Excellent post!

as.

Since at baccarat a player can virtually bet up to $500k or more per hand, casinos want to be sure that shoes offered won't present any detectable bias, so they rely upon the best random shufflings.
Technically it's not the BP results' distribution that matters (with all the infinite derived roads) but the rank card distribution.

Good news is that there's a relationship between BP results and rank card distribution, now I'm adding a new factor that is the B/P hands gap.

Smaller is the B/P hands gap (especially if BP deviations seem to be "too much" restrained along the course of a shoe) and higher will be the probability to get "undetectable" patterns because such productions tend to get "too many" overalternating events that do not correspond with natural coin flip distributions.
Obviously I'm not referring to long chopping lines or short streaks, just a "weird" propensity to not producing a more natural deviation belonging to a binomial proposition.

On the other end, rare shoes will produce a higher than expected number of B or P deviations, so in some sense what lacks in such productions is the "average" distribution.

If we split the possible patterns into 1) an overalternating mood (OA), 2) moderate or strong deviations (MSD) and 3) average deviations (AD), we'll see that the most part of shoes will belong to the 1+2 category rather than the more exploitable 3 category typical of more common random shoes.

What classifies gambling games is the absolute uncertainty about the next outcomes, yet a decent number of statistical deviations must happen and of course main part of OA and MSD belong to the extremes of the spectrum.

A kind of symmetrical or asymmetrical plan is hugely affected by such propensity as low deviations make more probable to encounter S patterns than A patterns, that's why itlr S>A.

So when too many hands seem to be 6-card resolved, think that the symmetry will be predominant (after all ties come out way more often when 6 cards are used) and the same when the BP ratio seems to get very low deviations along the shoe's course.

Nothing wrong by taking the S side when proper conditions are met, yet the asymmetry will reign supreme especially when S patterns had shown up too often than expected at previous shoes.

Clustered symmetrical patterns

Clustered symmetrical patterns (that is S-S or S-S-S and so on) happening at a shoe make more probable the formation of another symmetrical pattern at the same shoe, the reason beyond that won't be discussed here.

More specifically, different productions are more or less probable to deal S patterns of some level where of course the main class happening will be 1 (single S) or 2 (double S).

Almost always when clustered S events happen, there's more room to get an A pattern clustered at any level (A-A or A-A-A, etc) as rank cards cannot be arranged to constantly get symmetrical situations for long (statistically impossible when 3 or more different random walks are considered).

After all it's a lot more probable that occasional HS players (those who can seriously hurt casinos) will bet toward symmetrical patterns than asymmetrical ones. And such players look for the Big Road, giving a damn about what certain bac scholars try to say.

Taken from another point of view, the line (random walk) getting many A and singled or no S will take the lead over the other ones, sometimes two or rarely three different lines will present clustered S, a sure sign that that shoe isn't playable.

That's one of the precious tools we're looking for:

Once a S clustered pattern had shown up at two different lines (random walks) so far, that shoe is considered as partially unplayable unless our data suggests that a given specific S cluster is more likely to be interrupted by an A event.

Keypoint is that we do not want to guess interminable winning hands, just restricting at most the unfavourable S patterns as the rule at baccarat is to lose and lose and not to win.


When a shoe is weirdly dealing too many S hands, do not try to alter the flow and let it go without betting (don't make the mistake to chase S patterns and let alone A situations).

Next week we'll see the exact percentages of S/A ratios in relationship of the actual production.

as.

Hi Al, welcome back 

Yes, people tend to bet too many hands hoping that trends/antitrends last forever (or at least until a loss or a couple of losses come out).

Obviously the concept of trends/antitrends doesn't exist at all, it's just a human concept set up to try to guess more hands than expected and normally it doesn't work.

In any instance almost any pattern move around a long term 0 sum (of course B patterns tend to be longer than P patterns), yet it's impossible to catch the infinite sub distributions unless we'll try to "limit" trends/antitrends by a lenght factor.

The process accumulating wins must be very slow, so once we've secured a win or few wins we have to defend it as it's more likely to encounter short W sequences than long W sequences.
Long W successions work as a sort of "jackpot", the same way slot machines act.

