A proficient random walk must falsify the hypothesis that each new hand will be totally independent from the previous ones.
The doubles vs superior streaks distribution is one of the best examples to provide.

The common denominator is that to be really profitable any random walk must show up more superior streaks than doubles, of course knowing that doubles must come out anyway.
So we must restrict them by a 0 (no apparition), 1 (an isolated double) or 2 (a couple of doubles).

Whenever doubles show up clustered three (or more times) in a row, we'll wait for another double coming out after a superior streak.
And so on.
Superior streaks need to be assessed by a back to back scenario, meaning that isolated superior streaks will be less likely than clustered superior streaks.

Among the four common roads (BR, byb, sr and cr) some roads are better than others in doing this.
It's this difference that counts, the element that helped us to devise what to look for.

as.

Hi AJ!

There are infinite ways to consider a coin flip succession: of course no matter how we operate, itlr everything will follow a 50/50 statistical probability. Thus no way to beat it, EV=0. If the game is taxed (what happens at every casino game), EV will be negative.

But at baccarat the card distribution is asymmetrical and finite, rules dictate that sometimes one side is more probable than the other one and the asymmetrical pace of key cards will affect a large part of the more likely patterns distribution.
That means (at least in our opinion) that bac successions (shoes) are "biased" at some points, so the idea that each new hand is completely independent from the previous one(s) is totally wrong.

Most hands are unguessable but not EVERY hand is unguessable. More precisely, many hand ranges MUST follow sooner or later a kind of propensity. A thing that we had discovered by running infinite random walks (mechanical betting) applied to the same shoe successions in order to dispute the common knowledge stating that baccarat results follow a kind of 50/50 INDEPENDENT proposition.
Our "main" random walk is the best practical way to get EV+ spots, well knowing that for sure there are better random walks to exploit (yet needing a lot more time to be used).

 
You observe the first pair of series of 2 Vs Larger Series, and the pair after that is what you consider to be, more often than not, different from the first pair formed?

Yes, this might be a relatively exploitable kind of propensity (at least from a sd values point of view), there are many others applied to the class of pairs belonging to the same category.

More later

as.

Let's consider the doubles/superior streaks patterns regarding the first and the second situation showing up per every shoe dealt. 2= double, 3=superior streak
Here's a brief real shoes sample. First sequence is the natural B/P succession, second succession is our main random walk:

