Patterns

The baccarat invulnerability relies upon the fact that it's impossible to 'restrict' the variance terms of the results, meaning that anything could happen anytime and anywhere.
In statistical terms this means that the 'improbable', even though being carefully calculated, will surely happen providing to get a fair amount of trials.
So after an 'infinite' amount of shoes we'll surely face an all B or P hand shoe or a whole BP chopping shoe or, well more likely, a whole 'streaky' shoe without any single showing up. (Btw, we have crossed through this last situation more than once). 

Anyway to get an idea about how's unlikely to get some 'negative' patterns for long, consider this simple mechanical and progressive betting plan.

Notice that we're not saying it's a sure way to beat baccarat, just that these random walks will disrespect the unbeatable features belonging to a typical random walk as they are more prone to roam around the 0 point or taking a given univocal direction (no matter which side we'll bet at).

Our random walk #1 will bet toward singles and doubles after any 3+ streak happened (that is any 3 or 3+ streak happening at either side), so 'hoping' that such streak will come out more isolated than clustered or that 'isolated' streaks will come out more clustered than isolated (see later).
If any 3+ streak comes out clustered (back-to-back) we simply stop our betting, waiting for another 3+ streak occurrence.

Beside the obvious first-step progressive betting scheme after a single apparition was missed (otherwise a second winning Banker bet would get us losers for the vig), we'll raise our standard bet in two occasions:
- after a winning bet in either one of the two steps (at least up to the point to erase a previous deficit) and
- after a single losing two-step bet.

No need to try to erase a previous deficit too fast, it's casinos' hope to know that sometimes sh.i.t happens for long (in either way), let shoes to be dealt and those random walks cannot get negative values too distant from the 0 point.
Obviously we should consider that every bet will be burdened by a math EV- return.

Then our random walk #2 is more patient as it'll act just when two 3+ consecutive streaks had happened, the same target being singles and/or doubles.
Same progressive features to be utilized.

Actual long term results of such plan at real live shoes

Both random walks #1 and #2 get a common 'enemy': that is series of three or more consecutive 3+ streaks.
Actually those situations will surely come out but they cannot neglect for long the more likely propensity to show up as isolated as an average live card distribution (being dependent of the previous results and surely finite) will make some limits over their back-to-back apparition at the same shoe.

If you'd test a relatively large sample of live shoes, you'll see that, more often than not, just one of the two random walks will take a decisive positive line as 'complex' patterns will take a huge amount of trials to show up a possible propensity working at both random walks.

Is this big.horn.stuff stuff as many fkng mathematicians will surely bet their as..ses upon?

Ok, so let's take the casino's part.

A sky's the limit progressive player will first bet that A (a+b) will be more likely than B (c) by wagering that A-A and B-A will be more likely to show up than A-B and B-B. (Of course from a theorical point of view a+b=c).
So casino must hope results will take a c clustered line.

But say the same player had noticed that A is more likely to come out by rarer B clusters of two that seem to be prevalent than isolated B (so c>a+b but c-c<a+b) , so now casino must hope to get c-c-c clustered patterns than c-c spots distributed by more likely lines.
Hence this player wouldn't give a fk about random walk #1, just more focusing about his/her higher bets by following random walk #2. 

Now this casino should hope to deal shoes presenting a lot of either A-B or B-B spots (r.w. #1) or B-B-B spots in a row not intervaled by more likely B-B-A patterns (r.w. #2).

BTW, it's a sure long term finding that the more 3+s streaks are clustered, better are the odds to cross through single/double patterns in the remaining part of the shoe.

A thing we'll look at the next week.

as.

In this interesting paper the only (partial) positive conclusion for bac players is restricted into this passage:
The only possible winning strategy is to catch the trend(either the Player or the Banker) and to bet on that side.

Next let's see this passage:  This implies almost independence of the game in
probability. Therefore the previous outcomes have no effect to the next outcome. In theory, it is
meaningless to decide which side to bet on according to the outcome sheet.

