Hi KFB, good thread and link!

I totally agree with your comments;IMO and especially at gambling we should be way more interested about the probability of something NOT happening.
Then (at gambling) there's the art to try to avoid the total impact of those "improbable" events that sometimes could be even turned in our favor.

Maybe we should use the key factor why casinos will get huge profits: time.

as.

Example.
How many times a different than 6-7-8-9 winning point category comes out as clustered (some shoes sample)?
0= no clusters, 1= one cluster and so on.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1.

Ok, it's more likely that such 0s derive from a 6-7-8-9 winning point happening at P side than at B side.
At the same token, it's more probable that 1s come out from a 6-7-8-9 category falling at P side than at B side, so stopping the opposite category to be clustered more than one.
And so on.

as.

Differently than pure coin flip independent propositions, per each shoe dealt (8-9 points) vs (any other winning point) move by more detectable ranges, moreover 8s and 9s are slight more likely to show up at Player side than at Banker side.

In fact the total number of 8s and 9s final points at B side account for a 27.4% probability whereas at P side the same total number is 28.8%. (naturally Naturals probability remains perfectly symmetrical between the two chances).
Even 6s and 7s final points are asymmetrically distributed accounting for a 26.3% at B side with P side getting a 28% probability.

Cumulatively 6, 7, 8 and 9 final points get a 53.7% probability at B side and a 56.8% probability at P side.

Therefore if we'd "think" that the next final point or close to the next final point will be a 6,7,8 or 9, we'd better wager Player and not Banker.

Definitely the vast majority of winning points fall into the 6-7-8-9 category.

On the other end, Banker side gets an asymmetrical probability to ends up the hand by a 4 or a 5 point accounting for a 19.4% probability vs a 14% Player probability to show up the same 4 or 5 final points.

There could be all the variance you want, yet itlr any 6, 7, 8 or 9 point is advantaged at various levels to win the final hand.
And as we've seen there's a mathematical factor shifting such points category towards the P side.

In other words, whenever we think that B side won't get a 5 or 4 initial two-card point and, more importantly, that the next final point will be a 6-7-8-9 point, wagering Player side is by far the best option to make.

In fact: Naturals are getting a perfect symmetrical probability to come out but an asymmetrical payement.
All other 9s, 8s, 7s and 6s points get a probability shifted towards the Player side, not mentioning (again) that the payement is quite diverse (0.95:1 than 1:1). Even at no commission tables, such points category will benefit more by wagering P side than B side.

Exaggerating the concept, it's like we just try to get rid of those "low" final winning 5 and 4 points markedly privileging Banker side; almost anything else is going towards Player side for a reason or another.
Even if it seems that many huge points will succumb to greater points or whether a high point falls many times at the "wrong" side.

Naturally B predominating shoes are getting a real threat to this plan, but this is just one unidirectional random walk to be taken care of as the vast majority of the times B streaks need very long sequences to get univocal results at ALL different random walks considered.
If this shouldn't be true, baccarat wouldn't exist.

as.

To cut a long story short, knowing that all 8/9 winning points battle by a kind of coin flip with any other winning point, assuming that cards are asymmetrically distributed along any shoe dealt, and taking care of other tools, we could split every shoe dealt into two distinct categories:

1- Condensed BP pattern shoes (low or very low CFS);

2- Diluted BP pattern shoes (huge or moderate CFS).

Of course the derived random walks (A/B, r/b, etc) will get different lines (very often taking an opposite route) at any shoe dealt but eventually featuring one of the above categories.

It's obvious as hell that at some portions of the shoe (sections) things could easily take a strong opposite way than assessed previously, but we have found to be particularly profitable to make an approximated shoe model first, then trying to make some possible adjustments along the course of it.

After all we just need to be right by few steps per any shoe dealt, one step ahead should be our main goal all of the time.

More later

as.

