Thanks for the link KFB!

It's an interesting list of course, especially for black jack and video poker players.
I agree about the South Point, probably the most crowded Vegas casino at any hour of any day for a reason.

As baccarat player, I would mention which casinos offer commission and no commission games, but more importantly what's the average action at the tables.
Normally the baccarat action in US outside Vegas is good or very good. For obvious reasons it's not the case for Vegas casinos.

It's really sad to play alone or with just another player or asking too many times for "free hands", especially for low frequency bettors.

This is my list based upon the baccarat average action (number of players) in Vegas casinos (no downtown casinos are considered here).

Good action

- Gold Coast
- Palms

Medium action

- Aria
- Palace Station
- Bellagio
- Venetian
- Durango
- Paris
- Stratosphere
- Red Rock
- South Point
- Rio
- Orleans
- Caesars Palace
- Rampart


Low action

- Wynn
- Encore
- The Palazzo
- Fontaineblue
- Resorts World
- Cosmopolitan
- MGM Grand
- MGM Park
- Treasure Island
- PH
- Boulder Station
- Mandalay Bay
- others

Not coincidentally the two most crowded casinos are close to Vegas Chinatown: you'll be surprised to see several tables open (and full of players, especially at Gold Coast) in a unsuspected Monday morning. A thing happening only at Macau.

A more technical thing (considered worthless by "experts" but not by us) is how the shoes are shuffled. In Vegas shoes are not manually shuffled so either a machine do the job or preordered shuffled decks are utilized.
Since most players like to peek at the cards, more and more preordered shuffled shoes are dealt in Vegas.

Then there are several additional factors to award a "best baccarat tables in Vegas" prize.
Mostly are related to min/max betting limits, HE, general atmosphere, propensity to deal many free hands or dealing a new shoe before the end of it, then average skills and 'composure' of the other players (generally speaking there are more good local players than good tourist players). Etc.

From a strict HE point of view, the best Vegas baccarat casino ever was (or still is, we don't know) the "D" in downtown where Banker winning bets were burdened by a mere 4% vig.
Besides of a short lived experiment made at Sahara casino in the 80s, where there wasn't no commission at all at B winning bets (lol), by far "D" casino offered the best baccarat tables in the history of this game.

as.

Hi KFB! Thanks for your interesting reply.

Can you elaborate this passage of yours?

Sometimes(not always) we may win FIRST (due to skill or luck). Then have the option to:Press to our win, regress to our win, set aside that wager for a perceived better entry, press higher,...etc all the while compounding our initial base unit.


Thanks in advance.

Take care.

as.

Hi KFB!

You wrote:

My opinion differs on the progression part(Posprogression is the path mi amigo). HOWEVER, the pos progression must be applied against "An increasing improbability", then set aside, then reinserted again later on. In other words, not inserted with the expectation for a single event to continuously repeat in perpetuum. Many players have unrealistic expectations for "same-event streaks". that's my opinion.

I understand your point and I totally agree about the "increasing improbability" topic.
What I would think is that, generally speaking, a positive progression will concede to the house those (albeit relatively rare) overalternating WL sequences where any win is not properly balanced by the following loss, meaning that in any case in order to win we need some winning clusters to show up.

Since most bac movements, yes, distribute themselves by a slight number of homogeneous clusters than by an overalternating fashion, it could be a point to wait that some (slight improbable) overalternating situations had shown up, then betting toward deviations on either side of the "model". Up to a point, as you correctly sayed.
We continue to support the idea that if an advantage comes out, it must show up by a larger number of winning than losing situations, so the betting amount shouldn't be our main problem to take care of. But in any instance raising the bet where supposedly favourable conditions are coming out doesn't hurt us either. To say the least.

@Alrelax

You're right, yet casinos know by an absolute certainty that more bets are placed greater will be their profits, otherwise they won't get the players such luxurious comps or, even worse, a rebate on their losses.

Most high end casinos know very well the baccarat vulnerability, yet they keep relying on the "human" vulnerability this being proportionally related to the number of hands wagered.
Math is just an additional factor not the cause of it.

Success is not a goal, it's just a by-product

as.

