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.

Here's a couple of shoes producing all wins.

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

Again, ub#1 both sides: WLWWWWWWWWWWWWWWWWWWWWLWWL

ub#1 on Banker side: WWWWWWWWWWWLWL

ub#1 on Player side: WWWWWWWWWW

ub#2: LW

Easy shoe, isn't it?
Here we can bet blindly and odds are that we can't lose, mainly for the relative absence of doubles.
The actual r.w. played got eight straight wins.

The second shoe is less polarized and more intriguing yet forming all wins (again eight wins):

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

ub#1 both sides: LWWWWWLWWLLWLWWWWWLWLWWWWL  (-6 units before tax)

ub#1 Banker side: LWWLLLWWLL  (-14 units before tax)

ub#1 Player side: WWWWLWWWWWWWWWWW  (+12 units before tax)

ub#2: WWLWLL

Now differently than the previous shoe we don't have univocal winning lines on all "roads", actually the overall plan will provide a cumulative loss. And trying to only bet the positive Player side sequence is worthless itlr (imo).
This is the classical example where place selection and probability after events tools enlarge our expectation to win many hands consecutively.

To clarify a bit, I've inserted my ub plans just to show that in any case there's a kind of relationship between those roads and the actual r.w. utilized.

In the next post I'll show which bets I really wagered, even on the first "bad" (unplayable) shoe that provided a fictional profit but just by coincidence, meaning that itlr betting on a bad shoe (good shuffling)  can only produce a loss.

And of course there are all those 'more likely' shoes that constitute the most likely scenario we have to face (or not).

as.

I start with one of the shoes I would classify as unplayable but mates didn't want to wait or change table, mostly for the appealing 9 Banker streak showing at column #6.
Quite likely many members here would find this shoe as a good shoe.

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

Applying my ub plan #1 on both sides: LWWLWWWWWLLLWLWWLL

at Banker side: LWWWWWLWWLL

at Player side: WLWLWLWLWWLW

ub plan #2: WWW (all bets won at the very first attempt as B doubles were followed by a single each time)

Since before vig any L= -3 and W= +1, we see that no ub #1 derived road provided a profit by flat betting.
Things went better by betting for W clusters at ub #1  Banker side and by isolating L at ub #1 Player side.
Nevertheless in the entire shoe the number of Ws is too low than Ls, thus imo there's no point to guess bets into a "losing" shoe.
Needless to say that the longest Banker streaks (especially the 9-streak, of course) have shown many unfavorite initial points ending up as winners.

Moreover all other r.w.'s I'm used to playing finished the shoe as losers (except the aforementioned ub #2).

This shoe, at least by the way I'm considering things, is relatively rare among the real shoes world.

Once we have known this shoe texture (lol), probably the best course of action to get all winnings would be to adopt a simple two times betting toward a Banker streak of any lenght forming a WWWWWWWWWW sequence (with 6 winning bets on the first 1-unit attempt and 4 wins on the second 2-unit one).
Practically speaking that the shoe never produced two or more consecutive Banker singles.
And this scenario happens with a too low frequency to be exploitable (at least in terms of  8-10/14 consecutive wins.)

Next I'll present a shoe producing all wins.

as.
Modify message

Glad to be back again...

If we consider outcomes as a mere succession of BP hands of given lenghts, we're missing important random walk features as any single result is affected by math probabilities acting within too long terms, giving the actual dispersion a too much weight over the entire model.

Therefore we shouldn't focus our attention about how much a given side will be more probable than the other one, instead about how long certain more likely events are silent.
And those "gaps" or conversely considered positive "runs", must be estimated about a general probability and an actual probability made on each shoe played/observed. And without any doubt a linkage of events is one of the best tool to use.
Even though itsr (in the short run) it may appear as an identical world to fight against.

Imo best option is to build a preordered betting scheme capable to win all the spots we decided to wager for the entire lenght of the shoe by a simple flat betting approach or, best, by a double betting model.
Of course we know that we can't guess neither any single hand nor half of hands dealt, Or, for that matter, the slight majority of hands wagered when the hands' number is too high.

For example, say we want to utilize a betting scheme applied to BP outcomes made toward getting one B or P single at any stage.
Well, itlr some very rare shoes will form all B/P streaks with no single in between, but you can bet everything you get on your name that the common three derived roads (beb, sr and cr) won't get this feature no matter how whimsical is the actual card distribution.

At baccarat when we register what happens after a given result had come out at a given pace, we are challenging the supposedly random world to really work randomly forever and ever.
Technically speaking, we are challenging a supposedly random world to act regardless of place selection and probability after events tools.
Those tools scientifically prove or disprove a real randomness of the results (and/or a complete independent production) thus whenever we consistently find that the model we're studying is going to form dispersion values way more restricted than expected,  we get a good feeling.

Tomorrow I'l post real shoes we have played at different locations.

as.

