The CSM statistically insignificant sample (but we played such shoes) provided:

Out of 124 shoes, 36 shoes haven't shown up a single 1 (29.03%, expected range=25%) and 88 of them one or more 1s (70.96%, expected range 75%).

Out of the classificable isolated or clustered 1s (91), 66 1s came out as isolated and 25 1s as clustered.
At this CSM sample the slight propensity surpassing the 3:1 ratio at the previous sample evaporated as a proportional greater amount of 1s clusters came out (27.47% vs an expected range of 25%; isolated 1s 72.51% vs 75%).

Positional events (1s vs superior numbers) went like this:

First number = +10 units

Second number = -14 units

Third number = +6 units

Fourth number = +32 units

Fifth number = +7 units

Sixth number = -31 units

Overall a +10 units

The point is that regardless of the shuffling method, a general propensity (1s<than superior numbers) constantly acts, all other intermediate patterns need evaluations made on the previous patterns.
It's the card clumping factor. In fact at this sample, a way greater amount of huge numbers than the previous sample came out that must be balanced in some way along the same shoe.
Not everytime but most of the times.

Algos do recommend to play towards huge numbers (up to 6-8) only at the CSM productions: at this sample just 25 shoes haven't provided at least a 6 or superior number (nearly 20% of all shoes dealt).

Moreover each positional column roaming far from the 0 sum will be more likely followed by a column providing a positive sum, no matter what's the actual shuffle.

Then there's the specific streaks lenght tool.

as.

Here another sample of real live shoes coming from a CSM transformed into codes:

2-3-6-5-1-1
10-1-4-12
6-4-2-3-2-1
2-1-3-4-2-8
6-4-1-5-1-4
3-2-3-2-1-6
4-9-5-8
2-7-7-3-2
6-1-3-5-5-5
1-3-1-4-2-1-2
2-1-7-2-2-1
2-1-4-1-9-5
6-3-1-3-7
5-2-5-6-6-4
4-5-3-1-2-7
1-21-2-1-6
2-9-3-4-4
4-4-3-1-1-1-3
7-1-1-4-4
3-1-2-3-1-1
2-4-3-2-3-2
7-3-3-4-8
2-5-1-2-4
1-1-5-2-5
1-1-4-5-1-1-3
4-4-7-4
4-1-1-2-3-1
1-1-3-1-2
8-1-4-2-4
4-6-6-2-2
2-6-1-4-2-2
3-2-10-3-5
1-1-2-2-3-3-3
9-14-5-1
2-7-3-8-2
4-1-1-5-2-1
2-5-3-7-1-3
3-12-4
17-4-3-1
7-9-3-6-1
3-5-1-4-9
7-2-2-3-2-1
3-3-3-20
1-1-2-8-1-4
2-2-4-3-1-4
1-2-2-3-6
9-5-3-5
6-10-7-9
6-4-3-1
1-2-2-7-11
2-1-2-2-1-7
3-2-3-2-5-8
17-2-2-5-6
4-2-1-1-1-1
1-1-3-1-2-1-4
2-1-1-5-2-5-5
2-13-8-7
4-1-9-1-9
10-6-9
2-4-1-3-1-9
1-4-2-5-15
3-2-5-5-2
1-4-5-4-1-3
4-2-1-6-3
3-2-6-1-14
1-7-1-2-1-1
3-4-2-3-1-5
3-1-17
9-5-1-8-2
10-1-1-5
1-3-2-4-2
13-1-3-2
7-2-2-13-1
4-8-5-10
1-2-2-13
2-1-1-4-2
2-1-4-6-2
2-2-4-7-3-1-1
5-4-2-2-13
4-2-1-4-5-1
1-1-2-2-4-1-3
1-4-4-5-11
3-4-6-2-4
1-10-5-1-2
3-8-7-5-3
1-6-1-2-8-3-3
3-5-1-16
7-1-1-3-6
1-2-2-9-1
3-7-6-3-4
2-1-4-2-1
14-4
2-13-1-1
2-2-9-5-4
3-2-3-6
4-1-2-1-6-1
1-2-7-13
7-3-9
2-5-3-1-1
1-11-3-2
4-1-1-5-4
5-14-6
1-4-6-10
11-1-2-6
1-4-7-5
2-2-1-1-9

Thanks for your thoughts Al!