Single/few hands vs the whole picture

Suppose we want to consider patterns by the number of resolved hands (no ties) forming them.

Let's start with two-hand (A or B) patterns:

AA, BB, AB and BA.

Here the probability to cross a homogeneous pattern (AA and BB) vs a heteregeneous pattern (AB and BA) is 50%.

Three-hands patterns:

AAA, AAB, ABA, ABB, BBB, BBA, BAB, BAA.

Now homogeneous results (AAA and BBB) constitute 2/8 (25%) of the possible outcomes.


Four hands patterns:

AAAA, AAAB, AABA, AABB, ABAB, ABAA, ABBB, ABBA
BBBB, BBBA, BBAB, BBAA, BABA, BABB, BAAA, BAAB.

Now there are only two homogeneous patterns (AAAA and BBBB) vs 14 heterogeneous patterns. It's a 12.5% probability.

And so on.

Sooner or later every pattern will more or less coming out by the expected probability, yet per each shoe dealt such probability will be somewhat "biased", meaning that homogeneous and heterogeneous patterns will be more probably distributed by a kind of clustering effect.

Whenever such clustering effect acts at heterogeneous patterns, we'll get an easy job as an opposite side must come out at different levels: we might let some hands go before betting (for example privileging the exact value patterns already happened) or trying to "force" the model by betting two or three times in a row to get the searched outcome.

On the other end, homogeneous patterns being the less probable situation to face tend to consume "space", meaning that they somewhat decrease the probability to get the heterogeneous counterpart.

Cutting to the chase this complicated issue and knowing that cards are asymmetrically distributed along any shoe dealt, say that homogeneous patterns are surely (but slightly) more probable to be followed by a heterogeneous pattern, yet the process consume "space".
At the end and since we are forced to "approximate" at best the more probable patterns, say that a  homogeneous pattern showing up somewhat reduces the probability to cross multiple heterogeneous situations.

This thing could be better ascertained whenever we'll consider the common derived roads. Only very long (and unlikely) BP streaks will deny the heterogeneous patterns formation.

Another way of considering shoes is by assigning a progressive number to every consecutive same pattern (singles or streaks): itlr final total values will be restricted into well defined ranges and, more importantly, we'll see how's the probability an intermediate value will fit the average value or not.

Baccarat shoes are not a balanced mix of something, something is biased at the start.

as.

Hi KFB, thanks!!

Before thinking to play baccarat with an advantage, let's see the main reasons why we aren't supposed to accomplish that task.

1) Per each bet placed, we'll wager 1 unit to get an inferior than 1 economical return being in form of many kind of commissions at winning B bets and a general underdog probability at P bets.
It's the old math HE, obviously working whether the result distributions are really randomly arranged.

2) The vast majority of players think that a kind of progressive plan will make the job, in reality such "ploy" will increase the casinos' profits as those players are relying upon the mere LW patterns (in any permutation) coming out along the way.
Actually if they would know when things start to change, they should just wait for such spots without consuming money at previous worthless losing situations.

3) More hands are wagered and less precise will be the winning targets as most of the times anything can happen anytime.

Summarizing the worst baccarat player in the universe is anyone thinking that results are randomly distributed, making some fancy "progressive" betting plans and wagering a lot of hands.
Such player will get a 0 probability to win itlr.

Conversely, a possible long term winner must rely upon the partial "unrandomness" of the results, wagering by a strict flat betting scheme and betting very few hands.

What the baccarat literature "teaches" us:

a) Best bet to make is always the Banker bet (rattlesnake.stuff)

b) Any new hand is a completely independent hand from the previous one(s) (bighorn.stuff)

c) No matter when we'll decide to bet, each resolved bet (no tie) will get an average 50.68% or 49.32% probability to show up (strongest desert tortoise sh.i.t)

Actually the game cannot be perfect randomly distributed by definition, as for any hand dealt key cards and game rules cannot form a complete independence in forming patterns.
We're deadly sure about that, meaning that after some conditions are met some patterns are way more likely than others and that's where our edge comes from.

We have already seen that a single result "going wrong" can shift more likely short patterns into a longer one, that's the unlikely situations where amateurs look for.
Of course it happens that many patterns "naturally" evolving in long patterns are getting an opposite and math unlikely help toward short patterns, yet itlr short univocal patterns will overwhelm the longest ones.

