST get a positive expectancy, surely susceptible to variance, but capable to get a positive long term ROI. Otherwise we're doomed to failure.

Technically speaking it means that every single Banker bet must get at least a long term 51.3% winning probability and every single Player bet at least a long term 50.1% winning probability.
It's not that difficult to assess those values after having tested your shoes.

Back to the main issue.

Baccarat probabilities are not comparable to either Brownian motion or gas kinetic probabilities, as the former involve a kind of dependent probability, say it's a linkage events' probability.

Easy task to find "more likely events" as B streaks vs B singles or P singles vs P streaks, unfortunately those patterns are way lesser distributed than what a favourable player's  payment dictates.

Therefore in some way the "actual" must not correspond to the "expected", meaning that not every single A/B distribution will follow the same expected lines.
Practically speaking, per every shoe dealt we need to concentrate the results either in order to lower the variance and to get a fully value of place selection and probability after events tools.

Place selection is the only sure valuable tool to know we're facing a real random world.
Thus and according to this rule, no matter which spots we decide to wager or classify, we ought to think that the BP probabilities will be always 0.5068 and 49.32 on any spot bet.
A total bighornshit.
As long as key cards were depleted from the shoe and according to the past features, only a perfect real random shuffle won't get hints to know where next key cards are distributed for long.

Simply put, a shoe can't get a valuable room to get the "place selection" validity confirming a total perfect randomness of the outcomes.
Thus we know to fight a partial unrandomness of the distribution and fortunately long term data show that some steps are "more likely" than others after the vig.

as.