Btw, I highly suggest you to read this book:

Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts by Annie Duke


as.

Clustering effect

Baccarat is a game of clusters of different lenght and thickness.
And of course at baccarat there are no real symmetrical situations: for example, a 9 falling on the first two Player cards doesn't get the same power than a 9 falling on the two first Banker cards.
The probability to get that 9 falling on either side is equal but the effects are not symmetrical.

This concept could be applied to many other key card ranks, 8s and 7s of course but even 5s and 4s follow the same principle.

Any shoe dealt is formed by different "states" that eventually equal the rank number but the situations forming outcomes and player's ROI start asymmetrically, stay asymmetrically and end up asymmetrically.
The main reason conditioning the outcomes itlr regards the key card distribution getting different powers depending upon the side cards will fall at.
Most of the times key cards determine those outcomes. Not every time but most of the time.
When the outcomes seem to be too whimsically produced (see next post), it means that the shoe is not playable (that is unprofitable). We name that as "a very low clustered shoe".

Baccarat outcomes are not B or P results. Yes, we need a B or P to show up in order to register our random walk lines as there are no other betting options.
In reality baccarat is a game of states and not an endless B/P sequence.

We've seen that there are tools to derive unrandom successions from a primitive random sequence, our task should be focused to assess when one or more unrandom successions will take just one step forward toward the clustering world.
To maximize the reward risk ratio, per each shoe played looking for just one step is more than enough to battle versus a sure EV- math game.

By far and without any doubt, our EV will be greater and affected by the most ridiculously low variance when we'll try to find out just one profitable state per every playable shoe.
This means to discard a lot of unplayable situations and naturally to possibly witness "all winning" shoes without betting a dime.
It's not a coincidence that those rare long term winning players after winning or losing their "key hands" simply quit the table.

Deciding to be ahead of more than one step per playable shoe is a sure risky move to put in jeopardy the actual edge we get over the casinos.
On average clustered states are slight more likely than expected and that is mainly due to an imperfect shuffling.

Consider baccarat in the same way as black jack works for card counters even though by totally different reasons.
At bj profitable card counting situations cannot last for long. The same happens at baccarat.
We want to play by concentrating at most our edge, challenging the bac system to show its flaws within very few spots.


as.

As sayed several times here, we want to play baccarat with you Al, it's very very likely our hyper selected betting plan will correspond to your methodology taken at different degrees.

Few bac players reached the experience level to ascertain what is worth to bet and what it isn't, that's why we need a strong measurement of our possible edge to verify this game is really beatable. Or not.

There are general and specific means to lower, nullify or invert the house edge. 

General means to lower the casino's edge

Reducing at most our betting rate is not only the best tool to lose less money but to define at most what the fk we're really going to accomplish.
If it's literally impossible to define a betting model capable to win at a fair coin flip proposition, let's think about what are our probabilities to win at a EV- kind of coin flip model.
Zero.

Naturally and to give the casinos the idea we're pure losers we can adopt a spread betting range wagering one standard unit per every hand dealt and betting 3, 4 or 5 x bet in the selected profitable spots.
They do not care a bit about it, every our bet will be EV-. At their eyes.

Of course casinos are simultaneously thrilled and worried about those rare maximum limit bets as the actual bet or next bets cannot be more wrong than the math negative edge applied (after comps and/or rebates).
I mean that no 5k or 20k bet can cross a real -1.06%/-1.24% negative edge as some lost money is given back to the player no matter what.

Conclusively, bac players that are proportionally losing less money are maximum limit bettors, at
the same time constituting a real threat over casino's pockets as the edge remains quite small.
Ask any supervisor casino you want whether he/she would be really enthusiastic about facing an occasional univocal and rare 90K euros bet coming from three different players.
They should have been happy but actually they didn't. Especially after the outcome.

Specific means to invert the house edge

Arrange the cards in the fkng way you want. You can put all same rank cards consecutively or alternatively or whatever you'd like, a most likely distribution or most likely arrangement will come along the way providing previous results are considered by a strict scheme.
A kind of profitable clustering effect will come out along the way by a stastical sensitivity and specificiity rounding 100%.