I've always thought that to ascertain a possible advantage, we have to measure it even though it could be affected by levels of imperfection due to several causes (variance, shuffling procedures, etc).

IMO only numbers could help to understand if there are vulnerable spots to take advantage from and of course the numbers I've provided are real numbers as those were shoes we put our money at.

As already sayed, algos 'approximate' a supposedly more likely flow of the outcomes at certain (few) determined spots by comparing several parameters that must converge into an univocal B or P bet placement.

as.

You've seen those outcomes, so it's relatively difficult to spot the "more likely" patterns coming around and definitely some shoes are collecting huge sd values (e.g. consider the 1-1-1-1-8-4-3 shoe or the 4-1-1-7-1-2 shoe).
Naturally I'd assume that you consider 1s as negative situations and greater than 1s as positive events.

Thus we have instructed our algos to "understand" that we can't rely upon a "general" more likely line as each shoe is a world apart, so when a 1 come out their action will be somewhat restrained or stopped.

Let's measure such real live shoes codes:

34 times out of 123 scenarios (shoes) no one 1 came around, so 27.64% (instead of 25%) of shoes dealt formed all winning numbers. It means that way more than 1/4 of the spots haven't provided a single loss.

22 times 1s came out clustered (1-1..) and 85 time as isolated (1-greater number than 1), so even here the expected 1:3 ratio wan't respected (79.43% instead of 75%).

Even by taking into account a 'positional' back-to-back shoes featuring a given number and assuming 6 steps at a 6-possible number code we got:

First number being 1 (-3) and every other number (+1) = +27 units

Second number: +15 units

Third number: -55 units 

Fourth number: +16 units

Fifth number. +8 units

Sixth number: +27 units

Overall it's a +38 unit profit (before vig) where algos entice our action.

It's important to notice that algos are sensitive to positional results, in our example not suggesting any bet at the third number being too deviated from the norm.

In addition, note that here 5 out of 6 positional spots will make us a profit and of course when a proper random walk is acting we'll be more entitled to get a win than a loss as more numbers greater than 1 are expected to show up than the counterpart.
(A good idea would be to get rid of the positional number getting worse results, but I do not want to complicate the issue).

Next I'll present other shoe samples belonging to the same shuffling category transformed into codes.

as.

Transforming bac shoes into codes

This is one of the most important tool we rely upon.
I'm presenting a short sample collected at a LV casino HS room.

After having applied a mechanical random walk stopping the action after some 'boundaries' and restarting it after one positive spot happened (and so on), we transform shoes as sequences of numbers.
Numbers refer to the lenght of clustering effect gaps.
So 1= no cluster, 2= just one cluster (a single back-to-back apparition), 3= a cluster of two consecutive apparitions and so on.
Numbers in brackets mean the last number wasn't precisely defined for the shoe ending up.   

Of course those sequences are not corresponding to an actual play, they just constitute a derived number succession.
Obviously each row is any shoe dealt.