Casinos prosper about our intrinsic inability to know what should happen about columns patterns and not about row patterns as most players rely upon rows lenght and not about columns quality.

No matter how's the specific random walk considered, any pattern is more likely to move around a 1 or 2 step.

as.

There are several ways to classify an asymmetrical or symmetrical pattern, just to make things simpler say that every streak followed by a single or every single followed by a streak is a first step asymmetrical pattern.
Whenever a homogeneous pattern happens as a single/single or a streak/streak situation, we'll wait  until a new different pattern will happen. 

What we're interested at is not the mere quantity of such situations but their average "gaps" (ranges) as very few shoes will disregard this important feature.

Moreover the Big Road linked with a proper random walk will make such ranges so predictable that the probability to win will reach astounding values.
This is so good that we could even think to adopt a kind of progressive plan.

Only problem is that sometimes there are some colliding events where we don't know which road to be followed. In such instances best option is not to bet anything and wait for the next spot.

Example of a real shoe restricted by cutting off many hands at the start and at the end of it. (A strong symmetrical unlikely shoe, btw)

(A= any single followed by a streak or vice versa, S= anything else) BR= Big road, ORW= our random walk

BR: A-S-S-S-S-S-A-A-A-S-S

ORW: S-A-A-A-A-S-A-S-S-A-S-S-A-A-S

Second shoe:

BR: A-S-S-S-A-S-A-A-A-A-S-A-A-A-S

ORW: A-A-A-S-A-A-S-S-A-S-S-A-A-S-S

More shoes:

BR: A-A-S-A-A-A-S-A-A-S-S-S-A-A-A-S

ORW: A-A-A-S-A-A-S-S-A-A-S-S-S


BR: S-S-S-S-S-A-A-S-S

ORW: A-A-A-S-A-A-S-A-S-A-A-S-S


BR: A-A-S-S-A-S-A-S-A-S-S-S-S-A-S

ORW: A-S-A-S-A-A-A-A-S-A-A-S-A-A-S-S


BR: A-S-S-A-S-S-A-A-S-A-A-A-S-S

ORW: A-S-S-A-A-A-S-A-A-S-S-S


BR: A-S-S-A-A-S-A-A-A-A-A-A-S

ORW: S-S-S-S-S-S


BR: A-S-A-S-S-S-S-A-S-A-A-A-A

ORW: S-A-S-S-A-A-A-A-S-S-A-S-S


BR: S-A-S-A-A-S-A-A-A-S-A-S-S

ORW: S-S-A-A-A-A-S-S-S-S-S-A


BR: A-S-S-S-S-S-A-A-A-S

ORW: A-S-A-S-S-A-S-A-S-A-A-A-A-S


BR: S-S-S-A-A-A-A-A-A-S-A-S-S-S

ORW: S-S-S-A-S-S-A-A-A-S-S-S

Notice the AAA(x) / SSS(x) ratio, for example. Or the A vs AA(x) ratio.

as.

Hi KFB!

Maybe you could recall that I've crossed through an ALL 1s-2s shoe, anyway getting 1s-2s strings of 17-20 or more is not that infrequent.
I understand that things so polarized are visible after the fact: it seems that whenever we'd try to bet toward singles or doubles a streak (perhaps just a 3-streak) suddendly come out 

It's true that heaven could be a nightmare (and vice versa) if we are not properly focusing on the game.   

Anyay it's good to hear you have won the previous 6 sessions. Not an easy task though. 

as.

Merry Christmas to everybody!!!

as.

Have a wonderful and successful New Year my friend!!!

as.

Thanks for your reply Al, that's what I was mostly referring to. 

Al wrote: IMO, it all equals out somewhat.  As with almost everything in the game of Bac, equalization is just about paramount.  Of course we never know exact turning points and at times, things do not equal out.


Same points were brilliantly discussed by KFB in his posts.

-------

Casinos make a lot of money from bac players not for the tiny HE but for a simpler reason:

They rely upon the probability that it's impossible to be more right than wrong at random sequences happening at a kind of coin flip game.