Another passage I've found interesting is this:
The simulation results are shown in Table 9. Compare Plan 4 with Plan 3, we note that the 'follow'
method seems to be better than the 'alternative' method, because all the losing game probabilities are
relatively smaller for the 'follow' method.


Then this: Note that the random walk is a typical nonstationary stochastic process. Every random walk
wanders away from the origin and is never guaranteed to return to the origin.


Our comments.

Not surprisingly this paper confirms that baccarat is an EV- game for players. Nonetheless authors have found that some strategies are less worse than others beside the fkng old 'better betting B than P' statement, also leaving a potential minuscule possibility to set up a strategy based upon exploitable 'trends' of some kind. 

We hugely respect such statistical experts, yet as pure empirical 'practitioners' we dare to make some considerations.

First important feature to look at is that such paper was based upon 'simulated' results and not over real ones.
Naturally we can't take only the possible minuscule good parts of this study and ignoring and just arguing about the global negative conclusion.
Anyway we've seen that at simulated 'random shoes' the 'follow method' tend to performs better than the 'alternative method'.
Notice that this finding totally collides with the old and verified very slight propensity to get the opposite outcome already happened.     
In our opinion the truth stays in the middle, not necessarily merging into a 'neutral' zone. (see later).

Secondly, this study examined just B and P successions, not classified by more 'complex' patterns, especially into the back-to-back form.

Third, we've collected valid reasons to doubt that in every scenario previous outcomes won't affect in some way the next results. At least such negation of 'place selection' supposedly indipendence works at live shoes data.

Fourth, we totally disagree about this study's conclusion:

'Every random walk wanders away from the origin and is never guaranteed to return to the origin.

That's true only whenever we're considering an independent and random source of results or at least over a simple BP successions examined at both simulated and real live shoes samples, but not at more complex baccarat patterns happening at real live situations.

Imo, it's the main mistake almost every scientist had made when studying baccarat (along with the fatal error to consider simulated shoes as the same as real live shoes).

Average shoe's card distribution is way more sensitive about 'complex patterns' successions than about mere B or P hands.

Theoretically complex patterns still belong to the 'random walks' category but in reality they work under a sort of 'conditional probability' where (depending upon the bet selection utilized) they either are proved to roam around the 0 cutoff or even better to take a long term univocal direction being well greater than the common B>P math propensity.

Main answers to that assumption?

First, the average key cards distribution being surely asymmetrical up to some level and for some sections of the shoe.

Second lower level, math two-card advantaged situations not involving key cards but getting an edge more often than not.  And of course even such feature will be asymmetrically placed. Up to a point.

Third level, asym hands math favoring B side. Differently to the two above factors, we know that on average this parameter will strongly shift the results just 8.6% of the times.

If we'd assemble such factors into a whole scheme, we'll see that itlr 'complex' patterns will tend to follow more probable back-to-back values.

After all, we can't think about a card distribution placing ALL key cards to one side for the etnire lenght of the shoe, not mentionting that such key cards must combine with valuable cards to provide a worth result (most of the times a zero value card).

Then it's impossible that a shoe will present univocal winning long streaks of two-card math favored higher points.

Finally, asym hands apparition per each shoe is well restricted into finite terms and of course very few shoes will get ALL asym hands to win after a third card is dealt to the Player side.

as.

Thanks klw!

Here's the link I was referring to:


https://www.koreascience.or.kr/article/JAKO201208040009207.pdf?msclkid=7a459b53ac4011ec901c1c5de08abc42


as.

Here another real live shoes data regarding the same plan I was referring to in my above posts.

First order cluster spots got 1974 winning situations and 632 losing spots (632 x 3 = 1896) that is a 1.04 WL ratio.
Again a too tiny shifted ratio to get the best of it.

Second order cluster spots got 445 winning spots and 103 losing spots (103x3=309) that is a 1.44 W/L ratio.

Even though such samples are quite small under the 'math' lens, definitely and so far there's a strong 'relative' propensity that second order cluster spots move around a kind of a way better probability of success not following general values applied to a coin flip model (we did bet B or P regardless of the B general math edge).