4-6-5-2-1
9-4-1-1
3-3-2-3-3
4-1-2-8-(2)
1-2-1-1-1-6
2-3-1-3-2-(2)
2-2-2-2-1
2-8-7-6
3-2-3-14-2
2-11-2-1-2-7
2-1-2-10-1-5
1-1-1-1-3-2-2
7-2-1-6-5
1-6-1-7-3
13-3-3-1-1
2-1-3-2-8-3-(2)
3-9-1-3
6-1-9-1-9
1-1-13-2-1-4
4-5-2-2-5-5
6-4-1-4-4
2-1-1-2-1-7
6-5-2-1-3
1-8-1-2-6-3
6-2-4-5-5
2-2-5-1-2
3-10-6-8
13-1-1-1
14-16
1-10-7
5-13-1-9
3-3-5-5
7-2-6-3-9
1-8-3-6-5
2-4-16-3
1-6-1-2
3-1-5-1-4
1-1-1-1-1-12-3
2-3-1-1
1-2-5-11
3-2-3-2-1-4
7-10-5-7
5-8-2-1-2-3
7-3-3-2-4-1
2-4-1-5-5-4
6-5-1-3-3
2-3-9-6-2
1-5-5-3-6
3-3-1-5-2-6
3-3-1-6-1
1-2-5-2-2-(2)
6-2-3-3-3-12
3-2-2-4-3-3
2-3-1-10
15-1-3-5-2
11-4-5-4
2-3-2-3-5-1-2
2-1-2-3-2-1-2
6-1-3-6-6-3-4
3-1-1-18
1-5-5-5-1-4
8-1-1-3-2
3-2-1-3-4
4-3-1-2-2
13-1-14
4-4-5-5-(2)
5-4-2-2-5-6
2-10-7-4
7-2-10-2
2-6-5-2-8
1-4-5-10-2
2-2-5-4-2-1-2
4-2-1-2-1-7-1-2
2-1-1-3-1-4
5-2-1-10-2
7-8-8
1-9-7-6
3-4-3-4-7
3-5-1-6-5
1-3-1-6-5-3
8-7-8-4
10-1-1-2
1-6-3-1-3
3-7-14
8-3-2-2-2-2
2-4-6-10
3-1-1-8
2-3-1-7-1-2
11-1-8-5
1-4-3-1-7
3-7-3-2
3-2-2-4-2-6-2
8-2-1-3-1-2
2-1-2-5-5
4-13-2-1
3-2-2-1-4
2-4-3-2
6-1-5-5
3-5-6-2
1-1-1-1-8-4-3
3-2-1-8-2
1-4-4-1-4
2-9-3-6
2-1-1-1-2-3-4
7-3-2-6
2-5-1-1-1-3
7-3-2
12-6-8
7-6-1-5-4
4-4-1-15
2-1-9-6-2
1-4-3-2-2-6
1-2-1-1-5-5
4-1-1-5-5
4-1-1-7-1-2
3-2-2-2-11-2
4-3-1-3-6
15-4-2-1-4
1-1-12-1-1-5
2-3-1-3-2-5
5-2-3-2-2
3-7-1-2
2-3-5-1-1-4
1-3-4-5-9-4

Anyone familiar with my pages knows that I'm assuming a 0.75%/0.25% W/L probability and to simplify the issue we consider the number 1 as -3 unit loss and any other number different than 1 corresponds to +1 unit win.

Despite of being a ridiculous short sample, we think that it could give an idea about how the variance will act and about how to extract an edge.
In poorer words, we'are deadly sure to expect worse or better scenarios, yet this is what happened at the premise we've played at.

More later

as. 

KFB wrote:

I have often pondered how I could convince the casino to offer a bet on Ties with a rule that high card wins (or low card).

I find particularly interesting this passage, can you elaborate a bit?

Thanks

as.

Thanks again for your replies!!!

Very few baccarat experts and players know that overall (both sides) the most likely pattern occurence is...doubles.

Of course this finding collides with perfect binomial independent productions and naturally we need quite of time to get at baccarat the doubles predominance.

Now the issue could be extrapolated and dissected into infinite ways, anyway converging on the main reasons why BB and PP should come out slight more often than not.

Whereas it's theorically and partially difficult to understand why B doubles constitute a large part of the B outcomes, P streaks are mathematically oriented to stop at some point and the least possibility to get a P streak is, a double.

On the other end and assuming a constant math force shifting the results, even single runs (wholly considered at both sides) should be polarized in their long term apparition, but that's not the case.

Empirically we might assign an important (albeit diluted) role to the average shoe composition enhancing streaks stopping after two back-to-back scenarios.

Superior streaks than doubles (starting with triples) follow the same slight propensity and so on.

Think about that: if casinos would fear long streaks happening and such long streaks would be quite frequent to happen, well the game wouldn't exist.
On the other end, system players relying upon such relative improbability to get long streaks would go broke soon as one or more long streaks must happen.

Obviously it's one thing to know what should happen more likely and a completely different thing to decide what to bet at the actual shoe we're playing at.   