I mean that the risk of jeopardazing a temporary profit within too short terms (or costant gaps)  would be higher than the reward of getting more wins by exploiting long W sequences.

Even worse is trying to catch favourable situations within too short terms when we're losing because the process of getting a fair number of W after a steady L status do not work in the majority of the times.

Mathematics teaches us about the value of the Maximum Bold Strategy applied to any EV- game (betting everything just in one hand).

More later

as.

Suppose we want to compare a black jack shoe with a baccarat shoe.

At bj, things are pretty straightforward: when the shoe is rich of aces and 10-value cards we'll get an edge (or at least we're supposed to get it) and vice versa when the shoe is rich of low cards.
Unfortunately here we have to bet any hand dealt and whenever the true count is going toward our side (nearly 12-15% of the times), raising our bet will make suspicious the house.
In addition, we can't know if the actual bj positive count could be distributed by a kind of L-N-H or N-L-H cards distribution (L= low cards, N= a mix of H/L cards, H= high cards relegated into the final (unplayable) portion of the shoe.
Thus we think to play with an edge whereas it's not.

At baccarat bighorn.sh.it happens just in the eye of the beholder.
Since we can choose from an infinite amount of random walks and wagering whenever we wish and with the amount we wish, the strategy cannot be prevented by any kind of "perfect" randomness.

Paradoxically we could cross better EV+ spots by waiting that S clusters of some lenght had happened at the same considered line, especially if the total count of A/S patterns was moderately/heavily shifted toward the right S side.

By selectively playing the A side we are challenging the production to deal multiple consecutive S patterns of different shape happening at specific lines, a thing that can easily come out by throwing an unbiased coin but never ever at a bac proposition unless for rare coincidental factors and for limited ranges.

A or S pattern steps

As we've seen there are two betting steps to ascertain whether a next pattern will be A or S, first step is slightly more likely to produce a win than a loss so in some sense we could consider the second betting step as a "backup" plan.

Registering the first or second bet result at any line considered is an additional tool to be more precise in our selection, thus enlarging our edge after a kind of strong deviation happened at either side of operations.
It's like to halve the negative deviations at the obvious cost of missing many favourable opportunities.

For example, it's extremely unlikely to encounter 1-step or 2-step S different patterns longer than 4 or 5 at each step, yet we should be prepared to face the most unlikelihood.

Think to run the same situation infinite times giving a damn about short term results.
If the production is considered as unguessable, long term results will mirror the expected results but it's not the case. 

Since you're not forced to bet any hand, in order to enlarge your probability of success you can wait for some negative deviations to happen before placing your precious money at either the #1 or #2 step (or both).
       
Do not fall into the trap of wagering something because you're called to unless a minimum bet is at least 10x inferior to your standard betting amount.

More hands you'll bet lesser will be the accuracy of catching the good instead of the bad.

as. 

QuoteHi Asym

Casinos like randomness and randomness dislikes patterns.



that's a great gambling quote.

Thanks, KFB, thanks!

The problem is that IMO more often than not real random productions are likely to STOP patterns instead of prolonging them. Especially at baccarat where the production is finite for the average key cards impact and surely asym based for the rules (B>P).

as.

Casino owners do not fear anything but occasional HS players getting an unusual high number of long streaks and, maybe, productions privileging the S patterns coming out steadily.
Everything else, the so called "unguessable chaotic world" will go at their favor.

Therefore in some sense it might be better to bet towards the "everything else" than the remanining situations.
Providing to know when and how such remaining situations should be more likely to show up.

More later

as.

Assuming a 0.75 probability (W+1, L=-3), symmetrical patterns tend to slight overwhelm the asymmetrical ones at most shoes dealt.
The problem to bet symmetrical patterns is that they are a two-step proposition, meaning that to get the full value of any sym pattern we have to pospro every single bet.

Moreover and for an obvious "balancing" factor, many shoes will form endless Asymmetrical situations, those where it's virtually impossible to lose for the main portion of the shoe.