And we need just one clustering step to be ahead.

as.

There are no wrong or right methods to beat (or not) this game itlr, there are only methods that do work.
Meaning that our method after a decent number of trials had to get profits by flat betting.

It's quite easy to confuse the steady probability of success with the dynamic long term WL probability typical of baccarat.

Itlr (and even in most short run situations) probability of success line tends to get the zero value, whereas WL dynamic probability must get an ascending line formed by "infinite" positive or negative short segments where positive segments are either longer or more frequent than the negative conterparts.

Probability of success is symmetrically placed no matter how deeply we've built our progression plan. No way a strict math progression without a valid bet selection could get the best of it for long. Itlr positive fragments will be equal in lenght and frequency as the negative counterparts, even though we know that B>P. Actually the B>P factor is quite volatile and restricted to rare situations (we well know this).

To beat this game itlr we need to find the unsteady situations where our plan might discard the potential B/P plan variance, exchanging it with the more regular A/B registration made on several steps.
Card speaking, it's like we are challenging the system to provide univocal math advantaged spots acting for long and at different degrees instead of a natural more likely balanced key card falling.

Our datasets show that dissecting the shoe into an average number of 4 or 5 key situations will make the highest player's edge. Yet remember that not every shoe is playable.   

If any bet is insensitive to past decisions, why the hell a given flat betting plan will get a slow but steady positive ascending line?

as.

However the negative will generally be produced and held much longer than the positive experiences within the subconscious reservoir and that is what makes it so dangerous especially at the gaming tables.

True, and it's a fact proven scientifically several times. So you can safely erase the adverb "generally" :-)

as.

Babu thanks for your reply.
Yep, there's a lot of confusing stuff in this thread, but there's also a common trait working on.

Imo, in order to find possible baccarat flaws one of the best approach we could make is to compare real baccarat results with a "control" model derived by a coin flip model. Shoe per shoe.

We know that bac results are "biased" by either the slight asymmetricity and slight card dependency, but differently to coin flip propositions bac real probabilities are moving around a more confused world as the actual key card distribution will make a major role about the long term outcomes.

Everybody quite familiar with both baccarat and roulette knows that baccarat streaks tend to be shorter than roulette streaks.
Indeed at baccarat there's a very very slight propensity to get the opposite result already happened.

But that's not the point, the important feature to investigate upon is that a part of seemingly same streaks lenght are formed by different quality factors.

And on most part of the shoes, the "quality factor" cannot last for long as deeply influenced by the asymmetrical nature of the game favoring B and the actual key card distribution.
Even without considering the real quality nature of hands, itlr back to back hands taken at different pace will form different probability lines.

That's why itlr common derived roads will form more long clustered doubles on Beb and SR or clustered longer streaks on Cockroach road than Big Road registration.

For example, you need at least a 3 x sample to get a consecutive ten double sequence at Big Road than at Beb or SR.
The same concept applies to Cockroach road regarding longer streaks probability.

That doesn't mean to set up a method about simply mining doubles on Beb and SR or mining long streaks at Cockroach road.

Anyway, derived roads inventors were real geniuses (probably involuntarily) to set up the foundamentals of a long term winning plan as there are only two Big Road conditions making univocal results on all three derived roads: long singles sequences and long streaks.
Both quite unlikely.

Remember, we do not want to win many spots per shoe, let alone one spot per every shoe dealt. Just one.

as.

Example.

A strict selected streaks approach could help us to define how things really work at baccarat even though we're considering simple B/P results.
That is considering mere B/P big road streaks happening at each shoe dealt.

Hypothesis

Knowing the ascertained math asymmetrical BP general probability, BP streaks distribution coming from real shuffled shoes are not following everytime dispersion values typical of a still 0.5068/0.4932 probability model.
Simply put, that the probability to get B or P at different spots taken will be different than the expected unbeatable values, meaning that some spots could be EV+ for the player.
A possible cause of such an effect should rely upon the finite key card impact acting along any shoe.