Really? No way.
Actually bac successions are far from being randomly distributed, let alone mirroring an independent coin flip game.

A coin flip toss succession relies about a constant 50/50 probability to get H or T, meaning that any hand has no link with the past outcomes.
More deeply, no "general" plan could be devised as anything can happen everytime.

On the other end, bac successions are the by product of a finite card distribution, now key cards (nearly 30% of total ranks) will make a huge impact on the long term results, then nearly 30% of the deck is neutral (0 value cards).

The average key cards/neutral cards concentration/dilution ratio is the main reason why patterns will be asymmetrically or symmetrically placed.
Obviously there are many other secondary situations to get a W or L hand, yet we can safely assume that key cards distribution (0 value cards as well) are more asymmetrically than symmetrically shaped.

Baccarat (mostly for the third/s card impact) is sensitive to many "incidents", so what is naturally asymmetrical seems to be symmetrical shaped.

Nobody investigated so much how first two-initial cards will affect the final results in terms of W/L ranges.
Let's run some shoes, consider the common 4 roads (BR, ByB, SR and CR) and tell me if you would find some patterns to rely upon. I guess the answer will be in the affirmative field.

But, as we know, fkng third(s) cards will tend to destroy this plan.

Nonetheless, a BP succession and its derived sequences are entitled to get a bit larger number of asymmetrical situations, of course in proportional relationship of the general probability to happen.

Anyway the decisive tool to take care of, in our opinion, is that once a symmetrical pattern had shown up, we must wait this will ends up as the more likely distribution works at new fresh successions always fighting against a less likely another new symmetrical distribution.

After all and per every shoe dealt, the probability to cross asymmetrical spots not forming at least one cluster is 0.
On the same line, asym/sym distribution will take a strong kind of RTM effect, meaning that possible "(unlikely) symmetrical consecutive and different patterns will get the room to more probable asymmetrical shapes.

See you in a couple of days, I'll provide many examples extracted by live shoes data.

as.

Hi KFB!!

re: third card.
    Do you try to hypothesize if the next hand will include a third-card draw? Meaning the next hand will potentially have a total of 5 or 6 cards dealt(and then use that"3rd card potential", in your decision making for deciding which side u will wager??)

That's an acute observation.

Actually any 5-cards hand starts with a math advantaged side (greater two-card initial point and, at a way lesser extent, bac rules favoring B), of course we do not know which side will be kissed by such math edge.
Sure as hell, this math edge will shift the results itlr in the sense that "miracle third card catching" will be overwhelmed by a way more normal flow of the cards.

On the other end, 6-card hands are the epitome of the randomness as now there's a wider range of cards determining the final result.

The bold conclusion we've reached is that in reality there is no randomness in the distribution of two-card higher initial points: they'll move by more likely ranges, period.
A thing confirmed by the infinite random walks we may build after the original BP succession.

Unfortunately many hands are resolved by 6 cards and naturally a quite number of 5-card hands will help to win the unfavorite side.

Whenever many hands are resolved by 6 cards (and remember that ties are way more probable to come out in this situation) the BP sequence and even (partially) the sub successions derived from it tend to take more whimsical lines than expected.

In some sense, the 6-card hands are the only real random situations baccarat can provide. Those are representing a kind of independent (unbeatable) coin flip toss even though we know that itlr we'll win half of them and we'll lose half of them.

Since we can't know when a 6-card hand will show up, we have found particularly useful to consider the shoe patterns by exploiting the asym/sym nature of them, now by forcily assessing the actual BP results and their derived sub sequences.

In any instance, it's obvious that any shoe dealt is affected by a strong asymmetry (Alrelax pointed out several interesting situations to grasp), the problem is to find statistical tools to know when to bet toward this ad when to stop the betting (or even wagering FOR it).

More on that later

as.

Let's consider this real shoe at the common original and derived roads (BR, Byb, SR and CR); "arw" is our main random walk. All patterns are considered under the lens of A/S patterns.