In some way we may conclude that the more we are waiting for certain 'more probable' patterns to show up, greater will be our probability of success capable to erase and invert to our favor the EV.

Btw, WARS ARE PROVED TO NEVER EVER BE AN ANSWER TO SOLVE PROBLEMS. MOST OF THE TIMES WARS BACKFIRE TO THOSE STARTING THEM.


as.

If we want to test the effectiveness of our idea, we should make a lot of experiments.
The purpose of experimentation is not to convince other people but first to convince ourselves. (Galileo).

I'll meekly add to that: 'providing we make experiments under the most replicable conditions we'll meet at the real tables'.

Dice controllers do not test their ability by tossing cubes into a 3 ft felt (al least not eventually) or using Monopoly dice.
Even at black jack some literature has shown that the mere 'high/low cards' parameter could be misleading, so more depending upon how are really shuffled the cards.

Imo, before testing several thoughts should be made when thinking to try to beat baccarat.

1- beside side bets and anyway with many caveats, pc simulated shoes are worthless. We need real phisically shuffled shoes to test our ideas.
I know it's a way faster process to collect data from pc than from a real source, but we have to understand that we'll risk our money at real tables and not at 'simulated' situations, no matter how's sophisticated the software employed.

2- Live shoes are surely affected by a 'bias' of some kind. Even if we do not know the precise directions this bias will take (almost always splitted into sub sequences), such factor will produce a sort of 'asymmetrical' world where a number of some 'expected' situations will come out unproportionally with the number of 'unexpected' events.
Sh.i.t (or heaven) comes in clusters, therefore as long term winning players we must rely upon the remaining non sh.i.t or non heaven world constituting the vast majority of the outcomes.
We already know the importance of setting up numerous 'limited random walks' to bypass such problem.

3- A 'simple' pattern as one single or a double or a 11 streak means nothing.
Instead, we should be interested about the back-to-back probability of getting something, being more expected or not by assessing the actual 'cluster' ratio that will be surely unbalanced in some sections of the shoe.
Sometimes the 'unbalancement' patterns ratio will be too tiny to be exploited but this is the exception and not the rule.
After all gambling is just a 'streaks' issue otherwise progressive plans would have destroyed it the day after its invention.

4- Derived roads do confirm the non real randomness of the bac outcomes (or at least they tend to amplify the baccarat flaws we're talking about), so I'll invite you to register each live shoe under the common four registration lines (BR, byb, sr and cr).
Just the BR must be classified as to instanly get all derived roads you could use a free software by googling 'baccarat scoreboard' working very well on your cell phones.

Notice that no one registration line will be superior to another one (albeit giving slight different long term results), yet by examining four different lines we're simply amplifying the number of betting spots (with the downside of crossing through some colliding spots).

oOoOo

In some way we should compare baccarat to black jack with important favourable features working for us:

- no need to bet anything (or worth) unless we'd think to be advantaged;

- black jack is a one-side bettable game but baccarat is a two-side bettable game;

- the 'no entry at mid shoe' rule doesn't apply at baccarat;

- baccarat scholars are considered by both mathematicians and casinos as pure clowns, that is sure losers.

It's funny that casinos are more worried by facing a sudden $60 bj bet placed by a $20 standard player than a $10.000 occasional wager made by a railbird fellow.

as.

Thanks KFB!


Same plan applied to a different live shoes sample

The beauty of playing baccarat worldwide is that sometimes you meet interesting people wishing to share some ideas about the game.
I'm particularly attracted by players that like to write down and collect the shoes they've played at, on one occasion I've encountered a couple of guys realizing the importance to consider only real live shoes and when they told me they got a fair amount of them I've invited them to share their data with ours.

We completely agreed that while considering live shoes a 'perfect random shuffle' is just a coincidence and not the rule.

So they sent me their live shoes sample that's even greater than ours (by a nearly 50% more amplitude).
We run the same plan as seen as above and here are the results:

First order cluster spots W/L ratio was very close to 1 (1:1), meaning no significant deviations went on either side.
Since we are constantly obsessed by a bet selection capable to get more wins than losses, we took this result as a kind of normal 'losing' situation to look for.
Therefore we are not so interested about a possible leptokurtic curve, the best to set up a progressive plan upon.
 