Before posting real shoes, I stress again about the importance that in the real world two card initial points distribution is a lot different than the same distribution coming from a continuously shuffled source.
BP distribution is the most random situation we can rely upon, we need to build a random walk considering what happened in the past at a given pace and in various spots. Sometimes we can't get any hint as our r.w. is producing results too much deviating from the "norm".

And people making a living at numbers will bet about the probability that something is more likely to happen and not about some distant probabilities forming a sort of jackpot.

For example, the probability to lose a certain series of two-step wagers per every shoe dealt in the universe is zero. Not 0.000001 but zero.
Of course we can't afford to lose two, three or more losing situations, hence we need to spot the situations where the W part is more likely than due vs the L part.
Our edge comes from long samples and not by a fake control of short term outcomes, the fuel of amateur players.

Forget real results, itlr the side getting the two card higher initial point is favorite to win by an astounding edge.
But if we consider every single outcome in the normal way we're destined to fail.
By registering outcomes by either a place selection and probability after events points of view we'll get a more precise picture of how much the shoe we're playing at is affected by a strong or light key card distribution dispersed in the various portions of it.

That is we should set up a cutoff point about those whimsical spots that seem to deny the math.
If baccarat would be played without the third card impact and even accepting a reasonable vig over the wins on both sides, well it wouldn't exist.

as.

Thanks Garfield!

Say we wish to use a method dictating to bet that the first streak on either side must be a double instead of a 3+ streak (or vice versa).
Such streak of unknown lenght must come out after a BB or PP pattern. Then we bet respectively P or B whether our method privileges doubles or B and P if we like 3+ streaks.
Of course the wisest move will be to bet B after BB and B after PP, but that's not the issue I'm referring to.

Nevertheless, we could insert one more parameter, that is WHEN this BB or PP happens in our shoe. Technically speaking, how many singles had shown before a BB or PP pattern comes out.
Long term data show that the first portions of the shoe are the most "randomly" placed, that is that our random walk will get more unfavourable results than in the subsequent portions of the shoe. Of course unfavourable must be interpreted as "random world".

Random world is defined by actual card clumping getting certain mathematically favorite situations, itlr we can't hope to win with a 3 P initial point vs a 6 B initial point even though in our shoe the fifth card is a 4 or a 5.

Since we have an expected probabilty that a 75-hand shoe will produce some patterns, we should compare our actual results to those expected values.

For example, we all know that the general probability applied to a 80-hand sequence dictates to get 1/4 of singles and 1/4 of streaks, of those streaks half will be doubles and half will be 3+ streaks and so on.
But those values are true only when a perfect independent model is working, more importantly in the real world such values are affected by either the actual asym strenght and by key card clumping.
Since a perfect random world MUST BE insensible to place selection and probability after events tools, we must find the situations to dispute those common statements.

In simple words, whenever certain strong or moderate streak of homogeneous patterns came on the first part of the shoe we're playing at, next outcomes are affected in some way forming (by a linkage of events registration) more likely outcomes in the subsequent parts of the shoe.

Of course B/P events are just the bricks, we need walls to ascertain what's more likely to happen.

Next some shoes we have played.

as.

Instead of thinking as baccarat as a BP outcomes game, we should consider the average probability to get a shoe composition prompting certain degrees of math advantaged situations.
Thinking this way we cannot give a fkng damn about short term results that only give the players false illusions or harsh disappointments.

It's a kind of edge sorting technique obtained by statistical tools and randomness considerations.

Itlr, results are the product of math advantaged situations making hopping lines of various lenght from one side to another.
We can't guess any single decision or many decisions, let alone the situations whether the inferior two-card point will win as unfavorite. But we could estimate, according to the actual shoe we're playing at, how many times a given side will be kissed by a math advantaged two-card situation.

Actually per every hand played there's no greater advantage than estimating which side will get the highest two-card point.
At a lesser degree (nearly a 7% inferior edge before vig) comes the asymmetrical situation when betting Banker.
Alas, at least from a strict long term advantage point of view and without other tools, a simple B/P flow "study" cannot help us in decipher what is more likely to happen in the shoe dealt as a percentage of results is strongly affected by short term variance negating math (apparently). 
We need more.

One of the first answers that could come into our mind is that outcomes are not so randomly placed. But we need to possess solid definitions of randomness to state that. And simple B/P succession assessments do not make the job by any means.
The second answer is about the average key card distribution forming more likely results for given lenghts.

In any case, we need a solid strict scientifical proof that our method will get results way different to the expected values, either by disputing a real randomness of the game and/or by confirming a possible "average" key cards distribution theory.

It's a sure undeniable fact that without a strict flat betting strategy getting a long term edge, any baccarat player sooner or later will lose everything put at stake.

Next time I'll post our results about real shoes played at high stakes rooms.

as.