Method (material isn't discussed here for obvious reasons)

We've set up precise parameters to try to disprove our hypothesis.
After any streak of given lenght has appeared on any shoe, we wanted to test the "back to back" same streak lenght probability acting along any shoe, a supposedly almost 50/50 probability as B>P, albeit this last being a very volatile probability.
Therefore, we assumed B=P, assigning a greater value to the actual key card distribution.

Hence we've classified streaks among the more likely situations happening along any shoe that is restricting them within three different classes: doubles, triples, and 4-hand streaks.

"Back to back" means that whether no given class appeared so far, no one classification could be made.
In a word, that if a given streak apparition not happened so far, in our eyes that streak class  wouldn't exist in the shoe we're facing at.
This help us to reduce the general probability related to the actual probability.

Any real streak of given lenght up to any 4-hand streak (this value is set up only for practical reasons) will proportionally fight with an equal or superior lenght streak, but it's way more probable than expected that some streaks of given short lenght will get at least a single win on relatively "short" sequences of hands dealt.

Tomorrow a post about how this simple plan will get the best of it by any means.

as.

Gambling results are made of gaps, that is the number of intervals between a given event appearance and the opposing counterpart.
At baccarat BP probabilities are more or less corresponding to a A/B binomial model.   

Over a given sample of outcomes, higher is the number of gaps greater will be the probability to detect the apparition of one of both sides.
Thus it's way more likely to "be right" within a restrict progressive betting range on a 26-hand sequence like this:
AABABBBABABBAABAAABABBAABA than on a same 26-hand sequence as AAAABBBAABAABBBBABBAAAABBB

In the former example we got 16 gaps, in the latter the gaps number is 10.

Actually a simple flat betting procedure dictating to wager the same side happened last will produce (before vig) a -7 units and a +7 units.

In reality those two different sequences, whether compared to a virtual independent 50/50 model, formed patterns quite different than expected.

The former sequence is made of 9 singles, 5 doubles and 2 triples (average 50/50 probability being respectively 6.5, 3.25, 1.625)

The second sequence is made of 2 singles, 3 doubles, 1 triple and 3 streaks superior than 3.
(the final BBB sequence cannot be registered so far to any class other than a superior pattern than a double).
Of course the probability to get streaks superior than triples on a 26-hand sample is 0.8125.

Card speaking and thinking about average values, this means that in the former sequence key cards were more likely equally distributed on both sides and that in the latter sequence a strong key card imbalance went out for "long".

Many out of "key card" parameters will form the real BP results and all related AB outcomes (think about asymmetrical hand scenarios), but itlr and sure as hell, most gap numbers will be sensitive by the actual dynamic key card distribution prompting a great, average, light or neutral impact over the results.

Of course there's a natural relationship between gaps and streaks lenght that goes well beyond a mere 50/50 probability or a general whimsical asymmetrical strenght.

A thing we'll see shortly.

as.

Happy Holidays Al!

Be sure the new temporary forum "lockdown" won't be protracted over time as the previous one.

Thanks! 

Happy 2021 to everyone!

as. 

Excellent point, at least in the way I got it.

Probability can only be precisely ascertained by collecting from large datasets the limiting values of relative frequency of the events we're interested to classify.
Moreover to prove the complete randomness and to deny possible exploitable defects of the game, such classifications must be totally insensitive to place selection and probability after events tools.

And fortunately this is not going to happen, for good peace of the many stating that, for example, no matter when we start or stop our betting the probability to get a B double (ties ignored) will be 0.5068 x 0.5068 or that a PPPP pattern probability is totally insensitive of the previous hands quality taken at diverse ways.
Average values corresponding to math general probabilities itlr do not mean a fkng nothing to me as they are mixing here with there, up with down, that is just considering back to back results.

Baccarat is the prototype of a dynamic probabilities model, an ever changing proposition that should be investigated by comparing the actual dependent and dynamic probability model with a  coin flip "control" model. Shoe per shoe.

