As professor emeritus of statistics at University of Cambridge D. Spiegelhalter stated in his book, random is often "clumpy", so lacking of "regularity".
 

Hence whenever things seem to be "too regular" for long (multiple shoes), we should raise our suspicions that the production isn't random.

Obviously we might think that a kind of "regular model" could be easily beaten but it's not the case at baccarat.

A coin flip study found that per every 20 tosses, there's a 78% probability of getting at least a 4 streak.
And the probability of getting streaks not superior than two (a double streak) is just 2%.

Now I'm figuring out what you are thinking about the last finding: "Hey, at baccarat there are a lot of sequences producing singles/doubles for many hands, we can't believe of that 2% percentage".
And actually bac hands are not coin flip successions.

Remember that among all patterns, at baccarat doubles are the most likely occurence, then there's always the "random" factor to be examined at both coin flip and bac productions.

Then "clumpy" could be interpreted as the dynamic propensity of getting things either more slight concentrated than diluted by an exact or near expected probability to appear.
And at baccarat doubles (for their high probability to appear) could be easily come out clustered (that is by a back-to-back fashion).

Therefore symmetry and asymmetry could be viable tools not to simply ascertain what's more probable to come out next, but to make an estimate about the effective randomness of the production.

As sayed numerous times here, paradoxically we are in better shape to guess "more due situations" when the production is supposed to be either perfectly random or affected by a huge unrandom bias then in the other miriad of intermediate possibilities.

Moreover at baccarat random clumpiness gets an average probability to appear in terms of quantity and frequency and when such values tend to be disregarded for long we can safely conclude that we're dealing with pseudorandomness othan with supposedly "normal fluctuations" dictated by a pure randomness.

More later

as.

For obvious reasons concepts examined here are quite simplified. 

Every soul knows that RNG provides pseudo random successions as they need an initial "starting seed" to properly work.
Real random RNG sequences are generated via atmospheric noise and frankly we can safely rule out their role at baccarat productions.

So whenever cards are arranged by a RNG software, we know that the subsequent card distribution will be pseudo random, so virtually presenting a kind of bias.
It's not an easy task to detect when and how a supposedly more likely situation should be entitled to come out, so we could start to study how different sub successions would perform on average at those pseudo RNG sequences.

In our opinion one of the tools that would help us most is the detectability to  spot "more likely" A or S patterns as key cards or math advantaged two-card situations cannot be symmetrically or asymmetrically distributed for long unless for short term variance issues.

Here a brief list of RNG shoes coming out from the same source (as always A=+1 and S= -3)

1) A=13, S=5

2) A=19, S=5

3) A=16, S=4

4) A=11, S=6

5) A=12, S=5

6) A=12, S=5

7) A=22, S=4

A=12, S=5

9) A=13, S=6

10) A=6, S=5

11) A=13, S=5

12) A=13, S=6

13) A=18, S=4

14) A=10, S=6

15) A=13, S=2

16) A=5, S=3

17) A=9, S=6

18) A=11, S=6

19) A=17, S=3

20) A=20, S=2

21) A=13, S=5

22) A=18, S=3

23) A=13, S=5

24) A=18, S=5

25) A=16, S=4

26) A=19, S=3

27) A=16, S=3

28) A=11, S=5

29) A=14, S=4

30) A=6, S=5

31) A=16, S=8

32) A=9, S=7

33) A=17, S=2

Total number of A= 451, S= 154 (x3= 462)

As sayed above, the S events will slightly overcome the A events counterpart, anyway the A/S model is well balanced (as expected).

Now let's see HOW those S patterns had shown up:

-75 times as isolated (singled)

-29 times as clustered (two or more times in a row)

About those 29 times S patterns came out:

20 times they came out double clustered and 7 times clustered by a more than two level (2 S patterns haven't limited for coming at the end of the shoe)

Now about the A patterns:

- 97 times as clustered

- 25 times as isolated.

Even though this sample is insignificantly small, we see that RNG software productions will differ from other form of shufflings where a kind of "clumping card factor" works more extensively, so privileging the A events.

Nonetheless, when we deal with pure numbers (no matter how random or unrandom placed) we're getting a very strong advantage, providing to carefully selecting the spots we'll we wager at.

RNG productions tend not to elicit any S isolated situation, maybe to make a multilayered progressive scheme at S-S vs S-S-S-...patterns that will be surprisingly balanced along the course of the shoes encountered.

On the other end and due to a kind of "unnatural" S clustering effect, RNG productions will make way more probable to cross A clustered patterns of any lenght, especially when one or two A isolated situations came out.

Even knowing this, there's no possibility to set up a RNG software capable to get rid of the A clustering effect happening at the infinite random walks we can build from the original BP succession.

Summarizing:

When finite RNG sequences are taken as a form of randomness, more probable situations are spottable along the way.
In fact, RNG successions are totally incapable to fit the RVM definition of randomness and without any effort to prove otherwise, RNG can't provide real random productions by definition.

Actually we can't give a lesser fk about complicated statistical/math formulas swearing that what we have to deal with is a constant perfect random model.

Perfect randomness doesn't exist and for that matter even the "probability" concept doesn't exist.

See you in a couple of days.

as.

In his must read post ("wagering smart"), Alrelax written this:

* Because you can only win a smaller amount of wagers in any session unless it is a rare session.

That's one more reason to consider every session as totally independent from the previous ones.
Or more precisely that the "very good" is quite rare to happen and of course that the most likely expectation we'll get is to lose (in absence of a carefully conceived plan).

We've seen one million of times that the "session" concept doesn't exist, unless for actual conditions we suspect to be "too random" or "not random".

In fact casinos' profits come out from:

-HE
-negative variance (NV) for the players

players profits could only comeout from:

-positive variance (PV)

Since NV=PV and the HE works only for the house, NV+HE > PV yesterday, now and in the future.

The only tool we could exploit at our advantage is to someway restrain the NV by taking care of the actual "random" conditions and this can't be done by stopping an attack after one or two losses or by modifying the betting amount but to  register and classify several results springing from the allegedly same production and to adhere at most at the actual situation we're dealing with.

More later about S/A ratios.

as.

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.