Asymmetry and symmetry

Baccarat is a sure asymmetrical model as card ranks cannot be distributed proportionally along any portion of the shoe dealt. And there are many cards forming a bac shoe.
Moreover when cards are properly shuffled, different ranks are getting a "more likely distribution" producing a large number of "low" asymmetry and few sections of "moderate/high" asymmetry.

Virtually the symmetry doesn't exist unless for a coincidence; And we can't forget that the two fighting events (B and P) will get an asymmetrical probability at the start.

But if you want to try to make a living at this game you should understand that there are many different shoe productions incorrectly considered as equal when they are not.

Randomizing a 416 cards shoe is not an easy task and actually we players cannot have a bit of knowledge about how and how much shoes are really randomized.

The only situation to get more informations is when a new shoe or a same shoe is either manually or repeatedly shuffled under our eyes and this thing happens quite rarely.
In fact nowadays the vast majority of bac shoes are:

- machine shuffled (mainly by a SHFL machine), utilized more than one time with two alternating decks;

- preordered shuffled, utilized just one time.

Honestly and besides Vegas and some other US casinos, we do not trust any casino in the world so we're prepared to assume that cards cannot be properly shuffled at any shoe dealt.

The utmost interest of any casino in the world is to offer random situations, yet strong unrandom distributions itlr tend to favor the house and not the players.

Think about those "weird" blackjack infamous shoes coming out in a row when the distribution sounds as low cards/neutral cards/high cards and where it's almost impossible to extract an edge.

Believe me or not, our algorithms had taught us to realize when a shoe is profitable (so enticing a larger number of bets at that shoe), neutral (so itlr producing a slight loss for the EV-) or unprofitable no matter how deep we'll select our betting.

At the end the common denominator is the asymmetry level: When asymmetry reaches too high values at the shoe played (B category), we're navigating the "tourists' hope", meaning that this shoe is too much affected by a NOT average distribution enticing a possible negative multilayered progression. Anyway best option remains to stay still.

On the other end, those more probable shoes belonging to the average category might be exploited even better by a progressive multilayered positive plan, especially towards clustered events of low levels of happening.

Example.

No matter what random walk utilized, suppose we're taking care of doubles vs superior streaks.
Thus 0=no double (so a superior streak), 1=one double intertwined by two superior streaks, 2=two doubles between two superior streaks, and so on. 

More probable asymmetry levels about doubles move around 0, 1 and 2 levels.

The actual (real) shoe went as 0, 0, 0, 3, 0, 1, 2, 1, 0, 2.
A derived road went as 0, 0, 0, 0, 1, 0, 3, 1, 0.

Another shoe:

0, 0, 0, 4 (so 3), 0.

Derived road: 4 (so 3), 1, 1, 1, 2.

Now let's take the opposite situation, that is superior streaks vs doubles.

3, 0, 1, 1, 0.

Derived road: 4 (so 3), 1, 1, 0.

Tourists hope that "huge" numbers will come out for long or that a given same number will show up as long as the shoe could.
Professionals will take the same route whenever LOW numbers come out shortly but when "huge" numbers (dictating a greater than average level of asymmetry) seem to be predominant (suggesting a moderate/high asymmetry level) are simply not interested to chase a kind of "too deviated" world, maybe discarding from the possibilities very low numbers as 0.

We're fully aware that those considerations are directly falling into the Gambler's fallacy world and actually we have no reason to let "experts" to think otherwise.

All baccarat players are pure donators, period. 

as.   

Hi KFB, thanks, it's the same for me. Even if I don't reply very often, I really read and reread every post you present here.

Distribution of pattern numbers

That given numbers alone cannot get us an edge by predominating over other numbers is sure as hell, yet each shoe dealt will present a "more probable" numbers distribution for the finitess of the elements producing the results and for the related math features.
For example, when a huge number (3) shows up, we have to "guess" what will be the more likely next number to come.