BR: S, A, A, A, A, A, A, S, A, A, S, A, A, A, A, A, A, A, A, S, A, S
ByB:A, A, A, A, S, A, S, A, A, A, A, A, A, A, A
SR: A, A, A, S, A, S, A, S, A, A, A, A, A
CR: A, A, S, S, A, A, S, A, A, A, A, A, A
acr:A, A, A, A, A, S, A, S, A, S, A, A, S, A, A

There are 78 spots to look for, 17 of them are S, the remaining are A.
Even by choosing randomly a betting spot at any line, we'll get 61 profitable spots and 17 losing situations (17 x 3 = 51). 

Another real shoe.

BR: S, S, S, A, A, S, A, S, S, S, A, A, A
ByB:A, A, A, S, A, S, A, A, S, A, A, S, A, S, A, S, A
SR: A, S, A, A, A, A, S, A, A, S, A, S
CR: A, A, A, A, A, A, A, A, S, A, A, S, S
asr:A, A, A, S, S, A, A, A, A, A, A, A, A

There are 68 bettable spots, 22 of them are S (22x3=66) the rest is A.
Despite of the unlikely 21/6 S/A deviated scenario happening at BR, A events still predominate (a bit) over S events.

See you next week

as.

Most bac players try to spot symmetrical situations whereas itlr asymmetrical spots will slight overwhelm them in terms of quantity.

If the results would be decided by the first two initial cards without the intervention of the third card(s), well the game wouldn't exist at all. (Obviously I admit a kind of vig on each winning bet).

The reason is because the CFS more often than not will take not homogeneous sequences, getting the room to more likely successions.
This theory could be better ascertained whenever we run multiple sub successions derived by the BR: most lines take an asymmetrical way to distribute the A/B outcomes, in the sense that the symmetry represent a kind of incident.

Obviously a symmetrical world in relationship of its general expected probability to appear must "catch up" sooner or later and this thing can only be accomplished by coming out heavily clustered or strongly intertwined by few asymmetrical spots.
But such natural situations are not entitled to happen simultaneously at two or more sub sequences and when this unlikely scenario shows up, we've got to accept it and wait for the next spot.

More later

as.

Thanks KFB, thanks!

After all, imo, we have to rely upon the "average card distribution" with its limits (and deviations) and not a general slight math propensity happening just 8.6% of the times.

9s, 8s, 7s and 6s as first or third cards will get the same symmetrical probability to show up as second or fourth cards.
The same about naturals (34.2% of total hands), hands that almost always will win right and then.
Yet at both scenarios the payment is way different.

Back to the A/S topic.

I'll present some real shoes by two different A/S successions, first is the common Big Road and the second one is our main random walk. A= 1, S= 3

A-A-A-A-A-A-S-A-S-A-A-A-A-A-S-S-S-A-A-A-A-A-A  (A/S = 18/15)
A-A-S-A-A-A-A-A-A-A-S-A-A-S-A-A-A-A-A-A (A/S = 17/9)

That's an easy shoe, quantities shifted toward the A side will make things easy.

A-S-A-A-A-A-A-A-A-A-A-A-A-S-S-S  (A/S = 12/12)
A-A-A-S-A-A-A-A-A-A-S-A-A-A-A-A  (A/S = 14/6)

Same as above.

A-A-A-A-A-S-A-A-S-A-A-S-A-S-S-A-S-S-S-A-A (A/S = 13/24)
A-A-A-A-A-A-A-A-A-A-S-A-A-A-A-S  (A/S = 14/6)

This shoe is more intricate as the first line is heavily shifted toward the S side, yet the second line remains deviated at the A side. 

A-A-S-A-A-S-S-A-A-A-A-A-S-S-S (A/S = 9/18)
A-S-A-S-S-A-S-A-A-A (A/S = 6/12)

Ouch, symmetry (whatever intended) happens...both lines are strongly deviated toward the S side.

A-A-A-S-S-A-A-A-A-A-A-S-A-A-S-A-A-A (A/S = 14/12)
S-A-A-A-S-A-A-A-A-A-A-A-A-S-A-A-A-A-A-S-S-A-S (A/S = 17/18)

Another shoe where the asymmetry seems to hide, not a too harmful shoe though.

S-A-A-A-S-A-A-A-A-A-A-A-A-S-A-A-A-A-A (A/S = 16/9)
A-A-A-S-A-S-A-A-A-A-A-S (A/S = 9/9)

In this shoe the global asymmetry, even by showing up just at the first line, returns to be predominant.