This help us to define when the asymmetrical feature will make a greater, neutral or lesser impact over certain outcomes than expected, or vice versa when the simple key card distribution will prompt at valuable degrees more likely patterns on the mere prevalent "coin flip" general attitude.

as.

Building several registrations by cutting off a nearly half part of the BP decisions has proven to be particularly effective in reducing dispersion values. Thus disproving the common concept that no matter which spots we decide to bet the probability to win or lose remains the same.

When we put two A/B opposite situations to fight against, we'll expect to get the same WL gaps distribution.
For example, after a given A/B four hand sample, the probability to get AAAA or BBBB will be 2/16.

Of course putting to fight mere B and P decisions on the same 4-hand sample will get, itlr, different distributions as B>P, but we know that such slight discrepancy won't do the job as being too much affected by volatility.
More precisely, we can't guess the spots where an asymmetrical hand will take place, because it needs a lot of favourable circumstances to appear. Moreover, we can't build a profitable betting plan onto a 8.6% whimsical probability.

Our hypothesis was built on the idea that certain portions of the deck are more affected by the slight asymmetrical nature of the game and, more importantly, by the finite key card distribution any shoe dealt provides.
And only a kind of "coin flip" A/B plan applied to several registrations could do the best to find out if we were right or wrong, as we had assigned the A=B variable.

The above AAAA or BBBB (or ABAB or BBAA for that matter) possible patterns springing out from a 4-hand sample after our new "hand cutting off" will become: (* symbol stands for a hand not belonging to our registration)

A*A**AA  or

**B*BB***B or

A**B*B**A or

*B*A**AA

and so on for every of the possible 16 patterns any 4-hand will be formed.

Now  we should expect that itlr A*A**AA = AAAA, **B*BB***B = BBBB, A**B*B**A = ABBA (lol) and *B*A**AA = BAAA.
In a word that every * symbol won't intefere with the AB general probability to show up.
And this is not going to happen. At least when given cutoff points are considered.
And actually whenever none or few * symbols build a given pattern, higher will be the probability to fall into the unwanted "random" world.

According to our results, most of the time there are only one or two spots per playable shoe to make a substantial EV+ bet. Thus bet the maximum limit allowed at that table, period.

Nevertheless and considering the casino comps and the gambling attitude of most HS bac players (not mentioning the camouflage approach, we never know), the probability to get all winning hands per playable shoe is well greater than expected after vig.

If we think we are crossing a kind of profitable shoe, along with our main wager plan we should even consider a meek "side bet" to start with, parlaying it until the end of the shoe as the probability to get all winnings will be well proportionally higher than expected.

Probably this last assumption is one of the best accomplishment one should look for, getting a given set of all winning hands per shoe.
Playable shoe, I mean.

as. 

Btw, special thanks and Merry Christmas to all readers of my section.

as.

Our datasets show that best edge comes from a random walks registration/actual BP results ratio  set up at 0.56.
That is on average our random walks must register a slight superior amount than half of the actual BP decisions coming out.
A quite interesting percentage I don't want to discuss here, anyway now we know that the supposedly random world and/or the very slight dependent world we are compelled to face is proven to be more restricted than we think, just by getting rid of nearly half of the unnecessary BP outcomes.

Our new derived collective extracted from nearly 56% of the total BP resolved hands should follow the common probability laws but it happens it's not the case.
Some spots are more likely than others, more importantly dispersion values are well more restricted than expected, meaning that the silliest progression ever invented will get the best of it by any means.

If our aim is to get just one large (maximum limit) unit profit per every new collective formed, our edge will be so huge that we will bored to play baccarat anymore by a lack of suspence.
   
In our experiments, we've tried to raise (or reduce) the already substantial edge by discarding a larger (smaller) amount of hands but with no avail.
It's like that the 0.56% cutting hand percentage is the best number to look for.

Next I'll post real betting situations.

Sadly I fear it's more likely to beat baccarat than to destroy this fkng virus.

as. 