Long tests have taught us that after a 3 number, there's a very slight propensity that next probable number will be 0 or 1, then 2.
Thus the least probability is assigned to another 3. It means that back-to-back "huge" number patterns are not coming out around any corner.
This shouldn't lure us to bet for any number different than 3 after a 3 even though a same succession won't form many simultaneously derived lines having the 3-3... shape.

Even worse is thinking that after a 3-3 succession, best bet to make all the time will be against one more 3 number.

Actually any 3 single number should be considered as a sign of a moderate/strong asymmetrical distribution deviating from the more likely "light" natural asymmetry.
Good news is that an interesting part of total shoes won't perform a single 3, so giving us a kind of "freerolling" by betting any of the other numbers.

On the other end of the spectrum 0s vs any superior number or 1s vs (2s-3s), will constitute the core of the light asymmetry.
Now differently than other mentioned techniques getting a 0.75%/0.25% general probability, here we are talking about a kind of 50/50 probability propositions.
Naturally linking 0s and 1s vs anything else will merge into a 0.75 p. 

Interestingly and obviously, the light asymmetry (0 and 1 numbers) tend to come out either  clustered at some levels or rarely distributed along any shoe*.
Most of the times single shoes do not produce balancements of a previously silent number, paraphrasing it's the classical example of "very good shoe" (no balancement) or "very bad shoe" (many balancements, thus chaotic undetectable flow).

*: Chasing the light asymmetry to be clustered is a way minor mistake than chasing a number never happened or few happened so far, especially if it's a huge number.

Labeling a shoe into a more probable category ASAP

Schematically and even knowing that things could (!) change along the course of a shoe, we'll have just two shoe types:

A- Light asymmetry predominant shoes (average shoes)

Patterns are consecutively short, huge numbers come out rarely or even not at all.   

B- Moderate/strong asymmetry predominant shoes.

One or two long patterns apparition is a long term reliable tool to look for, two huge numbers coming out rapidly are a fair sign of strong asymmetry somewhat affecting next shoe parts.

There's another important technical factor helping us to approximate at best which A or B category each shoe dealt belongs to that I can't discuss here.

At the end, average shoes entice a low numbers betting placement; Conversely B category should orient us to get rid of just one number: 0.
That means to encourage the use of a multilayered positive progression at A shoes and a multilayered negative progression at B shoes.

See you next week

as.

Hi KFB! Thanks for your interest.

In a couple of days I'll be back.

as.

Bet selection Target

It's the average shoe card distribution, in a word we do not need to guess anything so just focusing our attention about the more probable fluctuations of opposite elements that of course roam around a 0-x range.
0= no given pattern appearance, any number different from 0 (x) is a fluctuation considered at various levels (1, 2, etc) of the same given pattern.

Obviously each number will "fight" with the superior class number and itlr we'll expect the same inferior class to be equally distributed with the superior class (for example 0= any number different than 0, 1=any number different than 1, etc).
Not surprisingly most likely numbers to encounter are 0, 1 and 2.

But what we really need to build a successful plan is to spot how's the more probable shoe distribution in terms of numbers.   
 
Baccarat successions

Each shoe is sensitive by a strong asymmetrical card distribution that not always translate into an asymmetrical results succession.
Say that when something seems to be too symmetrically placed it's just for coincidental factors.

At any rate, such asymmetry must be transformed into numbers as computers like numbers and not "feelings".
But as humans and knowing that we can't use a software to predict the outcomes, we'll have to approximate at best which numbers are more likely to come out and especially WHEN.
Simplyfing, we should use a kind of on/off action for every pattern situation coming out, conceding a fair room for mistakes.

Even by enlarging the number/amount of bets placed, when in doubt the best move to take (by far) is to stay still.

Silent numbers, repeating numbers and gap numbers

Every asymmetrical model relies upon the likelihood that something didn't happen or happened too little to be properly considered.
Naturally we have to take into account that each number will fight against a proportional superior number.