01) 3-3; 3-2

02) 2-2; 3-2

03) 2-2; 3-2

04) 3-2; 2-3

05) 3-3; 3-2

06) 3-2; 2-3

07) 2-3; 2-3

08) 3-2; 3-2

09) 2-2; 3-2

10) 3-2; 2-3

11) 3-2; 3-3

12) 2-2; 3-2

13) 2-2; 2-3

14) 3-2; 2-3

15) 3-2; 2-2

16) 2-3; 2-2

17) 3-3; 2-3

18) 3-3; 3-2

19) 2-2; 2-3

20) 2-2; 2-2

21) 2-3; 2-2

22) 2-2; 2-2

23) 3-2; 3-2

24) 3-3; 2-2

25) 2-3; 3-2

26) 3-3; 2-3

27) 2-3; 3-2

28) 2-2; 3-3

29) 2-3; 3-2

30) 3-3; 3-2

31) 3-3; 3-2

32) 2-2; 2-3

33) 2-2; 2-3

34) 3-2; 3-3

35) 3-3; 3-2

36) 3-2; 2-3

37) 2-2; 3-2

38) 3-2; 2-2

39) 3-2; 2-3

40) 3-2; 3-2

41) 2-2; 3-2

42) 2-2; 3-2

43) 3-3; 2-2

44) 2-3; 3-2

45) 3-3; 3-2

46) 3-2; 2-3

47) 3-2; 3-2

48) 3-3; 2-3

49) 2-2; 2-3

50) 2-3; 2-3

51) 2-2; 3-2

52) 3-3; 3-3

53) 3-2; 3-2

54) 3-2; 3-2

55) 2-2; 3-3

56) 3-3; 3-2

57) 2-2; 2-3

58) 2-2; 2-3

59) 2-3; 2-3

60) 3-2; 3-3

61) 2-2; 2-2

62) 3-2; 2-2

63) 3-3; 3-2

64) 2-2; 2-3

65) 3-3; 3-3

66) 2-2; 3-3

67) 2-3; 3-2

68) 2-2; 2-3

69) 2-2; 3-3

70) 3-3; 3-3

71) 3-3; 3-3

72) 2-2; 3-3

73) 2-2; 3-3

74) 3-2; 3-3

75) 2-2; 3-3

76) 2-2; 3-2

77) 2-2; 3-2

78) 2-2; 2-2

79) 2-2; 3-2

80) 2-3; 3-2

81) 3-3; 2-3

82) 3-3; 3-3

83) 3-3; 2-3

84) 2-2; 2-3

85) 2-3; 3-3

86) 3-3; 3-3

87) 2-2; 2-2

88) 2-3; 3-2

89) 2-2; 3-3

90) 3-2; 3-2

91) 2-3; 2-2

92) 2-3; 3-3

93) 2-3; 3-3

94) 3-2; 2-3

95) 3-2; 2-3

96) 2-2; 3-3

97) 2-2; 2-2

98) 3-3; 3-3

99) 2-3; 3-2

100) 3-3; 2-2

101) 2-3; 2-3

102) 3-3; 2-2

103) 3-2; 3-2

104) 2-3; 2-3

105) 3-2; 2-2

106) 3-2; 3-3

107) 3-2; 2-3

108) 2-2; 3-2

109) 2-3; 2-3

110) 3-2; 2-3

111) 3-2; 3-2

112) 3-3; 3-3

113) 2-3; 2-3

114) 3-3; 2-3

115) 2-3; 3-2

116) 2-3; 3-3

117) 2-3; 3-2

Out of 117 couple of doublets, the first succession formed 63 homogeneous patterns (D-D or S-S) and 54 heterogeneous patterns (S-D or D-S); the second succession formed 43 homogeneous patterns and 74 heterogeneous patterns.

Overall there are 26 situations where BOTH doublets will get an homogeneous pattern (2-2, 2-2 or 3-3, 3-3), thus the remaining 91 events will present a heterogeneous pattern more probable at our random walk.

Obviously there's no a guaranteed rhythm to rely upon, but if a kind of propensity is entitled to show up it'll be by longer positive sequences than negative ones and of course by shorter negative events than expected by a "unguessable" proposition.

The concept could be applied to any BP sequence linked to the CR road or, at a lesser extent, to the small road.

As long as any new hand will not be supposed to provide a conflicting event among different roads, heterogeneous events will cumulatively (slightly) overwhelm the remaining possibilities.

as.

Limiting the field of operations is one of the key to try to beat this game.

Suppose you want to only consider doubles vs superior streaks so singles and 3+ streaks won't be included in our plan.

Is it a good move to hope that doubles or superior streaks simply considered will be distributed in such a controllable way that some unlikely successions won't knock out our plan sooner or later?

That's impossible.
We can't allow those natural (albeit unlikely) card distributions forming endless double or superior streaks successions capable to destroy our plan.
On the other end trying to stubbornly get the best of those unlikely univocal successions will make the casinos' fortune as they are too rare to be exploited.

Example.

Say we want to bet that the very first pattern of every shoe dealt will be a double OR a superior streak. It's not important the real nature of such streak, we want to check how many times a double or a superior streak will start the shoe distribution at any of the innumerable sub successions.
Since doubles=superior streaks and as math teaches us that no matter when we consider a 50/50 spot the probability remains the same, sooner or later we should encounter a 12-15 or greater homogeneous streaks distribution getting a 12/0, 15/0 or even 20/0 ratio.

Now let's consider what happens next after a starting double or a starting superior streak situation per every shoe dealt. That is we want to assess the very second streak nature limited within the "double/superior streak" category.
Our data suggest that the probability that the second streak will be completely independent from the previous one (so getting the common sd values applied to an independent 50/50 proposition) is not so unguessable as many experts keep stating.

More later

as.

Ok thanks!!!
It's an issue we agreed with KFB too.

as.

What's this (I mean the numbers)?

1-10 (Strong and Follow whatever is appearing)

11-16 (Stronger or Immediately turning weak and follow)

as.

QuoteAs you said:

"Extremes" rarely happening make the fortune of recreational players or of those very rare acute players capable to ride those unlikely situations; everything different than that will make the casinos' fortune or creating the basis where professionals will make money."

