Polarization of some random walks

Mathematicians and many gambling experts have demonstrated that either each baccarat hand dealt is a new (undetectable) hand and/or that many known systems have no possibility to overcome and invert the HE.

Whereas the first argument is completely false, it's correct to state that known systems (based upon i.dioti.c math assumptions) have no one possibility to win itlr.

We can't win at a math EV- game by using math tools, but we might win by disputing the perfect randomness of the shoes dealt, that is proving that NOT every hand is a new hand completely unrelated to the previous one(s).

Of course such unrandomness will present itself by different levels, many times difficultly to be detected (or getting too significant levels to be grasped) but sure as hell itlr the so called 50/50 (coin flip) proposition with all the related statistical consequences will go right down the toilet.

A paradoxical finding is that more efforts are made to provide "random" shoes, better will be our probability to get an urn getting a close than average or greater than average R/W balls ratio.
The reason is because more key cards are dispersed, higher will be the probability to get detectable patterns having a superior likelihood to show up clustered at some point.

Such supposedly (verified) propensity could be ascertained by classifying the streaks lenght by merging two adjacent streak classes: We've seen to take care of 2s and 3s vs superior streaks or 3s and 4s vs superior streaks.

We know that in an interesting portion of total shoes dealt, 5/5+ streaks do not show up (especially whenever a given random walk is acting), so giving us a kind of "frerolling", meaning that we can't lose a dime in the process.
Counterpart losing situations may come out when low value streaks show up as isolated between such 5/5+ streaks and now the problem will shift to the more likely singles distribution, so denying a proper number of streaks.

Singles vs streaks sequences

If we'd think that some streak classes will stop before than expected, we might infer than even singles will show up more clustered than isolated.

Actually this is true, providing to consider one side of the two possible successions, meaning that what happened as clustered at one side tend to be slightly clustered and vice versa.
In fact both sides coming out as long singled outcomes are the least scenario to encounter. 

That's a big edge over the house for the reasons that one shoe cannot be equally pattern distributed for long.

We'll get through this next time.

as.

Thus the R/W balls ratio will be always uncertain but the R/W balls distribution will take more likely lines as being somewhat restrained by an asymmetrical probability of success working at an already asymmetrical card distribution.

Obviously the common B/P sequence is the worst succession to take care of, as considering just one side of the operations: The simple back-to-back successions.

Therefore in some sense we should try to amplify the asymmetrical cards distribution factor, challenging it to bypass our two betting steps asymmetrical plan for long.

Thinking that everything will show up anywhere and anytime is reasonable; thinking that the R/W ratio will always deviate towards the W side (where it's more difficult to spot valuable R more probable sequences) is not only impossible but also never happening in practice.

At the start of the shoe we'd assume the R/W ratio should be 3:1, then we must act accordingly to what the actual shoe is producing.

More on that later

as.

KFB, thanks of your very kind words!
And thanks Al for your comment.

Here you are!

Trying to grasp what the shoe is producing is paramount, but knowing the more likely pattern ranges is very important either.

A good shoe is good only after it is displayed on the screen and the "good" adjective is a purely subjective assessment.

On the other end, many pattern distributions per each shoe move around more likely ranges: Those are objective findings that could be worth or not, I guess that those are more important than what people think.

When we play baccarat we shouldn't hope for anything as we should already know what could be more probable to happen or not, that is we're playing probabilities.

Put 48 balls in a urn where 36 balls are red winning balls (+1) and 12 are white losing balls (-3). Then extract all such balls and arrange them in a sequence.
After a very large number of trials, it'll surely happen that the first 12 balls extracted will be  all white balls and of course every other possible combination will happen.
So we should be prepared to set up a strategic plan capable to be ahead for every possible combination, obviously taking care of the relationship about the more likely distributions.

Suppose to increase the number of white losing balls at the same time decreasing proportionally the  number of red balls (total must be 48).
Now after all balls were extracted, catching the red balls spots will be more difficult, especially when after a given number of balls distributed white balls seem to be "too" silent.

Obviously in this example we do not take care of a possible dependency as we'll never know the real R/W balls ratio.

More later

as.

The above A/B situations were deeply studied after having measured the sd values of many two opposed "complex" patterns reaching quite different values than expected, so the idea so loved by mathematicians that each new hand is EV- no matter what is a total completely bighorn.sh.it.

The sd value is the watchdog of randomness, thus whenever two opposing events will show lower than expected sd values after large trial samples, well we know that sometimes the game stops to be random (that is unbeatable) as some sequences become unrandom (so beatable).