On the other end, more likely numbers as 0,1 and 2 (at different levels of apparition) must be considered not only by their "quantity" but even by their "range apparition".
Notice that such numbers are assigned to each pattern we are willing to classify.

Merging huge numbers into the same category

It's an old story if you have already read those pages.
Fluctuations equal or higher than 3 remains fluctuations of 3.
In our opinion this is the main factor why bac players would think to get a kind of (fake) advantage whenever huge numbers come along.
Actually huge numbers make the casinos' fortune, luring players to bet toward endless profitable situations that by any means are less likely to happen than a more "splitted" world.

On the other end, when such unlikely situations happen acute players must stay still, giving a fk about short term flukes.

Choosing the situations when to bet or not, how to devise the best low risk/reward betting plan will be discussed next.

as.

A progressive multilayered plan based upon the shoe "average" card distribution

Suppose that we feel so confident about the game that we want to increase significantly the number of bets placed, now by quitting our beloved flat betting scheme.

Our very large live shoes sample will constitute the basis and we'll try to manipulate the most deviated shoes into consecutive or short gap situations, so to test whether not average shoes can destroy a progressive plan.

More later

as.

It's a honor for me to be here sharing ideas with KFB and Alrelax (and some others), true real world class experts (and foremost real players as we are).

KFB wrote:

Though your post isn't about Ties. When debating coin flips with Bac or other supposedly even-chance games I always remind the other person that coins don't have Ties(land on their edge). Ties' affect on the overall outcomes are often overlooked IMO. Especially their influence on length of streaks. It is my opinion Ties absorb potential slightly more from one side.

Excellent point, IMO.

Always considering ties as a kind of "neutral" outcome constitutes a possible mistake; there are no evidences that a baccarat betting model/approach isn't affected by ties, actually and accordingly with other scholars we have found that shoes particularly full of ties are less detectable than "poor or average tie" shoes.

Unless a player is mainly interested to get comps, I'd suggest to avoid to wager at those heavy tie shoes as more often than not the entire picture is somewhat blurred by a more random (so undetectable) production.

as.

For example take the results table two posts above.
Say we're betting towards 0 or 1 at the very first occasion of every shoe dealt.
21 times out of 133 no 0 or 1 had shown up, of course that means that per every no 0-1 situation, we are going to lose 4 hands in a row.
Theorically all those 21 times could come out consecutively so destroying every sophisticated multilayered betting plan (well prior to that 21 cutoff point).

On the other end, if 21 times out of 133 are losing hands (2) clumped together, we'll expect the remaining winning hands to be astoundingly clustered.

Moreover notice that 36 times out of 133 there are no consecutive doubles for the entire shoe.
Then and at any stage of the shoe, the more probable "number" to encounter is 1 and of course number 1 doesn't fight with 0 but only with number 2.

So let's discard all 0s and see how many times 1 and 2 come out at the very first step of any shoe dealt:

- 74 times a 1 number came out;

- 20 times a 2 number came out.

Short term variance?
Bighorn.sh.it.

Again "unusual" card distributions could come out in a row, but at the end the asymmetrical average shoe composition will make more probable to cross low levels of so called "symmetry" than the opposite situation.

Do we want to consider the second step of any shoe dealt?

Now we get:

- 38 times a 1 number came out;

- 13 times a 2 number came out.

Even though now proportionally taken 2>1 (just for one step) we see that those patterns are roaming around the neutral cutoff point, meaning that strong deviations privileging the symmetry do not take the room of the more likely asymmetrical situations.

In fact even the third step (when applicable) is shifted towards the 1 number and not towards the 2 number.

17 times a 1 number came out;

4 times a 2 number came out.

Those simple examples should give the idea that more selected will be our betting plan better will be our positive results, variance considered.

Asymmetry will always reigns supreme over the symmetry. Yesterday, now and in the future.
Even if a card distribution is voluntarily manipulated to get long symmetrical patterns for long.
A theorical (illegitimate) thing that could easily bypassed by building some random walks derived by the original succession.

as.