Winning just one unit per each shoe played

One unit win and not per every shoe dealt...it might sound as a ridiculous goal no bac player would be interested to get.
However the more we are deviating from this basic achievement, higher and faster will be the probability to lose our money.

We can't hope to win an inferior amount than one unit, that is being ahead of just one hand (before vig).
But we've seen that simple progressions may find profits on precise LW points, so transferring the problem about the probability that, besides immediate wins, after a single losing spot the next hand should more likely get a win instead of another loss.
 
The fact that we're restricting the range of one unit wins within single shoes played relies about the supposedly (ascertained) probability that the statistical irregular strenght coming up on our favor collides with the sure mathematical steady force acting all the times.
Meaning that for practical reasons, on average the statistical strenght takes its greatest value on very few spots.

Of course betting a lot of spots with a huge betting spread entices the idea we're there to gamble, in the meanwhile collecting valuable comps.
But I assure you that most bac pros I know do not give a fk about comps, thus exclusively betting the spots they'd thought to be profitable.

We know that to be really profitable itlr Banker bets must get at least a 51.3% probability to get us an edge, Player's bets need a probability equal or higher than 50.1%.
Combine those probabilities in any B/P betting range you wish, at the end you must get a proper percentage capable to invert the HE. Otherwise you're just fooling yourselves and making casinos' fortune.

Interestingly, long term random walks data show that in given spots it's way easier to find the spots where Player side will be neutral or favorite to win than to cross the opposite situation, even though general rules make Banker more favorite to win regardless.

It's like assigning certain given variable cutoff values to the probability that Banker will be more likely than Player, naturally taking into account the general 8.6% asym probability distribution and the actual BP distribution prompting different random walks.

I can't see any answer other than the actual key card distribution, knowing that when given  portions of the shoe show a strong or moderate key card balancement, outcomes will be more fkng affected by a huge "undetectable" volatility.
Sometimes the key card balancement will be so hugely represented that no valuable betting spots could arise.

Odds are that whenever key cards are strongly balanced on the initial/intermediate parts of the shoe, subsequent portions of it will be less affected by a kind of key card concentration factor that tend to come in our favor.

From casinos part are there ways to forcefully balance the key card distribution along any shoe dealt?
Who cares, we got means to take notice of that and of course I'm not talking about this here.

Next post will be about the decisive importance to discard many outcomes we're not interested to insert in our registration.

as.

Playing with an edge means that we want to falsify the theory that no matter how and when we decide to bet the dispersion values are following all the time the numbers derived from common probability.

To do that we've set up multiple betting lines within the "coin flip" A/B scheme but well knowing that the results cannot come from an independent source, moreover affected by the rules asymmetricity.
Naturally the general B/P probability varies a lot depending upon the sections of the shoe where key cards are more or less concentrated.
It's literally impossible that every single hand will follow the 50.68/49.32 probability as there are no card distributions eliciting such exact probability.

Taken from a different point of view, we could even object about the perfect random nature of the outcomes as the place selection and probability after events tools will get different values than expected, thus disproving the perfect randomness.

We could assume that along any shoe the real probability will act at various steps depending upon the key cards distribution. And not by privileging one side, just certain patterns formation.

Efforts made in the past by eminent researchers were oriented to find spots where one side would have been more probable than the other one adopting a "black jack style" approach. Fruitless efforts we know.

In reality baccarat must be solved statistically, that is by taking advantage of the many intricate issues only very few players know.
It can be done, believe me.

In the endless process of studying deeply this game I have to thank:

- Richard Von Mises works, an eminent mathematician who publicized, imho, the strongest definition of randomness.

- Marian Smoluchowski works, a physics professor.

- Semyon Dukach inspiring ideas, one of the most famous member of the black jack MIT team that destroyed Vegas and many other casinos.

- Akio Kashiwagi, probably the best baccarat player in the world of all times.

- Glen "Alrelax", the only one person in the world besides my team colleagues I would risk my money with.

As long as outcomes are not coming out from either a perfect independent and/or a perfect random source, we know we'll get an edge.

as.