Hi Asym. Good topic(singles/doubles clustering). In your post #1001 above you said:

"...Attack #2: singles/doubles clusters vs 3/3+ streaks

This attack studies the average probability to get singles/doubles clusters, meaning we need to get one "fictional" winning hand (that is a single or a double) in order that a s/d pattern will be classified as an "isolated" outcome (1) or a "clustered" outcome (any number superior than 1)...."

So to clarify you are calling a cluster: A single-double cluster is like PBB or BPP in two consecutive columns on typical tote board??

"OR"

Do you mean a single P cluster is like bbxx P BBxx then very next column is precisely P , then fourth in a row column is BBBX or whatever as long as not a single P???

Thx in advance,

Hi KFB!

It's the first option you described.

More simply for any 'cluster' (value 1) I mean any single-single or double-double or single-double or double-single situations. 

On the other side, isolated s/d events are just two: single-triple (3/3+) and double-triple (3/3+).

The remaining possibility is to cross a triple-triple pattern without any single or double intertwined, a situation we are not interested about.

A further pattern plan is to consider the singles as neutral, so now the s/d plan shifts into 2/3 streaks plan having 4/4+ streaks as "enemies" (boundaries).

Again we can only have four 'cluster' possibilities: 2/2, 2/3, 3/2 and 3/3.
And just two isolated sequences: 2/4-4+ and 3/4-4+

Even here back to back 4/4+ streaks do not account.

The final pattern "analysis" made on a clustering/isolated basis is extracted by comparing triples (exact triples) and 4s (exact 4 streaks) vs 4+ streaks (that is streaks long 5 hands or more).
Now either singles and doubles are considered as irrelevant.
Same "rules": 3/3, 3/4, 4/3 and 4/4 are clusters and 3/4+ and 4/4+ are isolated patterns.

We can safely stop our streak analysis by setting up a cutoff limit when any streak longer than 4 happens, that is this is the maximum boundary where inferior pattern ranges are more likely to act.

Now we can examine the most deviated situations any shoe might form after trillions and trillions of trials.

1) A shoe entirely formed by 5/5+ streaks: no bet

2) A shoe entirely formed by singles: the s/d plan works

3) A shoe mostly formed by 5/5+ streaks: a relative big obstacle to the above plans.

Obviously it's a lot more likely to get a #3 possibility than a virtual all 5/5+ streaks shoe (#1) or a virtual all singles shoe (#2), but you can test your shoes (even by common random walks) and you'll see that the average 5/5+ streaks distribution is well defined by more probable numbers that very often account for a 0 value than for numbers superior than the expected probability to happen.

More later

as.

Thank you AsymBacGuy for not only your prompt response but also for such detail. Posts like this are beneficial.

Re: 2iar. A couple weeks ago I played a rare shoe that produced 14 consecutive P 2iars (e.g., yPPyyPPyyy,..etc). Meaning 14 consecutive PP turned to B. There were a couple of single "P" columns within this fourteen 2iar streaks but no PP went PPP.

After the 14-streak ended PP then went PPP and PPPT as its longest streak. But never produced a PPPP.
B was mostly typical in each column following the PP producing a mix of 1-4 Bs immediately following every PP. Several other strong events were showing too but they didn't have the 100% strike rate for going against the PP. Shoe had 5 Ties.

I did very well as I caught 12 of the 14 PP turns to B. I pressed aggressively through the 7th-8th win (Which was approximately the 8-9th "PP" turn). I was at (Tmax and Tmax+) on the 6th,7th,8th W. I then regressed back to my (base unit +15$) and reduced by -$5 on each succeeding W until the end.

Certainly, one of my better shoes for the month/ I don't recall ever seeing this many (14) consec PP turning to B.


Thx again,

Now with this simple classification we can consider EVERY POSSIBLE PATTERN HAPPENING per any shoe dealt, going from  an all 5/5+ streak shoe (#1 scenario) to an all single hands shoe (#2 scenario).

Considering the worst (or best) case scenarios is the way to instruct our algos to do their job even at the most possible deviated situations.

Of course in our humanly miserable terms, we won't expect to cross such deviations as the almost totality of shoes dealt will present way lower levels of deviations and under our way of thought the only objective obstacle to be overcome is the 5/5+ streaks "density" happening per shoe: better sayed, the room those unlikely streaks will concede to more likely inferior patterns.