Generally speaking, the Big Road is the basic succession where sym patterns seem to prevail over the asym ones, a thing happening with a slight lesser attitude at other derived roads (or multiple random walks we can build).

At any rate, clustered symmetrical situations belonging to DIFFERENT patterns and showing up as consecutively shaped are well controllable (so restricted in their average appearance).
Otherwise any bac player in the world (who genetically privileges symmetry) would easily win at most shoes.

On the other end, casinos know that besides their math edge patterns will whimsically show up by a kind of undetectable fashion.
Among all those undetectable situations, a fair portion of symmetrical (detectable) patterns come out naturally as long as long streaks and other homogeneous (humanly speaking) events.
This is what fuels the game as there's nothing to guess or hope for.

What we should do is taking advantage of the asymmetrical propensity acting infinitely even knowing that some sym different patterns can show up in a row but by more likely levels in the vast majority of the times.

Think about how it's impossible to deal back-to-back diverse symmetrical patterns for long at the infinite sub successions derived from the BP original one.

Depending about how's the actual production (manual shuffle, machine shuffling, etc), the best betting spots you should aim for are wagering toward A after a single S pattern or after a double S pattern.

Then betting toward A clusters cannot hurt, especially when a counterpart S had previously shown up clustered.

A-S-S-S(..)-A-S-S-S(...) patterns sooner or later show up (very rarely), who cares?
People making a living at games rely upon numbers more likely to happen.

as.

When in doubt about what to bet and among the infinite options we can choose from, I think the A/S distribution is the best to take hints from.
We've seen there are only three different patterns of so called symmetrical nature, everything else could be easily considered as asymmetrical.

More later

as.

Hi KFB!
15 B singles in a row? A real strong deviation!

Do you have the entire shoe?

Thanks!

as.

Think about how's unlikely to get a balanced ratio in relationship of the number of decisions dealt even by considering a perfect independent 50/50 proposition.
 
In addition, bac sides are asymmetrical at the start, then cards cannot be arranged by a balanced scenario for multiple sets unless for "coincidental" factors, surely being affected by a "finite" slight dependent effect.

If deviations are naturally going far from the 0 neutral point and itlr 0 is the theoretical target, many counter balancing deviations are more likely to be asymmetrically than symmetrically shaped.
Or, at least, symmetrical scenarios seem to be more controllable in their appearance and lenght than asymmetrical spots.

as.

The paramount tool to take care of is that once a pattern had produced a S event, we're not interested to care about its lenght. So 1 is equal to 2, 3 or even 10. We need to wait until an asymmetrical A event will stop its sequence.

Setting up two or three different fictional players betting for us is one of the key to possibly win itrl, providing to bet far and few between situations.

For example:

Player #1 will always bet for A-A situation (one time); it'll lose whenever isolated A come out (A-S)

Player #2 will always bet for (A-S)-A situation, that is betting toward A after a single S came out)

Player #3 will always bet after a (A-S-S)-A situation, that is betting toward A after TWO S had come out in a row.

To get ALL three players losing at the same time we need to cross a (S)-A-S-S-S(...) pattern, yet singularly considered each player will suffer from a SINGLE loss.

It's true that S-S-S(..) patterns will make both player #2 and #3 to lose but we know that more clustered are S patterns greater will be the probability to encounter A-A patterns.

If you set up a starting betting point after two or three S clusters (S-S or S-S-S-...) fictionally happening, probability to get A-A or S-A will be enlarged and giving you a statistical edge.

On the other end, most part of A isolated events come out intertwined by S isolated events.

Such propensity is so reliable that you'll find very few situations fitting a kind of A-S-S-S pattern.
Moreover it works at ALL infinite random walks you can build from the original BP sequence, so it's PRACTICALLY IMPOSSIBLE to deal shoes rich of S events without getting a proper exploitable amount of A situations.

as.

Thanks KFB, I appreciate it and I'm looking forward to your incoming comments!

I'll add just this.