Say we want to split our baccarat betting life into endless four-wager spots, anytime registering our W/L ratio by a simple flat betting strategy.
It doesn't matter whether we're betting those four spots consecutively or diluted at various degrees. Let alone which bet selection we would like to use.

Forgetting for now the game asymmetricity, the probability to win or lose all those spots is 1/16 (6.25%), the probability to win at least one wager over four attempts is 15/16 (93.75%).
Easy.

Now say we want to register what happens (by a mere FB placement) after a given not-bet outcome (W or L) had appeared.

The possible results are:

WWWW: +3
WWWL: +1
WWLW: +1
WWLL: -1
WLWW: +1
WLWL: -1
WLLW: -1
WLLL: -3
LLLL: -3
LLLW: -1
LLWL: -1
LLWW: +1
LWLL: -1
LWLW: +1
LWWL: +1
LWWW: +3

Of course the total sum is zero, anyway the symmetrical W/L situations among the 16 possible outcomes are just six (WWLL, WLWL, WLLW, LLWW, LWLW and LWWL).

Math teachs us that no matter which spot we'll decide to bet, any W/L pattern will get the same probability to appear. More specifically that at baccarat every spot wagered will get, itlr, a 50.68/49.32 probability to happen.

In reality the actual card distribution could endorse or not the probability to get, per every four-spots wagered, a symmetrical or asymmetrical situation.

Actually the above considerations reflect a perfect symmetrical 50/50 production, but baccarat is a slight asymmetrical game as itlr B>P.
It may happen that along the shoe we're playing at the slight asymmetricity will endorse a "fictional" simmetricity or, on the other end, increasing a natural asymmetricity.

How can we do to "solve" the problem?

as. 

To win at baccarat IN THE LONG RUN we need an advantage, a real advantage I mean.

Betting few spots alone, quitting when ahead or after a given loss, trying to not increase the wagers in negative situations (or increasing them in positive spots), betting any B/P situation alone whatever intended, any MM procedure don't make the job.

And any player wishing to play baccarat seriously must throw away the idea that baccarat is a succession of either 50/50 propositions or 50.68/49.32 still situations.
Those situations are unbeatable by any means.
See J.E. Kerrich experiments for reference and he was talking about a fair coin flip toss, so let's think about the long term results when instead of being payed 1:1 we are getting 0.9876 or 0.9894 return on our money per every coin flip.

Therefore we are forced to transfer the problem from dry math to a probability point of view. But at the same time probability world cannot be estimated without some math fundamentals.

Example.
We all know that at hold'em poker the odds that each player will get pocket Aces on the first two cards are 1:221.
Such odds are calculated by considering all possible two card combinations with the precise possibility to get one of the twelve A-A combinations.
Now suppose that in the 9-handed holde'm table we're playing at we are in seat #7 and we have reasons to think that an Ace will be more probable to fall into the first 3-4 cards dealt.
Is still 1:221 our probability to be dealt A-A?
Of course it's not.
Even considering the high variance happening at poker tables for either objective and more important subjective features, we could deduce that in that hand we are not generally favorite to win.

Even though the example is very distantly related to baccarat, we may infer that key cards determining itlr the most likely course of the result could be more or less concentrated in some portions of the shoe; with the important difference that at baccarat we get the luxury to know where (and options are just two) and how much a given key card had helped or not and by which degree the side it fell on.

Now we're not playing trends or general probabilities, we are going to wager spots where the probability to get a valuable key card falling at a given side is endorsed by some statistical features.

More on that later.

as. 

One of the worst approach one could make, imo, is considering bac outcomes in terms of simple B/P successions.
The game is too much affected by volatility to get hints from them.

Consider this simple BP sequence:

BBBBBBBBB

At hand #5 Player got a 7 initial point and Banker got a 2.
Banker pulled out a 6 and won the hand.

From another point of view and regardless of the previous four Banker wins quality, itlr the more likely scenario in this precise cards situation will be to form a BBBBP sequence.
Thus itlr our 9-hand Banker streak becomes a BBBBPBBBB sequence.

The fact that two or three cards combine to form the highest result shouldn't divert us from the notion that baccarat is a high card game.
Naturally two low cards (as 4-4 for example) could produce a very high result but iltr the number of 8s formed by 4-4 and 5-3 are way less likely than a simple 8-zero.
And of course the probability to get those low cards situation prompting an 8 is perfectly symmetrical.

Itlr, patterns are just the reflex of math probabilities that cannot be the product of simple linear card countings other than for very very small insignificant values (Jacobsen et al).

Since we cannot solve the bac problem mathematically, we have to dispute the real randomness of the outcomes, or better sayed, the actual probability to get a more or less shifted card distribution forming results at various degrees at the shoe we're playing at.

We know that a card distribution, no matter how whimsically placed, will get some limits of relative frequency, hence the model is dependant and finite.
A thing better evaluated by a place selection and probability after events tools that have nothing to do with simple B and P outcomes widely intended.

as.