True, every shoe is a world apart yet some situations are generally more probable to come out or, at least, not performing a huge volatility.

Definitely the game won't produce huge homogenoeus patterns for long/moderate time, especially if we put some limits about classifying a "pattern".
Setting up a limit to each pattern we're interested to bet at could be interpreted as a strong example of gambler's fallacy but it is not, IMO.

A possible reason beyond that is that a fair amount of hands will take an "unsound" math direction, so disrupting a kind of more "normal flow" that might be easily perceived as a long univocal pattern.

More later

as.

Real shoes sample (very slight penetration), only Big road displayed:
0=no consecutive doubles, 1= two consecutive doubles, 2= three or more consecutive doubles. 

1- 0
2- 1
3- 1
4- 1
5- 2
6- 1-1-1
7- 1-1
8- 1-1-1-1
9- 1-2-1
10- 0
11- 1-1
12- 1
13- 1
14- 1-1
15- 1
16- 1
17- 0
18- 0
19- 1
20- 1-1-1
21- 1-1-1
22- 1-1-1
23- 0
24- 2
25- 0
26- 2-1-2
27- 1
28- 2-1
29- 1-1-1
30- 0
31- 1-1
32- 1-2
33- 1-1
34- 1
35- 1-1-1
36- 1-1
37- 1-1-1
38- 1
39- 0
40- 2
41- 0
42- 1-1
43- 1-1
44- 1
45- 1-2
46- 0
47- 0
48- 1
49- 1
50- 1
51- 0
52- 0
53- 1
54- 1-2
55- 1-1
56- 1
57- 2-1
58- 1-1-1
59- 0
60- 1
61- 1
62- 0
63- 2-1
64- 0
65- 2
66- 1-2
67- 2-2
68- 2
69- 0
70- 1
71- 2
72- 1-1-2
73- 1
74- 2
75- 0
76- 0
77- 1
78- 1-1
79- 1-2
80- 1
81- 0
82- 0
83- 0
84- 1
85- 1-2
86- 0
87- 2
88- 1
89- 1-1
90- 1
91- 1
92- 1-2
93- 1
94- 2
95- 1
96- 0
97- 0
98- 0
99- 1
100- 1-1
101- 1-1
102- 1
103- 1-1
104- 1-1
105- 2-1-1
106- 1
107- 1-1-1-1
108- 2
109- 0
110- 2-1
111- 1-1-2
112- 0
113- 1-2-2
114- 1-1-1
115- 1
116- 0
117- 0
118- 1
119- 2
120- 0
121- 0
122- 2-1
123- 1-2
124- 2-2-1
125- 0
126- 0
127- 0
128- 1-2-1
129- 1-1-1-1-2
130- 2-1-1
131- 0
132- 1-1
133- 1 (s #19240)

It seems that longer streaks of consecutive doubles are not showing up so often, despite of being the most pattern occurrence.

as.
 

Coin flip successions vs baccarat successions

Comparing coin flip tosses with bac successions is a pure mistake as the former model remains always independent but bac results are somewhat restricted by the average key cards distribution and, more importantly, by their sure asymmetrical distribution.

It's obvious that besides of the key cards average distribution, baccarat card combinations forming huge points (e.g. 6-3 or 5-4, 2-5, etc) move around the same concept, so what seems to be perfectly "randomly" distributed actually it doesn't. By any means.

An overalternating W/L CFS movement will happen just when consecutive B/P doubles will happen, anything different than that will get a + or - clustered line.
Such feature could be better exploited by running several random walks derived from the BP original succession.

How many consecutive BP or A/B (whatever considered) doubles are going to show up per each derived road considered?
Maybe setting up a cutoff stopping value for each alternating succession might be a good idea.

as.

Relationship between probable and improbable events at baccarat successions

Only unaware casinos could offer side bets for final winning points, no matter how's the HE (well...up to a point).