House edge and finite dependent successions

There's a strong difference between wagering at an independent model or at baccarat.
Think about side bets: they are offered with huge HE just to prevent acute players to get the best of a finite dependent succession.
For example the tie bet being payed 9 to 1 instead of the common 8 to 1 keep assuring the house a strong advantage, yet no casino will offer this better (for players) payment.

So is it possible to make a plan capable to exploit tie bets no matter how much is the HE?
The answer is no, unless we want to live at bac tables without betting a dime for long (very long).
Tie favourable conditions are too rare to happen, but more importantly tie distribution is too much affected by volatility, a real enemy for players.

Tiger bets (B winning with a 6 point) move around a more depicted scenario (even featuring a higher HE than ties) but still difficult to chase for the same volatility issues.

The same about F-7, Panda bets and other side bets.

Curiously the best bets featuring the lowest HE and where all players (correctly) focus their main action are B/P hands but with no avail for the simple reason that it's very difficult (say almost impossible) to guess which side will be kissed by the higher point other than by luck.

Actually what we need to conquer a finite dependent model is not centered about the HE but about the volatility.

A perfect random (so totally unbeatable) distribution is any succession where each spot is completely independent from the previous ones and getting the same relative probability to appear without featuring "jumps" or "falls".
BP hands are sensitive of those jumps and falls but unfortunately we can't assess which side will be favorite unless, IMO, we are linking many hands together so to build "complex" patterns more affected by a diverse probability to show up.

More probable winning points

Most results are made by 7, 8 and 9 final points so if we're putting into a graphic the 7-8-9 category vs any other winning point (1,2,3,4,5 and 6) we might get an idea of the average winning points distribution (gaps, clusters, etc).
This graphic features a very low (controllable) volatility as besides the strong impact of 9s, 8s and 7s, many points will be formed by two or three card totaling 7, 8 or 9 winning points.

Actually some time ago we've found four casinos offering a side bet where players have to guess which point will be the final winning point, no matter which side won.
Tie hands are just a push (no win no loss).
Of course and without any doubt there's a HE so a continuous play will get only losses for the unfair payment at each winning point class.
But good news is that each winning 7,8 and 9 class will get a low variance for any shoe dealt so differently than any other bac side bet.
That means that a kind of conditional probability is working at many steps of the shoe, moreover enforced by card counting 7s, 8s and 9s.

That's one of the few occasions to make a sort of progressive multilayered betting plan based on the probability of success.

Actually even a simple selected betting made upon the sole 8 and 9 winning points vs all the remaining points move around a coin flip probability but getting a very low variance than real coin flip tosses.
 
Related considerations about BP hands

Higher final winning points will favor more the P side than B side, in fact Banker's advantage is mostly centered about 5 and 4 final winning points.

Therefore if we'll expect a 7,8 or 9 winning point, we somewhat deny most part of asymmetrical hands favoring B side.
Moreover P side is payed 1:1 and B side 0.95:1.

Guessing right the side getting a 7,8 and 9 final winning point is just a matter of short term luck, we need to think about the long term picture.

I know that confiding that very soon a 7-8-9 winning point will come out at any side it's way better than estimating which side will win (despite of the HE being nearly 5x worse at the former scenario), yet we shouldn't forget that what wins at 1:1 ratio is way better than what wins at 0.95:1.

Obviously if we'd think that the more probable next hand will be included within the 7-8-9 range, betting the Tiger bet is just a waste of money.

Next we'll see how BP patterns might be linked to get a kind of favourable side bet.

as.

Eagles 40-22

Good job.

as.

I can't understand why our software put a plus on Eagles side about the Louisiana wheather conditions.

as. 

Mmmhhh we're wondering why our computer told us it was "a slight advantage" for Ph Eagles...
Maybe it works better with bac algorithms than about football predictions....uahahahhah

as. 

Our computer never fails....

Now only a very unlikely bad beat could change a sure Eagles win

as.

Al wrote:

However if you believe in the reality of the game of baccarat and set aside your desires, you just completed one tiny (could be large) step and put on a great game face that can lead you down paths to your advantage.