Second order cluster spots W/L ratio got more 'comfortable' results as the W/L ratio was 1.31:1, that is a well higher value than it was at our sample, more proportionally 'balanced' toward first and second degree cluster spots.

There are some possible answers to that, the most important is that whenever we are considering a supposedly clusters propensity by 'general quality' and not by 'strict quantity', some deviations may easily happen for the actual 'volatility' of streaks lenght.
Anyway if we'd think that along any shoe dealt 'things must change after a X cutoff point' or 'remain at a steady level up to a Y value' (all due to the average card distribution factor), it seems that the more we're restricting the field of operations higher should be our probability of success. Up the point that we will surely invariably get a fkng edge over the house.

Many could ask: "ok, given the relative rarity of bettable possible EV+ opportunities, a 25k live shoes data study means nothing to me. Show me such possible propensity on several hundreds of thousands of shoes or, better, on millions of live shoes dealt".

Even assuming that we're betting an average amount of one hand per shoe, the probability to be ahead after 25k shoes dealt will be zero unless we've found out that a kind of propensity belonging to an average card distribution should work.
Hence after any 25k shoes sample considered, any bet selection capable to get an edge after the vig impact is a sure EV+ recipe.   

Moreover, if an original result succession is asymmetrically affected by reasons going beyond the natural math propensity and binomial features, every sub succession originated from it will follow the same principles as the card distribution 'bias' cannot be altered by different 'pace selections' outcomes.

That means that what happens at the original succession will present the same properties at derived situations.
For now we've just considered Big Road successions (second degree cluster steps > than higher counterparts), what about common derived road lines?

What about other betting plans?

as.

Maximizing the baccarat flaws


As long as we know that all 416 cards are inserted into a shoe and even if casinos would know precisely what is our strategic plan, the probability (voluntary or not) to arrange cards in order to get us losers is ZERO.
Just the math negative edge still works, period. Let casinos be glad about that.

Start with the assumption that if a third card(s) isn't involved in the results formation, the game would be so easily beatable that it wouldn't exist at all.
Actually third card was invented to promote a 'house' advantage centuries ago as players could only bet the Player disadvantaged side.
Only later the 5% vig was conceived to burden the now bettable Banker side (thus mathematically lowering players' disadvantage by a 0.18% degree.

For that matter baccarat inventors 'forgot' to add an edge about the Banker (house) scheme, that is still in use: That is that a Banker 4 two-card point should draw a third card whenever a third card Ace is dealt to the Player (actual bac rules dictate the Banker to stand).
In any other scenario, third card rules advantage the Banker side.

If we play a finite and dependent card game where two-card symmetrical spots are easily beatable, third card rules just tend to confuse but not altering the entire picture.
So even though third card rule won't be in use (91.4% of total hands) bac results are not a kind of endless 'coin flip' propositions as many ignorants (especially at 2+2 forum) keep saying.
So such ignorants are double ignorants (btw hating baccarat but particularly attracted by poker tournaments when many times their whole destiny relies upon a REAL 'coin flip or so' proposition).

Therefore there are two main fields to investigate:

- the possible divergence from a B and P two-card succession (symmetrical probability) distribution related to an independent coin flip succession (symmetrical distribution). First moves around a 91.4% probability over the total outcomes and the second over the 100% of results.

- the average third(s) card impact (8.6% probability) typical of baccarat over the outcomes.

Obviously the first factor will way more likely shift the results as being 10.62 times more predominant than the second one, yet the second factor could 'confuse' the more probable 'flowing line' by different degrees.

Good news is that itlr such different 'movements' converge into a steady more likely line as third card impact can prolong or stop a given pattern by probabilities that we may safely accept as 'symmetrical'.

I know that this sounds as contradictory for what I've sayed so far, anyway we should remember that we won't know the precise spot when an asymmetrical hand will show up and naturally the very slight verified propensity to get the opposite outcome works infinitely.