A-A-S-A-A-A-A-S-A-S-A-A-S-A-A-S (A/S = 11/15)
A-A-A-S-A-A-A-A-A-A-A-A-A-A-A-A-A-A (A/S = 17/3)

Again here the asymmetry seems to be cumulatively inferior to the symmetry.

A-A-A-A-A-A-A-A-A-S-A-A-A-S-A-A-A-A-A-A-S-A (A/S = 19/9)
A-A-A-A-A-A-S-S-A-A-A-A-A-A-S-S-A-A-A (A/S = 15/12)

Fkng good again. Let's continue to try to catch sometimes really "bad".

A-A-A-S-A-S-A-A-A-A-A-S-S-S (A/S = 9/15)
A-A-S-A-S-S-A-A-A-A-A-A-A-A-A-A-A-A-A (A/S = 16/9)

At the first line the proportional symmetry surely overwhelmed the counterpart, but the second line filled the gap.

S-S-A-A-A-A-A-A-A-A-A-A-A-S-A-A-A (A/S = 14/9)
A-A-A-A-A-A-A-A-S-S-A-S-A-A-A-A-S-S (A/S = 13/15)

Same scenario as the previous shoe, but now the A/S ratio was able to get a profit.

S-A-A-S-A-A-A-A-A-A-A-A-A-A-A-S (A/S = 13/9)
A-A-A-A-A-A-A-A-S-S-A-A-S (A/S = 10/9)

No bad shoe, both lines converged toward the asymmetry.

A-A-A-A-A-S-S-A-A-A-A-A-S-A-S-S-A-A (A/S = 13/15)
S-S-A-A-A-S-A-A-A-A-A-S-S-A (A/S = 9/15)

Finally, sigh, another two-sided symmetry oriented shoe.

A-S-A-A-A-A-A-A-A-A-A-A-A-S (A/S = 12/6)
A-A-A-A-A-A-S-A-A-A-A-S-S-S (A/S = 10/12)

Here overall the asymmetry overwhelms the counterpart by 4 (before vig) steps.

S-A-A-A-A-S-A-A-A-A-A-A-S-A-A-A-A-A-A-A-A (A/S = 18/9)
A-A-A-S-A-A-A-S-A-A-S-A-A-A-A-A-S (A/S = 13/12)

Results speak for themselves.

A-A-A-A-S-A-A-A-A-S-A-A-A-A-A-A-A-A-A-S (A/S = 17/9)
A-A-S-A-A-S-A-A-S-A-A-S-S (A/S = 8/15)

A kind of "balanced" shoe where one line will balance the other one.

A-S-A-A-S-A-A-A-S-A-A-A-A-S-A-A-A-A-S (A/S = 14/15)
A-S-A-S-A-A-S-A-S-S-A-A-A-S-A-A (A/S = 10/18)

A classic shoe where we can't do almost anything but accept the negative outcomes.

S-A-A-A-A-A-A-A-A-A-A-A-S-A-A-A (A/S = 14/6)
A-A-A-S-A-S-A-S-A-A-S-S (A/S = 7/15)

A perfect "balanced" shoe, so a slight negative shoe (for the vig).

A-S-A-A-A-A-A-A-A-A-A-S-A-A-A-A (A/S = 14/6)
A-A-S-A-S-A-S-A-A-A-A-S-A-A-S (A/S = 10/15)

Asymmetry is shifted here by 3 steps (before vig)

A-A-A-A-A-A-A-A-A-A-A-A-A-S-S-A-S-S (A/S = 14/12)
A-A-A-A-S-A-S-S-S-A (6/12)

An opposite situation as now the symmetry is 4 step ahead than asymmetry.

Overall in this small sample the raw asymmetry was 27 step ahead over the raw symmetry (before vig), but there are additional statistical tools to exploit this propensity in order to get the minimum vig impact.

as.

The above examples were built by registering one of the infinite sub successions we can extract from any BP sequence.

Suppose we want to run parallel sub successions, are the "vertical" A/S two or more sequences getting a complete undetectable random world?

More later

as.