Hoping to get an endless series of unrandom spots (no matter how long we've waited for them) is an utopy; confiding that an infinite series of "same situations" will stop before reaching the common expected sd values is a sure fkng certainty.

Streaks

Start to consider ALL streaks as belonging to just four categories:

a) doubles

b) triples

c) 4s

d) 5/5+ streaks

Obviously itlr a = b+c+d, b=c+d and finally b+c=d.

Good.

Since we are talking about a 0.75 probability, we might converge two adjacent streak classes fighting against any superior class (for example a+b vs c+d, or b+c vs d).

Say a+b =A or b+c=A.

At those both A events, the common maximum losing factor is d (5/5+ streaks) and we know that in the vast majority of the times d factor will be well limited per any shoe dealt going from a 0 range to a 5 or 6 range.
For sure itlr such 0-5/6 "d" range is constantly shifted toward the left side, meaning there will be dealt a lot more shoes belonging to the 0 or 1 category than belonging to the 4 or 5/6 class.

Such "unlikelihood" to form many long streaks should make more room to inferior streak classes happening clustered, but sometimes long chopping lines intertwined by those long streaks somewhat deny their apparition.
In the sense that a double, a triple or a 4 streak could come out isolated between steady chopping lines and longer streaks.

Actually and after having assessed that such inferior streak classes came out as isolated more than two times in a row, it's time to raise our standard bet as such unlikely shoes cannot stand for long.
I mean the reasons to raise our standard bet after finding such unlikely situation are greater than crossing two mere isolated A events showing up in a row that became three in a row.

In fact the propensity to get inferior streak classes clustered is in direct relationship of the total number of streaks happening per any number of hands dealt, therefore when few streaks of any kind happened so far (meaning many singles had shown up) the clustered inferior streaks factor will lose a lot of its value.

I'll try to better schematize that within a couple of days.

as.

Managing the inevitable harsh losing situations

Any strategy (especially when a progressive plan is adopted) will be susceptible to fail when very unlikely sequences will show up at consecutive shoes.
That's why is so important to play at a machine shuffled same shoe (MSSS).

In fact our long term data suggest that the average shoe's texture is more likely to come out at MSSS than at every other shuffling procedure.

Anyway and assuming A as positive (p=0.75) and B as negative (p=0.25), it's natural to expect very low values of A and huge densities of B.

For example B despite of its low probability to appear could show up consecutively clustered up to 6 or even more times in a row (anyway a very very unlikely event) and we know that we should be interested to bet toward A only after a single B or best two back-to-back B apparitions, then let it go whatever happens.

On the other end, the A-A category (the least possible clustered class) cannot be silent for long, so constantly managing to fight with the A-B opposite event (now forming an A isolated event).
Even here (B)A-B events may be classified by steps: one isolated step, two isolated steps, etc.
Itlr most A isolated situations will distribute by one or two levels, when not let them go.

Summary

AA = a natural mathematically more likely situation, yet belonging to a random world;

AB = same as above

BA = same as above

BB = same as above

ABAA = a natural math more likely situation, now beloging to a kind of very slight unrandom world

ABABAA = providing the use of a proper random walk, that's the situation we're really looking for as the cumulative number of ABABAA patterns will overwhelm the opposite ABABAB events by degrees capable to erase and easily invert the HE. Unrandom world, that is.

BAA and BAB = random world

BABAA = here there's a long term very slight propensity to get this pattern than the opposite BABAB scenario.

BABABAA = again the real edge we're really looking for (when a proper random walk is acting) as BABABAA patterns are way more likely than BABABAB scenarios. Another unrandom world.

The concept gets one of the best proof by arbitrarily putting cutoff values at streaks (for example streaks of 5/5+ being B) vs inferior streaks, as there are no many shoes dealt forming many 5/5+ streaks.
The sole problem is whenever such long streaks will be intertwined by long chopping sequences without no or few inferior streaks, a thing we'll see later.

as.

The average shoe's texture

The average shoe is any shoe dealt where a given probability to be ahead of something will be very close to 100% as some patterns MUST happen (as their probability to happen roams around low/moderate levels of deviation): It's just a matter of time that trigger patterns will happen; technically this is just a permutation issue artificially emphasized by raising the probability of success and by taking care of the "clustering/isolated" effect.

Suppose we have two different patterns: A having a 0.75 probability and B getting a 0.25 probability to appear.
Say that per any shoe belonging to this category there are 12 possible patterns we're interested at.
Thus out of 12 fighting situations, 8 will be A and 4 will be B.