Such 5/5+ streaks density varies in direct relationship of the actual outcomes' source and we already know that whenever a shuffling machine is utilized, a significant LOWER amount of those streaks will show up (at least by using our random walks).

Anyway and no matter the source, it's unlikely to get many 5/5+ streaks per shoe (otherwise and knowing the bac players propensity to bet towards streaks than towards any other pattern, HS rooms would not exist), say they move within a range going from 0 (no such streaks) to very low numbers.

In addition, we have shifted to our favor the clustering 5/5+ streaks effect as they do not give room to inferior (possible bettable) patterns being clustered at least one time as what didn't happen cannot come out clustered (and neither as isolated).

Actually the permutation factor makes a decisive role about our long term results as it tends to confuse the "density" issue with the distribution issue. 

Following data show how many 5/5+ streaks happen per shoe by adopting our main random walk
(some final patterns are undefinied in their lenght). This small sample tends to reproduce what could happen after thousands and thousands of shoes dealt.
Since our random walks start and stop their action after some hands are registered or discarded at the starting/final portions of each shoe, such numbers reflect lesser numbers than by registering every outcome at a 8-deck shoe: 

1
0
1
0
1
1
1
1
2
0
3
4
1
0
1
1
3
0
3
1
1
3
2
1
2
0
1
1
0
2
3
1
0
1
4
1
1
2
0
2
2
1
0
0
1
1
1
1
3
1
1
1
1
2
2
1
2
2
2
1
1
1
3
2
2
3
3
1
3
0
1
3
1
3
2
1
1
1
4
1
2
2
1
3
3
2
4
1
2
1
3
0
1
0
1
0
2
3
2
0
1
1
2
3
1
2
2
2
1
2
1
1
1
0
1
2
2
1
1
2
1
2
2
1
1
2
1
0
3
1
2
0
2
1
3
1
1
1
3
1
0
3
0
2
0
2
2
0
1
0
0
2
2
3
0
0
2
2
1
4
3
3
3
0
2
1
1
2
2
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
3
0
1
2
2
1
0
3
1
2
2
2
1
2
3
3
4
3
3
2
1
2
2
0
1
3
1
2
1
2
1
1
2
0
1
1
2
1
0
1

Totals

0 = 33

1 = 79

2 = 61

3/4 = 38

So out of 211 shoes dealt, the most probable situation belonging to the 5/5+ streaks is to expect just one such streak (37.44%), next comes the situation to face two 5/5+ streaks (28.9%).
Then there are the most deviated situations (0 and 3/4 streaks) globally accounting for 33.64%.

If we'd get rid of the 0 streaks scenario (15.33%), one and two streaks vs 3/4 streaks account for a 140/38 probability, that is a 3,68:1 ratio instead of an expected 3:1 ratio.

Numbers we should be interested about.

as.

Hi KFB!!

Thanks for posting your experience and for your compliments.

Yep, single Ps and/or double PPs can last for quite long time, probably this is the best basic "clustering" effect to look for. Providing to be patient and being capable to discard the inevitable "isolated" P s/d sequences coming out at many shoes, a virtue not so commonly represented  among bac players 

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.

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.

Hi Asym

In the post #1011 above you say:

"...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.
  ..."

On (a) do you mean relative to a coin flip or do you mean in comparison with "even chance ish" games like line bets in Craps?? Both?  Neither??

Thx in advance,kfb

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 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.

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.

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.

Here, you wager for doubles and you will not be very happy at all!

But.........Here you will win a very handsomely 10 units!  And I did just that exact thing on this particular shoe!

Asym in post #1016 above:

"...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..."

I agree 100%.
It is my opinion one should not seek to develop a holy grail that wins all shoes. We would simply be forced to utilize such a small bet size to buyin ratio. The wins wouldn't really "move the needle" as far as a % of the overall bankroll. Plus we would still have at least a small probability to bust.

It is my belief we are better off trying to handle a predetermined level of (-)Variance. Allow just enough buyin size(dependant on one's own hit rate) so we will still be in the game after the inevitable rough patches. Give ourselves a statistically and realistic opportunity and accept when it's not there. On the shoes we do indeed bust our buyin we should remind ourselves it can only lose down to (0). As long as we don't rebuy into that same bad shoe.

My preference is to utilize a pos progression so we win more when we see that same Variance as (+). Hopefully significantly more on the W streaks/shoes.



Continued Success To All,