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.

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. 

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.

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 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.

Great writing as always Asym. I do not think I have ever seen so many succinct statements in any one post.

*so the idea so loved by mathematicians that each new hand is EV- no matter what is a total completely bighorn.sh.it.

**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.

***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.

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


I look forward to your further elaboration.

Many thanks,kfb

Because.....................From so called gaming mathematicians to gaming experts of all types running tests and samples on baccarat running through hundreds of thousands or millions of hands, every single flat bet or mechanically triggered bet will fail ITLR!  Period.  End of story. 

As well, the people playing the game that are able to extract any kind of cash profits out of it, they do so playing a trivial amount of hands/shoes as compared to those testing with their statistics.  Period.

There are most certainly numerous ways to pull profits from the game and although none of them are guaranteed triggers which most everyone is searching for, they work very well for those people who understand what they are doing as well as the game and their emotions, while employing a rock solid M.M.M.  Period.

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.

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.

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.

After 5 resolved hands are dealt and assuming a perfect 50/50 A/B probability, only two hopping sequences are expected: ABABA and BABAB.
At both such successions either A and B come out clustered 'isolated', that is no streak happened at both sides.

In the remaining 30 out of 32 possibilities, A or B singled outcomes can only come out: (notice that eight patterns won't show singled A/B hands)

a) One time 12 times;

b) Two times 8 times;

c) Three times 2 times.

More specifically and considering ALL possible 32 patterns, the same A or B hand show up clustered just at six patterns (ABABA, BABAB, ABABB, BABAA, ABBAB and BAABA).

Obviously that doesn't mean that there's an advantage by betting toward a same A or B scenario to be clustered isolated, just knowing that by taking care of multiple 5 hands samples, a binomial probability produces such distributions.

Nonetheless, baccarat is not a coin flip game, any hand is not completely independent from the previous one(s) and finally one side is math more probable than the other one.
So the question is: Do we have tools to find out a possible factor capable to amplify the difficulty to get clustered isolated spots at BOTH sides?

More later

as.

Answer: Yes.

If certain random walks will produce a slight superior number of streaky shoes than average, the single probability is somewhat slight diminished, mostly as one side could be "singled" oriented for quite long time (due to the asymmetrical issues) but the other one tends to form more streaks than average (so kind of denying a back-to-back single distribution at both sides).

Since itlr almost everything will equalize, in order to restrict at most the negative variance an important tool to take care of will be to utilize the "clustering" effect.
Meaning that slight less likely (long) chopping sequences someway must balance those more probable shoes where singles come out isolated or by couples.
So when a long chopping sequence had shown up, we should be way less interested to make a bet at the future trigger (single), on the contrary isolated and coupled singles should entice us to make  more bets. 

Here a real shoes sample where isolated and double single patterns = W (+1) VS superior single patterns = L (-3):

- LLWLW

- WWWLWW

- WWWWWWWL

- WWWWWLW

- WLLLLW

- WWWWWL

- WLLWWWL

- WLWWWWWW

- LWWLW

- WLWLW

- LLWW

- WLLWWWWW

- LWWWWWW

- WLWLLW

- WWWWWWW

- WWLWWWWW

- WWWWWWWL

- LLWWWW

- WWWW

- WWWWLWWW

- WWWWWLW

- WWLWWW

- LLWLW(-1)

- WWLLWWW

- WLWW

- WWLWLW

- WWWWWLW

- WLWWWL

- WLWWWWWW

- WLWWLWW

- WWLWWWWL

- WWWWWWWW

- LWWWWWWL

- LWWWLWWWL

- WWWWLWWWW

- WWWWWW

- LWWWWWWWW

- WLLW

- WWWWWW

- LWWWLWW

- WWWWWWWW

- LLLWWL

- WLWLWWWW

- WWLLWW

- WWWLWW

- WWWWLWW

- WWWWWL

- WLWWWLWWWW

- WWWWLWW

- LWWWWWWLWW

- WL

- W(-1)

- WLWLWL

- LWWWLW

- WWLLWWL

- WLLWW

- WWWWLW

- LLWWWWL

- WWWWWWWL

- WWWWLW

- WWWWWW

- LLW

- WLWWLWL

- WWWLW

- WLWWWWW

- LWWWWLWWW

- LLWWW

- WWWLWW

- WWWWWWLWWWW

- WWWL

- WWWLWW

- WWWWWW

- LWWWWWL

- WWLWWLWW

- WWWWWL

- WWLWWWW

- LLWWWWWL(-1)

- WWLLWL

- WWWLWLWWW

- LLWWWW

- WWWLW

- LWWWLL

- WWWWWLWWWWW

- WWWWLW

- WLWLWWW

- WWWWWWL

- WWWWWWL

- WWLWWL

- WWWWW

- WWWL

- WLLWWWW

- WWWWWWL

- LLLLL

- WWWWWLWWW

- LWWW

- WWWLLW

- WWWLWW

- WWWWL

- WWWWWW

- WWLWLL

- WWWWLWLW

- WWWWWW

- WWWWWWWW(-1)

- WWWWWLWW

- WWWWWWW

- WWWLWL

- WWWW

- WWLWLW

- WLWW

- WLWWWLWW

- WWWWLLLLW

- LLLWWLW

- WWWLWLL

- WLWWW

- WLWWLWWLW

- LLLLLWWW

- LWWWWWL

- WWWWWWL

- WWWWW

- WWWWWWW

- LWWWWW

- WWWWWW

- WLWWLWWW

- LWWLWL

- WWLWWW

- WWWWLW

- WWWW

- LWLWW

- LLLW

- WWWWL(-1)

- WWWWW

- WWWWWWLLW

- WWLLWWLWW

- LWWWWLWW

- LWWWWWLW

- LWWWWL

- LWWWWWWL

- WWWL (18632)

as.