Yes, 'extremes' most certainly come and go with no protocols except gut feelings the highest majority of the times.  I have made handsome amounts of money when most others were either losing or stumbling enormously on the 'extremes'. 

One has to have a totally clear as well as a neutral mind-set when at the felt.  There is no other way, IMO.

Maybe you won't believe me, but almost half of our strategy is based upon the importance of exploiting some "extremes" as several times you pointed out here.

as.

Per every three C/I patterns considered, the mathematical probability of encountering three homogeneous C or I patterns is 2/8 (0.25%); on the other end when we're looking for a C-C or I-I subsequence happening at a 3-step scenario is 6/8 (0.75%).

Notice that a C/I proposition is quite different than a simple B/P proposition, because in the former situation more hands are needed to form a classifiable event (C or I).
Moreover many intertwined unclassifiable hands are just considered as "neutral".
The same about long clusters we're not interested to chase (for now).

Example.
We just take care of doubles as opposed as superior streaks (3/3+ streaks we name as S here).

A #1 shoe went as 2-2-2-2-2-2-S-S-S-2-2-2-S-2:

Doubles: C-C

Superior streaks: C-I

Both streaks considered: C-C-C-I

Now a more likely #2 shoe as:

S-2-S-S-2-2-S-2-S-S-S-2-2-2-2

Doubles: I-C-I-C

Superior streaks: I-C-I-C

Both streaks considered: I-I-C-C-I-I-C-C

Now a kind of opposite #3 shoe than the previous one:

2-2-S-2-2-2-S-2-2-S-2-2-2-2

Doubles: C-C-C-C

Superior streaks: I-I-I

Both streaks considered: C-I-C-I-C-I-C


In total and assuming a player will bet toward the same C or I scenario already happened we'll get:

1st shoe, doubles: +1, 
1st shoe superior streaks:  -1
1st shoe both streaks: +1

2nd shoe doubles: -3
2nd shoe superior streaks: -3
2nd shoe both streaks: +4

3rd shoe doubles: +1
3rd shoe superior streaks: +1
3rd shoe both streaks: -6

Look about how is relatively easy to follow a pattern even though the examples were made upon a doubles > superior streaks temporarily and unlikely propensity (when a proper random walk is utilized).

Let's make a real example. We'll take care about the cockroach road doubles and superior streaks distribution. (Many starting and ending hands are cut off from the registration).
D= doubles, S=superior streaks B=both streaks

D: C-I
S: I-C
B: C-I-I-C

D: I-I-I
S: C-C-I-I
D: C-I-C-I-I-I-I

D: C-I-I
S: I-I-C
B: I-C-I-I-C-I

D: C-C-C
S: I-I
B: C-I-C-I-C

D: C
S: C-C
B: C-C-C

D: I-C
S: C-C
B: I-C-C

D: C
S: C-C
B: C-C

D: C-C-C
S: I-I-I
B: I-C-I-C-I-C

D: I-C-I
S: C-I-C
B: C-I-I-C-C-I

D: I-I
S: C-I
B: C-I-I-I

D: C-C
S: C-I
B: C-C-C-I

D: I-C
S: I-I
B: I-I-C-I

D: C-I
S: I-I
B: I-C-I-I

D: C-C
S: C-C
B: C-C-C

D: C-C-C
S: C
B: C-C-C

D: I-C-C
S: C-C
B: I-C-C-C-C

D: I-C
S: I
B: I-I-C

D: I-I-C-C
S: C-I-I
B: I-C-I-I-C-I-C

Easy to find out the line where C or I symbols tend to get the greatest amount of shifts or the most limited homogeneous back to back patterns.

as. 

Basically for any two A/B opposed events considered there are only two different statistical shapes showing up along any shoe dealt:

C= clustered (AA.. or BB..)
I= isolated (AB or BA)

Thus and by now the clusters lenght won't be taken into account here.
So AAAA or AA or BBBBB or BB will be ALL clustered apparition.

Say we want to classify three C or I patterns in a row, of course we'll have 8 possible patterns:

1) CCC
2) CCI
3) CIC
4) CII
5) III
6) IIC
7) ICI
8.) ICC

In essence per each shoe dealt it's the rhythm of presentation of such 8 possibilities that counts, especially by knowing that after having "concentrated" the various patterns distribution in this way, the short sub succession won't be much longer than three (in our example), four or five steps.