A statement confirmed by taking derived roads as lines to follow, where blue and red spots do not fit the B and P requisites.

So our betting plan won't be sensible about B or P spots, considering them as virtually equally probable.

Data extracted on our real live shoes sample by playing one of our plans

For simpliciity only Big Road results are displayed here (flat betting scheme).

We got 19.934 winnings by wagering a first order 'cluster' spots.
We got 3907 winnings by wagering a second order 'cluster' spots.
We got 711 losing spots at the first order class and being neutral at second order spots. 
We got 1099 losing spots at both first and second order spots.

In total:

By wagering first order spot we got a 19.934/5717 W/L ratio.

By wagering second order spot we got a 3907/1099 W/L ratio.

Knowing the W=+1 and L=-3 ratio, the W/L was:

first order step: 19.934/17151 (1.16:1)

second order step:  3907/3297 (1.185:1)

Since we didn't make any difference about which side to bet, half ot such winning bets were decurted by the 5% vig.
So:

First step order: 0.95 x 9967 + 1 x 9967 = 9468.65 + 9967 = 19.435.65

Second step order: 0.95 x 1953.5 + 1 x 1953 = 1855.82 + 1953 = 3808.82.

So our real W/L ratio in units should be 19.435/17.151 (1.13:1) at the first order step and 3808/3297 (1.15:1) at the second order step.

Many could argue that a bit over 10k LIVE shoe results sample would be a too small insignificant one to reach some conclusions for, nonetheless we are not so naive to think that any system could get the best of it after even 2k or 3k of real live shoes.
Not mentioning the difficulty to collect a decent amount of live shoes data, the only ones we should care about.

After all, a keen player capable to observe/play an amount of 15 shoes per day, 5-6 days a week, needs almost three years to collect a 10k sample.

More importantly notice that second order clusters will get a higher positive EV, albeit needing more waiting time than first order spots.
You may ask whether higher order classes (third class and superior classes) will get a greater EV but our answer is that we are simply not interested about that for their rare appearance.

This is just one random walk derived from what I've written so far, next week we'll see how another different r.w. will perform on the same Big Road line.
With the consequences that sometimes multiple random walks will collide in the betting selection.

as.

To get an idea about that, in a couple of days I'll show you our betting line made on real dealt shoes.

as.

After having tested a large amount of live shoes, we have reached the conclusion that betting certain spots will provide a huge EV+, of course within the back-to-back probability terms that cannot happen constantly along any shoe dealt.

Say A= winning spot and B = losing spot and a, b and c will be 'equally' probable outcomes.

Most of the times A=B, yet in certain spots A (a+b) > B (c) or A (a+c) > B (b) by unproportional values erasing and inverting the HE.

In an independent and infinite model, we can't guess when A>B but at baccarat we could.

Especially whether we're considering different shapes of limited random walks belonging to the same back-to-back category.
That's because limited random walks don't fit the real randomness requisites by any means.

Deeper will be our bet selection higher will be our EV.

as.

If we'd distribute real live baccarat outcomes into a x-axis and y-axis graphic we know that one side will asymmetrically diverge from the opposite one than a normal bell curve and this happens by the obvious asymmetrical probability as B>P.
So our curve will be more 'vertically' pronounced at B side than at P side.

This thing becomes more interesting when we consider BP sub successions as the common derived roads, for example.
Now red and blue spots examined per every d.r. line doesn't necessarily follow a pure asymmetrical probability as blue=red.

At the same token and for good peace of mathematicians, some bet selections are not equal and we might get a better idea about that by collecting real live shoes samples into a curve, thus showing (or not) that some variance values are unequally distributed along a large sample of shoes dealt.

If our bet selection neglects the math asymmetry, so unwisely assuming that B=P or confirming that red spots=blue spots, we infer that the actual card features will make a slight greater role about the total outcomes, at least in terms of variance.

We have already pointed out the importance to select 'random walks' roaming at most around a 0 point.

In probability theory and statistics we may find a possible answer to this into the 'kurtosis' concept.