A "linear" strategy suggesting to always bet A vs S is not going anywhere as sooner or later we'll catch a SSSSSS..sequence or anyway a shoe or multiple shoes feauturing plenty of S.
On the other end even A clusters could suffer from consecutive isolated A but in the majority of the times such unusual "chopping" A line easily alternate with single S (A-S-A-S-A-S..).

Then by waiting S clusters of any lenght (and you'll have to wait quite a fair time to cross them), we know that more room is conceded to more natural A clusters (of any lenght) as a 3:1 probability can suffer harsh situations but not standing for long time, especially whether the production is RNG dictated.
In any case this doesn't fall into a gambler's fallacy concept, otherwise anybody would be enticed to wager only for symmetrical patterns so breaking down the house well more (and easier) than what MIT team did at bj.

Casinos like randomness and randomness dislikes patterns.
     
More later

as.

Suppose we are betting randomly the pattern #2, #5 , #8 and #15 of the Big Road. (two time pattern #15 hadn't come out):

S-S-A-A
A-A-A-A
S-A-A-A
A-A-A-A
A-A-A-A
A-A-S-A
A-A-A-A
A-A-A-A
S-S-S
A-A-S-A
S-A-S-A
A-A-A-S
A-A-A-S
A-S-A-A
S-A-A-A
S-A-A-A
S-A-A-A
A-A-A-S
A-A-A-A
A-A-S-A
A-A-A-S
S-A-S

What and when to bet at these successions?

If S= -3 and A= +1, before vig any line will get:

-4
+4
0
+4
+4
0
+4
+4
-9
0
-4
0
0
0
0
0
0
0
+4
0
0
-5

Total= +2

If adopting the strategy to play A-A one time and A after S one time we'll get:

(-3)(+1) = -2
+1
+2
+1
+1
+2
+1
+1
-3
+2
(+1)(-3)(+1) = -2
+1
+1
(-3)(+1)(+1) = -1
+2
+2
+2
+1
+1
+2
+1
(+1)(-2) = -1

Total= +15

Therefore if we'd assume a A=0.75 p and S=0.25 p, the expected A/S ratio is 3:1. So it's the average more likely ratio while considering four A/S decisions (when applicable).
Thus when an average ratio shows up no possible permutation will deny us to make a +1 or more probable a +2 profit.

In fact a single S among three As cannot produce any loss.

Within sets of 4 resolved hands, losing streaks can only come out when two or more S happens.

Anyway 4 S are just a loss of -3
3 S produce a loss of -6, -6, -3, -2.
2 S produce a loss of -2, -5, -6, -1, -2; and a win of +2.

0 S are always a +1 win.

Paradoxically we are in less worse shape when 4 S are showing up than when 3 S are coming out.
2 S are really hurting us just in two out of six possible permutations; in the remaining cases we'll get a -2 or -1 controllable loss and even a win of 2 units.

Run this situation infinitely (that here were taken randomly even if some positive variance happened) and let's see how many 4-decision sets are getting the negative 3 S or, at a lesser degree, the 2 S negative enemy.

A more aggressive plan needing a very large bankroll would be to double the A-A bet and the S-A bet after two or three losses in a row with the addition of betting the A patterns until they'll stop and until the deficit is recovered.

A plan at least 50x fold better than betting Banker in whatever sauce.

as.

@lovepreaks, regarding our post #1297

Each shoe will form a sequence of Asymmetrical (A) and Symmetrical (S) patterns; for each category  A could stand one time, two times or even for the entire shoe (a thing that happens not so rarely).
The same about S, but since we have chosen the 0.75 probability to define A and S, S successions are obviously way shorter and normally less clumped (so rarely going past three in a row).

Put into numbers and assigning A(+1) and S(-3), what we're basically looking for first is any +2 (+1+1, that is A-A) or -2 (-3+1, that is S-A) sums. Of course at both cases the first number is the unbettable trigger.

If a longer than two S sequence come out, we put a limit of interest at (S-S) meaning that so far we aren't interested about values more negative than -6.

Most players like to bet towards symmetrical patterns because asymmetrical ones tend to be perceived as "too chaotic" so more undetectable.
But it's not what we are betting but WHEN.