Good point, but IMO we should raise the ability to process the actual informations with the general more probable card patterns not giving too much emphasis to single results.
Itlr we'll succeed.

For example, and I'm referring to the KFB reply too, if we could restrict the range of an 8 or a 9 as a first card falling at Player side, we'll get a strong edge.
We do not need to be right every time, just more than average (general probability is 2/13, of course).
Into a general heavy symmetrical card model and without pc findings or other advanced tools, the easiest spots to extract a kind of advantage are those focused about the first card of any new hand dealt.

If the first card is a 7, 8 or 9 more than 3/13 of the times, we are in the position to reduce, erase or invert the HE in relationship of how much we are able to alter that ratio towards the left.
Of course even 6s belong to that category.

On the other end of the spectrum, zero value cards or aces, 2s and 3s perfom the exact opposite result (maybe eliciting B wagers).

IMO we do not need to win what happens at the shoe we're playing at, just winning the most part of the shoes we're wagering.

More later.

as.

Our computer says Eagles should be slight advantaged.

Let's see what happens.

as.
 

Hi KFB, thanks!

KFB: I like this/always good to see when a gamer knows this %. It is my opinion ones' wagering approach should be built up/out from this known value. Though it is my opinion this is seldom a static figure one simply needs to know the Mean/ expected range. If one is an advantage player it is my opinion we can see this fluctuate from approx -1.36% ---  +7.35%.


Yep, edge comes out when shufflings are close or very close to the "average category" and that means that key cards are distributed by more probable ranges.

For example, if we knew how many cards will be utilized to form the next hand, we're getting a strong advantage as:

a) 4 cards utilized: A perfect symmetrical situation where one side (P) is payed 1:1 and the other one (B) 0.95:1.

b) 5 cards utilized: An asymmetrical situation where only P6 and P7 points (11.8% probability with Banker having to draw) make Banker unfavorite to win.

c) 6 cards utilized: A complex asym/sym situation splitted into two different categories:

c1- A pure symmetrical spot where both sides must draw no matter how's the third P card and

c2- A former asymmetrical spot where the third card dealt to the Player must elicit Banker to draw.

Obviously any higher two-card initial point is strongly favorite to win the final hand at both categories.
Moreover any hand formed by 6 cards is way more probable to end up as a tie.

Mathematically scenario a) accounts for a 37.8% probability, scenario b) accounts for a 30.5% probability and scenario c) accounts for a 31.6% probability. The total is 99.9% instead of 100% just for the decimals.

Naturally and without any doubt any Banker bet must rely upon a 5-card hand because it includes a larger part of profitable situations for that side.

On the other end, 4-card hands and most part of 6-card hands will make the Player as the best bet to make for a symmetrical world coming out at the start or becoming 'symmetrical' thereafter.

So it could be useful to approximate at best those 4, 5 or 6 card ranges, in the sense that whenever we'd think that the next hand will be formed by 4 cards the best bet, by far, is the Player bet.

If we'd think that the next hand will be formed by 5 cards, odds are that we'll be way more likely to win by wagering Banker side.

If we'd think that the next hand will be formed by 6 cards, well we better choose to stay put or, at the very least, to make a Player bet with a kind of minimal tie side bet whenever 6-cards consecutive hands are coming out.

Since any shoe dealt is somewhat affected by a kind of conditional probability, it could be worthwhile to estimate the total of the actual number of cards utilized in relationship of an "expected value" verified by long term data.

By doing that we'll better approximate how many 5-card hands can come out in a row and the more likely levels kissing the same side or how many 4-card hands deny a side to lose for long.

6-card hands? They are only good for gambling.

as.

Thanks Al, I've read it. Good thread indeed.
Sometimes the boundary limiting a catastrophic session vs a profitable one is very thin.
Anyway it was one brilliant example of how things might work at baccarat.