Arrange the A/B successions whatever you want and you'll see that it'll impossible to build a sequence not getting at least one clustered A event.

Now we want to decrease the number of A by one point, that is now A=7 and B=5.
Again AA must come out at least one time and whether this is the case we'll get a lot of B isolated results.

Let's take a further step, now abandoning the "average" category: i.e. A=6 and B=6.
In this example A could show up everytime as isolated (as well as B) so forming only those two  successions out of 4096 possible combinations:

1) ABABABABABAB or 2) BABABABABABA

So just those two combinations prevent the AA formation.

Going down one more step: A=5 and B=7.

Now it's sure as hell that B will come out at least one time clustered, but this doesn't deny the possibility to get A clustered.

Assuming an average 12 fighting pattern range, shoe situations where A=4 or less and=8 or more can be safely discarded from the possibilities panorama.

Naturally I haven't mentioned the positive deviation counterpart, that is when A=9 and B=3, or A=10 and B=2, or A=11 and B=1, or finally when A=12 and B=0.

It's of particular interest to understand that wholly considered and itlr the number of A will be equal or even inferior to the number of B, underlining again that it's the average distribution that matters and not the numbers.
More precisely, the sd values of the distribution's shape of certain patterns.

as.

There are several ways to lose but there's only way to consistently win: That is being able to take advantage of the most likely winning/losing sequences the game infinitely provides, at the same time trying to get the lowest damage caused by unlikely events.

Since the HE constantly burden on us, long positive (unlikely) sequences should be considered as less important than long negative (unlikely) sequences, even though we've found a kind of an edge by spotting that some events are slight more likely than others.

To cut a long story short, it's way better to let it go a possible long positive sequence than trying to chase long negative successions to stop after they have surpassed a cutoff point of interest.

Thus even if you've ascertained and measured that after long trials in some circumstances A+B>C or that C<A+B (or consecutive C+C...<A+B), you need some time to exploit such propensities as each new shoe is a world apart.

Average shoe's texture

Mathematically speaking casinos get the advantage of a sure edge we can't do anything about, but casinos get a way greater advantage by exploiting a so called "statistical" edge, meaning that the vast majority of shoes dealt belong to the 'average' category, so forming low or moderate deviations of any shape and we well know that the main strategy of almost any bac player in the world is directed to get moderate/long deviations of some kind.

On the other end, some players do not properly take into account that at some shoes the "deviation" negative feature could last for long, forgetting that average shoes (negating any kind of substantial deviation) are more likely to come out only after a fair amount of shoes dealt.

Summarizing, casinos know very well that the vast majority of outcomes belong to an "average" category where most players will lose and whenever an unlikely strong deviation of any kind will happen, they are happy no matter what: Either that deviation will form a players' positive (wrong and temporary) enforcement or they simply let the results go in the wrong direction for long devastating the bankrolls of people thinking that things must change at the actual shoe they're playing at.

That's the reason why our algos mirror (by a opposite way) this casinos' "hope":

a-Not giving a damn about strong deviations at either side of the operations;

b-Getting the best of a more likely "average" world.

Both those points could be practically resolved by a simple clustering effect working or not at the actual shoe we're playing at.
 
Since A+B sequences must be 3:1 more likely than C event, we'll expect to get more clustered A/B sequences than A/B isolated sequences. We won't be interested about their lenght, just about their clustering probability to happen and this will be always overwhelming shifted toward the A/B side.

On the other end, C events should be more likely to come out isolated than clustered, but (as already stated here) itlr and without the use of a proper random walk, C clustered events will be equal to the C isolated events.
Yet things will change a lot whenever we start to consider the back-to-back C probability vs the C-A/B probability.
So C-C-C< C-C- A/B.
A propensity magnified by the use of a given random walk, always knowing that to get an A/B cluster of any distribution we need the appearance of either an A or B event.

See you in a couple of days.

as. 

KFB wrote:

It is my belief we are better off trying to handle a predetermined level of (-)Variance.

That's the key point.

More later

as.

Statistically speaking, at baccarat doubles are the most likely occurence among all possible patterns thus this plan seems to be unsound, yet the probability to catch long negative sequences will be perfectly symmetrical than crossing long profitable successions, but that's not the point of the method.

In fact the method cannot avoid the inevitable long losing sequences, but to get at least one win per every three hands dealt knowing that back to back low or moderate clustered consecutive streaks are not going to come out around any corner.

Before talking about the progressive multilayered plan, let's consider this shoe sequence.
We assume that the first hand of the shoe will start the BBPPBBPP... action, so if the first hand is a B we'll wager toward BBPPBBPP...and if it's a P the action will be PPBBPPBB...etc
In this shoe sequence (#33.317) first hand is a B.