OoOoO

The simplest tool to ascertain the "average" distribution of an asym/sym pattern are doubles.
Doubles are the perfect pattern to look for as they are the most likely bac pattern occurrence.

If you think the actual production you're playing at seems to be "undetectable" try to register some hundreds of shoes, then take care of how many consecutive doubles had happened on average.
If isolated doubles and two consecutive doubles vs superior double clusters are accounting for at least a 76.5% you'll be in good shape. 

Consider more than one random walk before reaching conclusions.

You won't bet many hands for sure and a natural variance is expected but you know to play with an advantage.
Moreover since the primary goal for any serious bac player is to win money and not getting thrilled by the possible volatile favourable circumstances, you can easily track how many times a first/second/third or fourth bet had won and acting accordingly.

For example, at any level of the four progressive multilayered bets you could respectively raise the standard bet by a 10% after a win and by a 5% after a loss.

I could provide a list of casinos worldwide where such a simple strategy will 100% work so far (providing to take care of multiple random walks) where, of course, shoes are machine shuffled.

Notice that the slight double propensity toward asymmetry is the best situation to hope for among the three different patterns examined (single, doubles and triples) even if considered by two S steps.

as.

@lovepreaks

Do you have a defined probability model for pattern transitions—particularly from asymmetric to symmetric (A→S) or symmetric to asymmetric (S→A)?
For example, is a 0.75 probability for A→S transitions a reasonable estimate?

Since we need to place two bets to define the asymmetry (if the first bet was lost), yes we'll expect A to get a 0.75 p, so the A/S ratio should be 3:1.
That's in theory because in many RNG productions the number of S is way higher than 0.25(!).

Nonetheless S status is more frequent but tend to change faster than at other shufflings.
Maybe betting A-A one time is the safest pattern to look for, then betting A after S-S.
 

Given that the same P/B sequence can sometimes generate multiple A/B outcomes, what specific rule or method do you use to assign A or B in those ambiguous cases?


Not sure if I intendend well your question.
Derived roads are still the simplest way to get A/B sub successions, as you know well only long streaks will make every random walk to be homogeneously shaped.

When in doubt to bet between two or more lines, I'm not betting at all. Anyway as a general rule of thumb I'll prefer the line presenting a triple and not singles and/or doubles.
Moreover the line featuring many streaks and few singles do not elicit any first bet (that would be a sudden win).
So the line that collected more first winning bets than second winning bets is priviliged.
Then there are other considerations to be made.   

When identifying a potential betting spot, does the row position on the tote board (e.g., first row vs. deeper rows) affect your confidence or decision-making?
If so, how do you weigh that spatial factor?


Space distribution of the outcomes is the most important tool to master IMO.
It's the CFS working at different velocities but with a kind of "average steps".
 
I know a couple of successful players adopting a pure anti-streak game (so basically toward a positive CF speed) capable to get rid of many long unfavourable streaks by making considerations about how hands went in that specific (so far short) streak.
They start to consider betting only from row #2 or #3, sometimes even #4 so the shoe is halved or  quartered or even more reduced. Then only three or four bets are placed. 


How were the five betting trigger patterns developed and tested?
Were they based on statistical simulations, real shoe analysis, or other forms of data modeling?


We have never utilized simulators, just real live shoes listed by different forms of shuffling. We own a casino's shuffling machine too.   

Beyond the five primary triggers, have you developed any secondary filters or conditions to avoid high-risk zones or long losing streaks?

There are 4/5 different strategies we currently use and of course we try to adopt the ones performing best at the actual shoe.

Unfortunately losing streaks happen and MUST happen.
We are sure to play with an edge but nobody knows how the actual shoe is arranged. That's why we make very few bets and play a lot of shoes.

We try to avoid to play at tie rich shoes or when many hands are resolved by 6 cards (it's the same math concept).

Another tool we look for is the number of naturals happening so far.
We prefer to face an average value of them (around 1/3 of total hands as you know).

Take care!

as.