Algos rely upon a couple of different back-to-back registrations (in the vast majority of the times things change a lot after a given number of hands dealt) but always in order to get empty slots at given rows.
That is "hoping" to get empty column ranges than 1 at given rows, so discarding all the situations where a determined row is back-to-back filled (no play).

Example.

Say that your plan is to get either one single or one double after any 3(3+) BP streak happened.
If two (or more) consecutive triples show up we stop the plan, waiting for a fresh new 3(3+) streak. And so on.
No way to get an advantage (unless a very deep multilayered progressive scheme is in order).
Things do not appear to be more appealing when 1-gap triples gaps should be followed by larger than 1 'no triples' situations.

Just to give an example situations as 3-1-3-2-3-1-3-3-1-3-2-3 are very rare to happen (that is five isolated losing sequences in a row--in bold). But they happen.

Now let's consider different rhythms of results' classification, so trying to falsify the hypothesis that every registration will be insensitive to the actual production considered random and independent.

Good news is that a possible 4 or 5 losing 1-step clustered range cannot happen after thousands and thousands of shoes examined: in the vast majority of the times (well beyond the math expectancy) 1-step events MUST be followed by larger than 1 gaps.

Superior streaks classes need a more calibrated action to be exploited as further we stay from the singles and doubles appearance higher will be the variance acting.

as.

The KFB hypothesis about ties needs a further post to be discussed.
Anyway I agree with him.

as. 

Nice thoughts KFB!!

I totally agree there's no way to beat the house by wagering a lot of hands unless we stay put for a way larger amount of hands dealt.

Besides the HE, it's practically impossible to guess many hands as possible 'triggers' float around steps sooner or later deviating 'too much' from the 0 value.
In such a model, perfect independent productions make no valuable points to be attacked.

At baccarat things are more restrained than what math dictates as each shoe is a world apart and deeply dependent to the actual card distribution.

Is this a "too general" statement to get a possible advantage from?

Bighorn.sh.it.

Anyone knowing the Smoluchowski's 'probability after effects' concept (not mentioning other statistical tools improving such idea) understands that an event or two (or more) events present sd values way lower than binomial independent models, providing to assign an "actual" code to each shoe distribution.

Of course such assumption needs to be stricly measured after testing large samples and we know that it's very important to consider productions under the same shuffling category.

Mathematically we have to dispute the common knowledge that after a given event the next event (or class of events) will get the same probability to appear.
Most of the times this is true, yet at a restricted part of possible outcomes, that's completely false.

Our studies have found out that alternating W/L flows are the least likely to happen or, better sayed, that are the least likely to stand for long, so privileging 'clusters' of something.
We do not know how much such clusters stand but we know they are more likely to happen, especially  when we raise the probability of success by betting two events vs an opposite event.

Suppose that we take care of a X event coming out 5 or more times in a row vs the same event showing up 3 or 4 times in a row.

General probability will say to us that 3 and 4 streak classes (p=0.75%) will be counterbalanced by 5+ streaks (p=0.25%).

From a math standpoint and assigning a 3 value to any 3 streak, 4 to any 4 streak and 5 to any streak equal or superior than 5, then considering back-to-back values we'll get such scenarios:

3-3 = 6
3-4 = 7
4-3 = 7
4-4 = 8
3-5 = 8
5-3 = 8
4-5 = 9
5-4 = 9
5-5 = 10

Each number will add to the next one so forming infinite (actually finite for that shoe) sums   performing pattern numbers slight more likely to happen. Especially after having ascertained that sums are sensitive to previous supposedly more probable situations, best if both two classes considered really happened at that shoe.

Obviously I'm not referring to the simple BP flow (and neither at common derived roads), as this effect is too restricted to be exploited (mostly as B>P so someway enhancing long B streaks).

as.

Mmhhh it appears to be delicious food....

Wine pairing?

I'd suggest a Chardonnay Brut or a Sauvignon Blanc...

Happy New Year!!!

as. 

Quote from: alrelax on December 27, 2023, 03:04:55 AMAs you said:  "b) what is really happening at the actual shoe dealt."

And that is what can be so clear to one person, yet so fuzzy to another. 