Our estimated edge

Since we cannot use our algorithms in real play and not trusting (mainly for technical reasons) online games, we're forced to approximate at best an already approximating way of considering an average card distribution. Nonetheless at the end our average edge lines up at around 3.46% after vig.
It's a real big advantage but unfortunately performing huge fluctuations related to the actual shoe card distribution.
       
That's why we strongly suggest a flat betting procedure as we can't know when and how many those expected profitable shoes are coming out at the single sessions we're playing at.

So per every $10.000 wagered, on average we'll expect to win $346; that means that after one hundred $100 bets we'll win 3,46 units.

Yet and even though the advantage remains as constant, we ought not to forget that consecutive shoes not belonging to an "average card distribution" class may easily come out in a row; on the other end and even if more probable to happen, multiple profitable shoes could give us the idea we're unbeatable.

In our opinion, at baccarat there's nothing to guess or hope for, we should just rely upon objective long term findings with all the intricated related statistical issues.

After all if we know that per each bet placed we'll get an average 51.73% ROI, we should just wonder how sweet is to play baccarat instead of keeping a 9-5 job.

BTW, there are no possible countermeasures to be employed by casinos.

First, it's virtually impossible to shuffle 416 cards by a not average card distribution for long.

Second, the vast majority of bac players not giving a f about the average card distribution topic (or not knowing its existence) will get the most advantage by shoes not belonging to that category, meaning that more shoes are deviating to the "average card distribution" class and better will be their (short term) results.
A thing particularly hated by casinos while facing very HS players, so hoping that sooner or later things will get a undetectable rhythm. And that's the average card distribution we're talking about.

as. 

Suppose we have decided to follow three patterns distribution: A, B and C.

Since per each shoe dealt we have strong reasons to think that a perfect balancement of the three patterns will be the least probability to happen, first we must choose if we're either acting from a quantity point of view or from a quality point of view.

Quantity is in direct relationship of a given pattern appearance (presenting two or more times), quality is any different pattern coming out after a given pattern (so the previous pattern stops its appearance).

We've seen that whenever a pattern hadn't shown up so far we might consider it as virtually non existent, so luring us to bet for the other two possible patterns.

On the other end, more hands are dealt and greater will be the probability to fall into a "silent" pattern, so stopping the other two patterns flow.

Our data have shown that quality takes a primary role over quantity, otherwise the game would be easily be beaten by following what happened.

After all, there are only two ways to lose several units in a row:

1) Chasing for long a silent quality pattern (fatal error)

2) Keep betting for too long toward clustered patterns.

Anyway it's the "for long" and "too long" that will make a decisive role about our long term results.

The important tool to look for, regardless of the random walk(s) utilized, is to properly ascertain whenever a pattern should be more entitled to get a cluster of any kind, knowing that a minor part of the total shoes dealt will increase the different patterns appearance.

Technically we know that gambling revolves about streaks, baccarat is revolving about streaks even more.
That means to build some derived random walks then assessing the lenght of such streaks in order to get them clustered or not.

as.

By Alrelax: "But, the player must know how to handle his wagering losing and winning hands during the course of the shoe and session.  And I have written plenty about that."

Yep, after all at baccarat each bet wagered will get either a tremendously wrong or an astoundingly good result. Sometimes a hand won't be resolved (tie) and it's not a coincidence this situation happens way more often whenever six cards are utilized to form a final hand.

Winning and losing hands are more probable to move around asymmetrical clusters, so basically it's the average lenght of such clusters that matters.

Patterns are just the by product of a more likely card distribution, that's why baccarat is not offered by dealing 1-deck or 2-deck shoes.
Casinos want a lot of cards to be arranged, technically that means to dilute or concentrate at most the key cards in order to prevent more probable patterns formation.

So one of the tools we could exploit, in our opinion, is to let many hands to go as sooner or later cards will align with a more likely distribution.
Not always this tool will help us to get an edge, most of the times it will.

More later

as.