More later

as.

For one moment say we want to make a living at this game.
We choose to exploit the doubles/all other superior streaks ratio happening at some random walks.

Mathematically itlr doubles= superior streaks, but this thing happens just when we'd consider B/P consecutive hands.

More important is what we'll expect by ANY shoe dealt in terms of doubles/superior streaks ratio.

Statistical data had taught us that most part of shoes will provide a doubles/superior streaks ratio shifted toward the right side. Meaning that at most part of shoes superior streaks will overcome the number of doubles.

Obviously an inferior part of shoes must provide a decent number of doubles as they must catch up such a natural imbalancement.

When a shifted asymmetrical ratio is working (here is superior streaks vs doubles), we'll expect more clustered shoes getting a final negative total than positive ones, the same about getting isolated losing shoes or two consecutive losing shoes.
The only important feature to properly take care of is WHEN and how much clustered doubles won't make room to get a superior streaks balancement. And this feature is in direct relationship of how many hands were dealt so far in the actual shoe.

Of course a professional player is not interested about how much a propensity will show up or being balanced by precise numbers, just content to know that a given shoe will more likely produce a doubles/superior streaks ratio shifted toward the right side.

Theorically the best mathematical move is to wager the previous deficit by adding one unit as it's sufficient to get any kind of superior streaks/doubles unbalancement getting at least one favourable step to erase any deficit. Then we'll restart the process, either by continuing to bet the same shoe or (better) to wait for another one.
This is a concept already discussed here.

Yet there are many tools to lower the betting amounts, lacking the precision of progressive schemes but being very welcome in practice. We'll talk about them next week. 

Example.
Data are extracted by Aria casino (LV) real live shoes (machine shuffling).
Final + or - values are the reflex of the doubles/superior streaks ratio, so any positive total is a shoe getting more doubles than superior streaks and vice versa:

01) +7
02) -3
03) -2
04) -5
05) +4
06) -1
07) -4
08) +4
09) -3
10) -2
11) -4
12) -2
13) even
14) -1
15) -3
16) +1
17) -3
18) even
19) even
20) -2
21) -5
22) -2
23) +4
24) +2
25) -1
26) even
26) +3
27) -4
28) -3
29) -3
30) -5
31) even
32) -4
33) -5
34) +1
35) +1
36) -1
37) -4
38) -6
39) -3
40) -2
41) +1
42) even
43) -2
44) -1
45) +5
46) even
47) -3
48) -5
49) -7
50) even
51) -1
52) +3
53) -1
54) +3
55) -3

In this insignificant small sample I do not want to emphasize the overall negative value (that is there are more superior streaks than doubles), just to point out that positive shoes are not coming out around any corner; then permutation issue is an additional factor to work for.

I mean that even though a shoe would end up as positive (unwanted doubles propensity overcoming superior streaks), an initial favourable situation (starting W) or any W/L sequence capable to get at least one step of advantage (LWW, LLWWW, LWLWW, etc) will erase any deficit.

To say the truth, those "even" situations are not going in our favor as the vig will impact our economical results.
In the remaining cases and given the relatively low number of fightings, vig will just reduce our wins.

A safest and wiser approach would be to raise the standard bet by percentages (10%, 20% or more) after any positive (so unfavourable) or negative (favorite) shoe.

Then adding a situational clustered/isolated factor as we do not want that some rare shoes full of doubles will pose a serious threat upon our plan.
A thing we'll consider next week.

as.

About streaks our random walk(s) provide interesting statistical features helping to devise a less than a hyper selection strategy.

For example, consider doubles.

Per any shoe dealt, doubles number should be equal to any superior streaks number, meaning that itlr the number of shoes of doubles/other streaks ratio will be equally distributed.
In the sense that at the end of each shoe the probability to get more doubles than other streaks (or vice versa) will be symmetrically placed.

Actually this isn't true, as itrl there are more shoes presenting superior streaks than doubles.
Obviously shoes presenting final ratios shifted toward doubles tend to get greater than average final totals just to try to balance a more probable superior streaks propensity happening for every shoe dealt.

More later

as.

Hi KFB!
A very good reading as always..I'm looking forward for more stories..

as.

The average shoe is a mix of various patterns, the common denominator is that two linked events (whatever taken) are more likely to come out clustered than isolated, then but only then the expected less likely opposed event should come out more isolated than clustered.