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

Considering the first hand as neutral (but starting a (B)BPPBBPP.... action) we'll get:

-++++-++-++++--+++-+-+-+-+----+-++-++--+--+++------+

We may even consider the perfect opposite counterpart (meaning we'd start the betting with the PPBBPPBB...betting mood) and we'll get:

-+----+--+-----+-++-++++++++-+----+++--+++--+--+-+-+--

It's true that at this shoe streaks superior than doubles account for a +3 overall ratio and that more or less the number of + will equal the number of -, yet there are important distribution features belonging to the - lenght at both differently taken subsuccessions.

For example, we'll get a greater probability than expected that after a single or a double losing sequence (- or - -) next hand will be a winning one.

Here another shoe sequence:

BB
P
B
P
B
P
B
PPPPP
B
PPPP
B
P
BB
P
B
PPP
B
PP
BB
PPP
BB
PPPPPP
B
PPP
B
PP
BB
P
BB
PP

Again what this shoe looks like under a BBPPBB... action:

+++--++---++-++++---++++-+++++++-+-+--++-+++-++++++-+-

Now the reverse mechanical betting approach (PPBBPPBB...):

---++--+++--+--+++----+++-+++++++-+-+--++-+++-++++++-+-

At this shoe things went even smoother.

People having at their disposal a seven or more figure bankroll do not give a fk about long term edge and let alone about our algorithms, they want to bet, win and gamble.
Yet most of them are not so stu.p.id, in the sense that after a greater than 3-hand losing sequence they'd stop their progressive betting, waiting at least for a single fictional win before restarting the action.
But only a small portion of them know that in order to win itlr one must realize that only a huge bankroll could cover the vast majority of negative fluctuations the game will provide, at the same time aiming for a relatively small profit per every session played.
 
See you next week.

as.

The "ignorant" double wagers mechanical betting (IDW)

It's an approach we've studied after meeting a HS player willing to bet progressively and not capable to wait for 'triggers', asking for a mechanical approach.

Say that instead of trying to guess this or that, regardless of the actual outcomes we'll implement a strict mechanical betting placement as BBPPBBPPBBPPBBPP....

Let's see what are the best or worst patterns to encounter:

1) A long double sequences synchronized with our betting

2) The same double sequences perfectly coming out oppositely to our betting.

As long as no "bad synchronized" back to back doubles show up, we're entitled to win at least one time in three attempts no matter how are the results.
So any chopping line of any lenght belongs to this category and of course any streak 3 or higher will catch at least one win.

More later

as.

Yes, that's why is so important to assign an important value to the "clustering effect" of something. That could happen or not in the actual shoe we're playing at.

H-money sounds as the example of the typical baccarat loser, that is one hoping to win big in short frames of time or, worse, to recoup the money lost in the same way. (Yet, this is the best mathematical approach to adopt at an EV- game).
It's very likely he could lose a lot of money even if he would want to mirror our bets.

as.

Baccarat is beatable as card distributions privilege the asimmetry and not the symmetry.

Despite that, per any shoe dealt such asymmetry is underdog to come out meaning that most of the times a kind of symmetry reigns supreme over the total possible results.

It's very likely that casinos do know what we're talking about, so enticing players to make a lot of bets into a symmetrical thus unbeatable world where the HE they take advantage from is a way minor factor role producing their profits.

On the other end, it's 100% certain that casinos do not know a fkng bit about how a symmetrical world would shift into a more detectable asymmetrical model other than by a simple "luck" factor.
After all they rely upon mere math statements and not about intricate statistical features where the decisive factor players should be really interested about is the sd value.

We'll see this in a couple of days.

as.

Hi KFB!!!

As you well know (probably better than us) there are several 50/50 propositions: The general factor working for all of them is the allegedly total independence of each trial, taken for granted that BEFORE every trial the real (not expected) probability is 50/50.

Coin flip successions were deeply studied by eminent experts and anyway they are not bettable at any casino. Yet they could be a fair theorical reference model.

Pass and don't pass lines at Craps constitute a slight world apart (and we've discussed some Craps concepts privately).

Probably the best practical example about both independence and virtual perfect 50/50 probability before every trial are represented by the EC distributions at roulette.

Of course baccarat is a 50/50 game only under the eyes of ignorant and clueless people.
Actually it's a strong asymmetrical game for two different reasons 1- B>P and 2- rank cards are unequally distributed along any single shoe dealt. And among ranks, key cards hold a decisive role upon the outcomes.