Basically kurtosis investigates about the maximum frequency point of a statistical distribution. 
There are three different types of kurtosis curves:

a) Leptokurtic curve

Elements of the distribution are closely concentrated around the mean, variance is minimal.

b) Mesokurtic curve

Elements are spread around the mean in similar but not necessarily in the same way than Gaussian curve.

c) Platykurtic curve

It's a frequency curve showing a kind of flat shape; dispersion values diverging from the mean are quite high.

Obviously when playing baccarat we should be interested to apply a bet selection following just one curve as we know that here and only here the vast majority of results (whether a proper bet selection is applied) will be placed around the most frequent situations that unproportionally neglect general math values.
If some situations seem to deviate too much from the expected profitable line (and there are some cutoff points), we simply accept this and go forward on next sections of the actual shoe or waiting for next fresh shoes.

So if you'd think to get a long term profitable strategy, register your results into a graphic and whether your results will follow a kind of leptokurtic curve, you'll know to be up on something.
Providing to classify a quite large sample of real shoes, best if considered under the most homogeneous circumstances.

as. 

Hi and thanks for your replies.

Of course it would be so easy to argue again about the worthless martingale strategy and naturally it's even easier to talk after knowing the real outcomes.

Anyway there's a common denominator about this bet selection (as 8OR9 pointed out) , that is a kind of 'trend following' approach hoping that in the selected circumstances Player side should be favorite to win. In addition to that, this player like to jump from table to table and betting mainly on the first portions of the shoe whereas it would be wiser to consider the shoe as a 'whole'.

Next, he chose to bet after a 'trend' reached a too high value to be exploited itlr. 
Nothing wrong about wagering towards 'long trends' but they must be caught at the start or at the very initial portions of it, thus playing with house money.
Imo this is more important when we have (wrongly) decided to only bet P side.

I've selected three different spots in the video.

1- Approximately at 16.40 shoe went as PPBBPPBB so 'hero' decided to bet $220 at P side, thus hoping that consecutive doubles will prolong (actually that the last BB pattern will form a double).
That this move collides with my unb plan #2 (after any B double next B pattern must be wagered either in B single or 3+ streak shape) means nothing. The problem is that consecutive doubles are more likely to happen at byb and sr derived roads than at Big Road. Especially when we must fight a natural math propensity to get more B than P.
Then after the pattern was 'broken' by a B 3 streak, subsequent bets were worthless even if we were to bet B side.
Notice that at the first lost bet B side showed a natural 8, then at the second hand B side won by a natural 9.
Third bet made things worse as the hand won by Banker was an asymmetrical hand.

2- At 44.19 a chopping line formed by three hands arose, the last hand being a B.
Hero bet $220 at Player hoping that the chopping will continue but lost.
After a BB pattern broke the chopping line, my unb plan #1 dictates to possibly bet toward a 3+ B streak (1-3) thus prolonging a 1-3 B line (and a 1-2 P line).
Actually we shouldn't be particularly worried about those spots as we've won at both lines previously.
Anyway, when in doubt, keep betting what happened and not what 'should' happen. No B doubles in the past? I won't bet toward them.
Third bet was a completely waste of money as there's no sensible evidence that a strategy will get the best of it by wagering after a precise streak of 3 had happened (no matter which side considered).     

3- Knowing these standard betting amounts, desperately wagering $1760 on the P side after a P 5 streak happened doesn't need any comment.
Hero got the 'misfortune' to directly fall into an asymmetrical hand (P=4, B=5 at the start) when betting huge, the fact that he/she lost the hand after six cards were dealt doesn't change the problem.
Probably most people would think that betting Banker after a 5 P streak would be a worse option than wagering Player.
Actually, imo, no bet should be made at this spot.

Casinos rely upon a slow math advantage flow, so at the same token our bets should rely upon a slow statistical advantage flow.

as.

We will discuss any single of his/her move in detail.

as.

Let's see how a 'new genius in town' teaches us how to play baccarat.

I'd suggest to patiently watch the video step by step, mainly by his/her shoe selection.

https://kzread.info/dash/baccarat-840-does-the-baccarat-king-lose-his-crown/gKmrr8FsmZjJns4.html

as.