At the same time  less likely events (as 2 or 3 numbers) whenever they show up clustered they are entitled to make more room at lower classes (0 and 1) being clustered at least one time.

Anyway as long as any number hadn't show up so far, we simply consider it as not existent. But this a difficult topic to insert in our plan.

Thus say our enemy is a 1 apparition vs a 0 and 2/3 event.

Itlr 1-1 are equal than 1-x, yet 1-1-x are more probable than 1-1-1

Nonetheless, clustered 1s are well definied in their apparition, meaning that isolated 1s are not getting sd values typical of a coin flip model.

I mean that clustered 1s are not overcoming the 1s isolated counterpart for long.

The same about isolated 0s vs clustered 0s.

as.

Say we assign a number range (0,1,2,3) to patterns having an asymmetrical or symmetrical probability to show up.

Thus

0 = 1,2,3

1 = 2,3

2 = 3

Since we want to falsify the hypothesis that 0 vs 1,2,3 or 1 vs 2,3 or 2 vs 3 propositions will get the same unbeatable sd values typical of an independent coin flip model, we are transforming the shoes into number successions then studying the number sequences.

So for example:

How much is the longest gap between two 0? Or, it's the same thing, how much is the longest gap between two numbers different than 0?
Or between two 1 or two 2/3 classes?
And what about 2 vs 3?
What are the more likely gaps of such propositions?

More interesting is the evaluation of how many times a given number will be followed by the same number or by a different number, of course taking care of the corresponding probability.
So 0/0 = 0/1,2,3;  but 1/1, 2/2 or 3/3 are 3:1 underdog to show up.

Besides of the 0/0 scenario, once a number will be followed by the same number we're not interested to know what will happen most, thus waiting for a new number to show up.
There are important exceptions about this statement, we'll see them later.

See you later

as.

We're deadly sure to play baccarat with an advantage but to reach this conclusion we had to dispute some common concepts made by experts denying any possible edge over the house.

a) Cards have no memory

Sure, but standing/naturals and drawing hands move around more likely ranges. The same about the important asymmetrical hands favoring the Banker. And those situations might be easily transformed into numbers.
Thus one hand means nothing, two-three hands could mean nothing, but ten hands most of the times mean more than one could imagine.
We need time to figure out how much a deviation will more likely stand up or stop. Yet basically casinos hope things will take a heterogeneous so more undetectable shape, in a word they try to take advantage of the "time" factor by two features:
- by playing a lot of hands the player has a zero probability to be more right than wrong for long;
- time dramatically increases the casinos' math edge, especially when players try to guess this or that without a solid foundation of how things really work at baccarat.
Translation: we need to understand how an "average shoe" looks like. Casinos win a lot of money not for the tiny HE, but because they get the full value of those undepictable "average" shoes where everything seems to stand too shortly to be exploited.

b) Hands are randomly distributed

This is the classic conclusion of those ignorant "I do know everything about baccarat and gambling" experts.

To say that each hand will more or less whimsically and eventually win is not the same that stating that winning/losing hands successions are forming W and L more likely (so detectable) ranges.

In fact, a baccarat random world implies sd values typical of a close coin flip game, then whether the perfect randomness should really act, every point considered of the rw succession must get the same results expected from a CF independent model. It's the simplified RVM definition of randomness.

This randomness definition can only happen at roulette where each spin is totally independent from the previous one(s) at every succession's point considered.

At baccarat each step will make a change (albeit being small) in the future probability considered by an expected long term probability and an actual probability.
It's a conditional probability acting at various levels, most of the times following the average shoe texture mentioned above.

c) Patterns are worthless

There are patterns and patterns.

Humanly perceived patterns are just constituting a minuscule part of all bac succession features.
In reality any B/P succession is the source of infinite A/B sub successions, the common displayed "roads" are just 4 or 5 different "pace/geometrical" shapes of the original sequence.

Stating that ALL patterns are worthless means to have investigated the thousands of sub succession possibilities, that is applying as a rule the same "fresh" probability to any new event coming out.
We're sure nobody investigated more than 20 or 30 different random walks before making any kind of statement.

Next time we'll see how our algos manage numbers by a fictional progressive scheme that sometimes will reach the real betting parameter.

as.