Yep.
Following what happens at the actual shoe is paramount (IMO), definitely.

as. 
 

Who we are to dispute the common notion that bac is an unbeatable game?

Answer: because we have managed to assign a code (albeit being imperfect) to each shoe dealt, a code capable to restrict the sd values typical of binomial models.
In poorer words, past hands make substantial variables to get advantage from.

What happened will be first considered by an asymmetrical or symmetrical fashion at different portions of the shoe, then added or substracted to what didn't happen.
Such operation will provide mathematical values (streaks specific lenght) where algos approximate at best the probability that a current state will change or stay and obviously we'll expect a slight greater number of restricted states in amplitude than superior (more deviated) situations.

If the above statement is true (and it will), it means that bac productions are anyway affected by a sort of unrandomness.

Since we consider outcomes under the lens of asym/sym situations, unrandomness doesn't get a univocal way to act, so increasing the probability to form a valuable and consistent amount of low lenght streaks (widely intended).

Proof is the code we'll assign at every bac shoe where some numbers will be slight more likely followed by a specific number or number classes.

as.

Baccarat sequences are made by a mix of random and unrandom events

Besides of specific shuffling considerations, any bac shoe in the universe will belong to a sort of "random/unrandom" (R/  U.R) model.
When the R/ your ratio surpasses an average value (R is too high), there's no way to beat the game: we could be just "lucky", the real thing casinos aim for.
On the other end, shoes affected by a "relatively rare" marked  U.R denominator are heaven, providing to know what to look for.

Think about a binomial independent model, dissect the sequences in every detail and let me know if you'd find a profitable pattern to exploit.
And in fact our algos lose and lose at those sequences: no surprise, randomness can't be beaten, period.

People (experts first) thinking that every bac hand is completely independent from the past occurrences are wrong.
Nonetheless, is not so easy to detect bac unrandomness, mainly because it shows up at different ways per every shoe dealt.

One of the most important thing to look for unrandomness is that it expresses subtly and surely by "complex" patterns.
And naturally we are always destined to ascertain the  U.R by approximating the situations where it should work.

We've found interesting similarities with sports betting: there are infinite variables shifting an outcome, yet nothing will happen for sure.

More later

as.

Thanks for the link!

Minutes? It takes hours to digest all those points 

as.

Algorithms action

Our algos move around two distinct probabilities:

a) what should happen on average and by which more likely ranges;

b) what is really happening at the actual shoe dealt.

If all of the time a>b, well the game wouldn't exist and if b>a it wouldn't be offered either.

Thus per every shoe dealt we have to approximate the different weight of such distinct factors and, no surprise, most of the times a=b or close to it.

Obviously the a=b scenarios are the best to look for and will correspond to an "average card distribution", the main parameter algos aim at.

Algos won't look for strong deviations at either positive or negative side of the operation, they prefer a more likely steady flow of the outcomes, albeit limited at different (so less easily detectable) rhythms of classification.

Yes, card distributions are considered undetectable, everything happens anytime and anywhere but always by a specific level of probability.
And as long as shoes (and cards) are dealt, such probability values will converge more and more to the a) point.

Shoe card distribution

Besides of the important specific shuffle production factor slightly affecting the 'average card distribution' I do not want to discuss here, each shoe dealt will follow or not certain "more likely" "back-to-back" patterns getting different but limited values.

Technically some "random walks" (that is two opposite fighting scenarios) are more limited in their apparition than what a binomial or slight asymmetrical bac model dictates.
That's where algos' edge comes from.

Remember that while playing a binomial game (even if taxed) streaks of something are the real enemy to get rid of.
Obviously no specific streaks classes are chasable better than others even though and generally speaking shorter streaks are more likely to form clustered patterns than isolated patterns.
Especially whether we take into account two or more streaks classes.

But symplifing a lot, the best empirical factor to get an advantage from is that a 'more likely' streak not happening so far shouldn't be included in our betting operation. Regardless of its general propensity to show up.
That means that providing a proper results registration, streaks of low lenght actually happened and coupled together will get very low variance values.
Naturally along the shoe's course things change, meaning that quite often a long streak will erase a previous streak classes flow.

More later

as.