Do large data teach us that itlr everything will show up by an expected well verified probability correspondent to a kind of coin flip game or 50.68/49.32 proposition?

Yes, if we do not know what to really look for and one of the tool we should be interested at is the consecutiveness of certain results applied to selected patterns.

Actually after having dissected thousands and thousands of shoes, we reached the conclusion that the vast majority of bac results PER SHOE move around seemingly 50/50 propositions by low levels or even neutral levels of asymmetry, yet rank cards cannot be homogeneously distributed for long so giving room to way more detectable shifted situations.

Streaks lenght is just one factor to be studied, consecutiveness of a given pattern is another one. Merging such those two simple factors provide an astounding probability of success capable to  erase and invert the HE.

In fact and especially whether some random walks are in action, bac streaks are shorter than at a 50/50 game, nevertheless in any instance we do not want to try to stop streaks unless they belong to specific back to back patterns.

More later

as.

Baccarat can't be beaten mathematically but by exploiting results by a frequentist statistical approach.
And one of the possible tool to utilize is to set up a kind of "boundary" plan getting room to more likely patterns of different levels.
The 5/5+ streaks distribution is just an example (see later).

Thus we can't rely upon certainty but upon probabilities and such probabilities become so overwhelming  vs randomness (or supposedly randomness) to assure us an edge.
Providing to wait for given situations to show up as we have verified that after a given event the subsequent event or class of events won't be proportionally shaped differently to what general probability laws dictate.

More hands we want to 'guess' greater will be the probability to fall directly into the random unbeatable world as the strong negative deviations will cause us a way greater damage than the symmetrical marked positive situations for the general EV- impact.

Streaks lenght and distribution

We've seen that per every shoe dealt long streaks (in our example 5/5+ streaks) are not coming out around any corner, but surely they will sooner or later show up by deviated values at either side (ranging from 0 to 4 or more).
Naturally some rare shoes make room to such long streaks without (plenty of singles and no inferior streaks) or intertwined by few inferior streaks coming out isolated.

In the former scenario and for the 'clustering' factor we always should get the advantage from, we won't bet a dime and in the latter case the consecutiveness of such isolated inferior streaks patterns will make a huge role in determining our edge.

Therefore if we assume as C= clustered inferior streaks and as I=isolated inferior streaks we know that itlr C=I.

Things change whenever we'd consider more complex distributions where the simplest is the back to back I occurence per any shoe dealt.

So after C or I anything could happen and the same after C-C, yet after I-I the most probable situation to face is to get a C and not another I. Obviously everything always related to the actual probability of success.
That is another I showing up after I-I sequence will be less proportionally probable than facing a I-I-C sequence.

In poorer words, we need quite of time to wait for such situations (I-I), but whenever they'll come out we can get an indeniable sure edge.
BTW, a propensity working at other similar pattern situations.

There are a couple of principal reasons to explain such streaks (and other patterns) propensity:

a) the general factor causing baccarat streaks to be shorter than at a perfect 50/50 proposition;

b) the finiteness of long streaks distribution, especially after coming out by a consecutive fashion.

In some way a kind of "conditional probability" is supposed to work, meaning that the room to get inferior streaks clustered at least one time is somewhat amplified after two "failed" attempts (that is after two consecutive isolated inferior streak classes happening).

It doesn't matter if our betting class is composed by 2s and 3s or 3s and 4s or even 2s and 4s.
Itlr I-I-C > I-I-I by values greater than the 3:1 cutoff ratio.

See you next week

as.

The number of 5/5+ streaks list provided above wasn't presented 'randomly': those numbers come from the same shoe shuffled by a machine and by an exact back-to-back order.

There are infinite ways to dissect such numbers presentation, one of the simplest (from a practical way of thought) is the probability to get consecutive shoes NOT getting 0, 1 or 2 'long' streaks:
at this very small sample we got a five and a four consecutive 3/4 streaks number per shoe.
The average probability (at least for this sample and taking care of a precise random walk action) any shoe provides 3 or more long streaks is around 18.3%.

So it's like losing 5 or 4 preflop all-ins in a row having AA vs any inferior pocket pair at NL hold'em.

What I mean is that at baccarat a supposedly propensity must always be taken very cautiously, even if considered by entire shoes.
It's obvious that consecutive "above average long streaks number" shoes do not deny a possible advantage but surely will make relative harsh times to deal with.
Moreover we have strong reasons to think that machines do not produce perfect random outcomes working for a same already distributed shoe, especially whether a sophisticated random walk will be able to pick up some "bias".

More later

as.