Thx Al!

After all 'biases' are just the sub product of card distributions that surely will produce innumerable combinations, but if patterns are examined into precise classes they form a way more restricted (detectable) world. Especially if multiple random walks converge into the same betting spots.
Not everytime but most of the times.

The main problem most part of bac players keep thinking is that such biases 'should' come out around every corner of the shoe.

Obviously we should remember that a 'bias' definition, at least by the terms discussed here, is just an event or multiple events getting a losing counterpart to be more silent than possible.
In other terms, that results will be more asymmetrical than symmetrical, of course in relationship of the proportional general probability to happen.

So imo there are two basic but opposite approaches to win.

a) betting large at very rare situations getting the least amount of variance (different random walks converging into the same betting line by very low sd values);

b) progressively positive wagering a relatively low amount hoping that sooner or later a single random walk 'bias' will get a fair amount of consecutive winnings, until we're satisfied of the actual shoe winnings or that the shoe is exhausted.

Imo only very experienced players could consider intermediate approaches, as those raise the casinos' expectation for the remaining part of bac bettors.

Our personal comments.

Approach (a) needs a vigorous patience for the rarity of betting opportunities, mainly as we need rare unlikely situations to show up at the start or intermediate portions of the shoe.
Naturally it's the best way to get the best of it. Not mentioning that a light negative progressive plan will accelerate the winning process.

Approach (b) needs a strong confidence about the probability that a single random walk will get its fair share of heavy 'biases', providing a finite number of betting spots (say >1 and up to 20, knowing what I'm referring to).
Moreover, more often than not such approach will put the player in behind for a quite long time.
A heafty pro of this approach is that now it's the casino fearing our large bets hoping that a stopping pattern will come out and not the opposite.

Of course there's a statistical answer about all this, we'll see it in a couple of days.

as. 

Multiplications of events

As early as 1926, the gambling expert Henry Chateau anticipated the important concept that no matter how we'd register the results and providing a random source of outcomes, any sub succession derived from the original one will get the same properties. He raised this issue in order to get more betting opportunities without waiting particular 'trigger' apparitions.

A similar concept was fully investigated years later by the eminent RVM math professor who posed the best basis ever of how to consider randomness.

Therefore, we could build infinite sub successions from the original one and nothing will change.
If the source of results will be random, the relative sd values will follow the common stats laws at every sub succession.

So we can write down on our paper only the odd/even results into two different lines, or just the outcomes by a 2 or 3 pace, or splitting the results into columns of 3, 4, 5 or even comparing a pre-ordered random registration to the actual outcomes.
If the source is random and any hand is independent from the previous one/s, the limiting values of relative frequencies will provide the same unbeatable situations.

At baccarat this perfect 'randomness' of the results seems not to work for reasons well known after having read these pages.

Taking for grant that symmetry is unbeatable and knowing for sure that asymmetry works for the most part of bac outcomes as cards cannot be equally distributed at each side, it remains to estimate the average probability that results will follow asymmetrical lines for some time and symmetrical lines for the other part.

Naturally asymmetrical lines follow both math features (B>P at 8.6% of the results) and actual card distribution features.
The first math factor is limited by its appearance as situations when B shows a 4 or a 5 (maximum asym math strenght) while P side is drawing are finite along any shoe dealt. Not mentioning that on asym hands B side will lose an average of 42.07% of the times no matter what.

On the other end, symmetrical hands are not so 'symmetrically' placed as many might think.
Long term data show us that independently of the side considered, a 'shifting' cutoff point (or points)  is/are constantly working making some results slight more likely than others.

Yet the important thing to take care of is that to be really profitable our method should pass every sub succession we wish to consider, meaning that a supposedly independent distribution will be more probable at every single sub succession whatever built.
This is one strong proof that results are not so randomly or independently distributed as a possible 'bias' is spread at different degrees along any shoe dealt.
Sometimes such bias is too weak to be exploited,  most of the times it will.

Again it's the 'clustering' feature that will help us to define the possible profitable situations.

as.