Fortunately we can do the same job by assembling the various BP hands distribution even though we know that half situations will go there and half will go here.
But by setting up a plan at BP hands we know to lose a lot of precision (so profitability) but facing a way lesser HE.

More later.

as.

Hi KFB, good thread and link!

I totally agree with your comments;IMO and especially at gambling we should be way more interested about the probability of something NOT happening.
Then (at gambling) there's the art to try to avoid the total impact of those "improbable" events that sometimes could be even turned in our favor.

Maybe we should use the key factor why casinos will get huge profits: time.

as.

Example.
How many times a different than 6-7-8-9 winning point category comes out as clustered (some shoes sample)?
0= no clusters, 1= one cluster and so on.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1.

Ok, it's more likely that such 0s derive from a 6-7-8-9 winning point happening at P side than at B side.
At the same token, it's more probable that 1s come out from a 6-7-8-9 category falling at P side than at B side, so stopping the opposite category to be clustered more than one.
And so on.

as.

Differently than pure coin flip independent propositions, per each shoe dealt (8-9 points) vs (any other winning point) move by more detectable ranges, moreover 8s and 9s are slight more likely to show up at Player side than at Banker side.

In fact the total number of 8s and 9s final points at B side account for a 27.4% probability whereas at P side the same total number is 28.8%. (naturally Naturals probability remains perfectly symmetrical between the two chances).
Even 6s and 7s final points are asymmetrically distributed accounting for a 26.3% at B side with P side getting a 28% probability.

Cumulatively 6, 7, 8 and 9 final points get a 53.7% probability at B side and a 56.8% probability at P side.

Therefore if we'd "think" that the next final point or close to the next final point will be a 6,7,8 or 9, we'd better wager Player and not Banker.

Definitely the vast majority of winning points fall into the 6-7-8-9 category.

On the other end, Banker side gets an asymmetrical probability to ends up the hand by a 4 or a 5 point accounting for a 19.4% probability vs a 14% Player probability to show up the same 4 or 5 final points.

There could be all the variance you want, yet itlr any 6, 7, 8 or 9 point is advantaged at various levels to win the final hand.
And as we've seen there's a mathematical factor shifting such points category towards the P side.

In other words, whenever we think that B side won't get a 5 or 4 initial two-card point and, more importantly, that the next final point will be a 6-7-8-9 point, wagering Player side is by far the best option to make.

In fact: Naturals are getting a perfect symmetrical probability to come out but an asymmetrical payement.
All other 9s, 8s, 7s and 6s points get a probability shifted towards the Player side, not mentioning (again) that the payement is quite diverse (0.95:1 than 1:1). Even at no commission tables, such points category will benefit more by wagering P side than B side.

Exaggerating the concept, it's like we just try to get rid of those "low" final winning 5 and 4 points markedly privileging Banker side; almost anything else is going towards Player side for a reason or another.
Even if it seems that many huge points will succumb to greater points or whether a high point falls many times at the "wrong" side.

Naturally B predominating shoes are getting a real threat to this plan, but this is just one unidirectional random walk to be taken care of as the vast majority of the times B streaks need very long sequences to get univocal results at ALL different random walks considered.
If this shouldn't be true, baccarat wouldn't exist.

as.

To cut a long story short, knowing that all 8/9 winning points battle by a kind of coin flip with any other winning point, assuming that cards are asymmetrically distributed along any shoe dealt, and taking care of other tools, we could split every shoe dealt into two distinct categories:

1- Condensed BP pattern shoes (low or very low CFS);

2- Diluted BP pattern shoes (huge or moderate CFS).

Of course the derived random walks (A/B, r/b, etc) will get different lines (very often taking an opposite route) at any shoe dealt but eventually featuring one of the above categories.

It's obvious as hell that at some portions of the shoe (sections) things could easily take a strong opposite way than assessed previously, but we have found to be particularly profitable to make an approximated shoe model first, then trying to make some possible adjustments along the course of it.

After all we just need to be right by few steps per any shoe dealt, one step ahead should be our main goal all of the time.

More later

as.