I guess that the above WL distributions won't make many acute players to lose, factors why this should be accomplished were widely described in my pages.

Our algorithms move around a sequential multistep on/off action, always based upon a given random walk.

1) Singles vs streaks: most distributions move around one or two singled distributions, an interesting part of total shoes dealt won't provide single sequences greater than two. Anyway one/two single situations are more likely to come out clustered than isolated.

2) When a single pattern surpasses the two cutoff clustered value, at the next opportunity we'll play toward a single/double pattern happening. In case of loss we'll wait for another single to show up before betting again toward one/two singled events.

3) Any streak will belong to 2, 3, 4 or higher class, but since the higher class is somewhat restricted in its apparition, 2/3 and 3/4 classes will more likely form clustered events unless the higher streaks are intertwined by long chopping sequences.

4) No matter how streaky is the actual shoe, either we'll win at single/double single sequences or  by assessing the average streak classes clustered distribution.

5) If the shoe presents many chopping events surpassing the 1/2 cutoff value and streaks won't belong to 2s or 3s, we do not have triggers to rely upon.         
Even if this possibility is the less likely to happen,  it do need further comments.

as.

Everybody knows that singles constitute 25% of total hands dealt, the remaining hands will arrange into streaks of different lenght.
So after 20 hands dealt, on average we'll expect 5 singles and 5 streaks; after 40 hands 10 singles and 10 streaks and after 60 hands 15 singles and 15 streaks.

Of course those percentages will equal itlr and also at the vast majority of shoes dealt, meaning that we will expect relatively low deviations.

Yet everybody knows that a single shoe is a world apart, the same about few consecutive shoes dealt.
Think about sections containing 6, 7 or more consecutive streaks without no singles and the exact opposite scenario.
Those are natural "strong" deviations that must be balanced along the way, otherwise the game would be easily beatable.

Anyway such balancement most of the time doesn't act symmetrically as the transitory deficit will be overcome by low or moderate changes of direction, privileging opposite short patterns than long patterns.

More later

as.

Normally anytime we choose to bet a side we hope to be more right than wrong, without giving the proper value to the numerous factors that might alter in our favor the hand's destiny.

Our algorithms act by a different and more sophisticated way: They collect the most number of actual shoe informations and they put them in relationship of a general probability ascertained after thousand and thousands of real shoes data.

It could happen that actual shoe results will substantially differ from "expected" outcomes, that's why we have increased the real betting parameters weight. After all it'll be way better to wait than hoping to be right at too confused situations.

Hoping for the best is the recreational players mantra, expecting the worst and playing the probabilities is the pros way to accumulate profits.

Let's see in a very simplified fashion what are our algos lines of operations.

1) Smaller is the number of bets made, greater will be the probability NOT to fall into the undetectable variance's realm.
It's not a coincidence that casinos want us to make a lot of bets, knowing very well that the probability to be right will esponentially decrease with the number of bets placed.

Notice that casinos will win a lot more money by exploiting players bad attitudes than by taking advantage of the HE, so mathematical issues take a minor role in that.

The math assumption why no matter how are diluted our bets the probability to win is always EV- belongs just to 2+2=5 losers.
Fortunately when a gambling game cannot be resolved by math it remains unbeatable.

2) Since the bac productions are asymmetrically produced whatever the reasons involved, selectively chasing the clustering effect of something will get more positive sequences in quantity and quality than expected by a perfect independent 50/50 proposition.
It's just a matter of time (and we should consider 'time' in a different way than casinos do).

3) Frequency and rhythm are both two decisive factors to take care of, actually casinos and mathematicians do care only about frequency not knowing a fk about rhythms of presentation.

4) Average sd values of certain pattern presentation and distribution.
If given random walks action applied to several thousands and thousands of shoes data provide 2.5 sigma negative deviation maximum levels, it means that the betting model is somewhat restrained in its negative fluctuations. On the other end the positive deviations counterpart had demonstrated to reach 3.5 or even 4 sigma values. A big edge, I guess.   

5) Raising the probability of success facilitates the clustering/isolated pattern distribution.

Anyone reading my pages knows that it's a good idea to rely upon a 0.75 probability distribution as being more detectable than a mere 50/50 or so probability.     
Actually there are times when a given losing bet entices the same losing side to be wagered again and situations when the simple random walks action suggests to bet a side independently of the previous hand's destiny.

Itlr the random walk action takes a primary role, yet when the first (losing) bet was made at Banker side, we have more reasons to bet again the Banker side for obvious reasons.
This is just the sole situation we might alter the random walk pace that we've instructed to consider outcomes as 50/50 placed.

6) More likely distributions

Whereas it's relatively likely to encounter consecutive clustered singles not belonging to the two category, it'll be slight less probable to encounter 2-3 or 3-4 lenght streaks not coming out clustered at least one time.

Exaggerating a bit and for the lovers of progressive plans, after two isolated 2-3 or 3-4 streak situations, a clustered 2-3 or 3-4 event will happen by degrees of probability well superior than what math dictates.

Of course the same progressive plan could be applied by a positive wagering "chasing" the clustered situations superior than two, relying upon the verified long term streaks propensity to form same or next to same lenght categories.

7) More likely events distribution

If we use a 0.75 probability to succeed, we'll get an expected W/L 3:1 ratio, but since any shoe is asymmetrically shaped such ratio will be disregarded several times along any shoe dealt. Say more often than not. 
Thus we should discard from our plan (in a way or another) those ideal average ratios as being less probable than what an asymmetrical distribution will be capable to do.

The list is not over yet.

See you in a couple of days.

as.