Hi KFB!

You've anticipated the exact point I would discuss about spotting light movements about a 0 point.

Say you consider two random walks applied at two streaks categories where each category includes a common first step winning class, then both class will diverge about the second step winning spot.
For example, one random walk is formed by 3-4 streaks and the second one is formed by 3-4+ streaks.

General probability dictates that we'll get an equal number of first step winning spot than second step winning spots, now splitted proportionally between those two opposite classes.
Of course to be true the general probability must take into account a kind of independent and random production acting at such precise streaks formation, meaning that everything will be equally probable so getting the normal sd values applied to a binomial independent probability. That is a unbeatable proposition.

We know bac streaks are not following a binomial probability by any means, either for math features (B>P) and for actual card distribution issues (a very slight propensity to get the opposite outcome already happened). An important decisive additional factor (never investigated so far) is that live shoes are not so randomly shuffled thus improving or not a general probability belonging to the former two fetaures.
Vulgarly sayed, math unidirectional propensity to get streaks of certain lenght will go directly into the toilet whether in the actual shoe the remaining two issues tend to overcome it.

In the attempt to try to exploit such features and to prove the dynamical unrandomness of the results, we could build a new random walk contemplating both different streaks 'lines' now studying the relative sd values.

To cut a long story short, the probability to get a common winning pattern happening at both random walks is moving around very low sd values once we'll take into account the xWW succession at one part and the WLW succession on the other one.
So dictating to bet toward the same outcome, that is toward a first step result.

Say streaks >2 at a given shoe show (a Aria, LV real shoe), btw it's a strong polarized shoe, not a 'easy winning shoe', as:

4, 10, 3, 6, 4, 4, 4, 5.

3-4 class will get W, L, W, L, W, W, W, L.
3-5 class will get L, W, W, W, L, L,  L, W.

Under the clustered/isolated betting spots converging into the same results (3), we'll get only the third step winning situation (W-W), yet we'll manage to bet just 4 times to get a xLW or WW pattern on both lines.
So we've lost 3 times winning just one time, anyway the actual 3:superior streaks ratio was a unusually 7:1.
Eventually we've lost two units (plus vig when applicable).

Say a kind of specular opposite situation came out as (Bellagio, LV real shoe) as:

3, 3, 4, 3, 5, 3, 3, 5, 3, 6, 4, 3

3,4: W, W, W, W, L, W, W, L, W, L, W, W
3,5: W, W, L, W, W, W, W, W, W, W, L, W.

Now we'll bet three spots (2nd, 9th, and 12th), all being winning spots.
The 3:superior streaks ratio now is a more likely 7:5 proposition, not balancing the previous 7:1 deficit.

Anyway and discounting vig, our random walk lost 2 units on that former very unlikely scenario and won 3 units on the latter yet proportionally unbalanced scenario as compared to the first one.

Cumulatively our new random walk found just 7 spots to bet at both shoes, eventually we have won 4 times and lost 3 times.
Notice that one shoe (first one) got a substantial abnormal deviation about the streaks appearance. More often than not, the 'first step' streak apparition will get its fair share of probability but do not confide too much about that as shi.t may easily happen for long.
Nonetheless this strategy will get you a sure fkng indeniable edge over the house, no matter how math 'experts' of my behind keep stating, after all they are managed to think about 'infinite' values where a random world will be in action and not about actual fkng real results.

as.

Good points Al.

I'll add my comments.

1) A clear frame of mind is proportionally related to the actual winning rate.
Most part of players expect to win more often than not at some portions of the shoe or after some shoes are dealt, unfortunately that's not possible with regularity. It's now that a 'blurred frame of mind' begins to work.
Only long term tests could improve a player's attitude to understand that sh.it can easily happens in clusters. 

2) There are plenty of studies showing that 'intuitive' thinking will slightly overcome a general probability of being right or wrong whenever a positive reinforcement of some kind is or was acting.
In simple terms we'll be more inclined to be right when we're winning than when we find ourselves to bet while in behind.

3) 99.99% of bac players tend to rely too much about common sense and too much about wishful thinking.
I mean that many times those two factors will converge into a misleading world.
I'd personally change the 'common sense' word with 'statistical evidence'.

4) Imo this point summarizes the above comments.

5) This is a wonderful point.
Casinos do not win a lot of money by their math fkng edge (side bets aside), but as players do bet too little at profitable spots and too much at losing patterns.
After a WWWWW pattern a player must get nearly the same winning amount being lost at the same LLLLL symmetrical sequence.
'Nearly' as the vig is a constant obstacle in terms of ROI.

It's a human attitude to start a session by betting small, then raising the bets whenever losing situations will invariably come out.
A perfect both mathematically and practically unsound move.

as.

Next week we'll see how some bet selections do not follow a perfect random walk movement, meaning that some BS steps move back and forward around a 0 point in the almost totality of possibilities.
One of the recipes to win itlr.

as.

Quote from: alrelax on February 22, 2022, 05:03:43 AM

Low ties 0-1-2-3 when there are plenty of hands out, tend to produce nice clumps of whatever.  Meaning, the presentations will basically follow something relatively easy to follow.  Higher amounts of ties say 5-6 and up, tend to produce much harder to follow presentations, etc.

Nice to hear from you this again, a further confirmation about that.

Shoes particularly rich of ties should fit the 'unplayable' shoes category.
We got even a theory about that.

Ties are more likely to show up when 6 cards are used to form a hand, that is where the most random world will take its place. As no key cards are more probably affecting the results at the start. 

So whenever ties seem to come out by a larger probability than expected, do not bet BP lines and get the fk out of that shoe very soon.

as.

Convergence in probability

No need to Wikipedia this concept that we can simply summarise into this passage:

"Stochastic convergence" formalizes the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle into a pattern.


Change the words 'essentially random or unpredictable events' with 'mostly unrandom events and quite predictable events' and 'sometimes' with 'more often than not' and you'll get a better idea of what I'm talking about.

There are no scientifical proofs showing that physically made baccarat successions are really randomly produced as they can't pass both the important 'place selection' and 'probability after events' features confirming the perfect random nature of results.
After all anyone thinking that baccarat produces random sequences infinitely should risk his/her money at other games.

So the vast majority of baccarat successions are made by limited probabilities oriented to produce more likely dynamic outcomes, of course at degrees well surpassing the fkng math negative edge.

But to get a substantial edge over the house we need our different limited random walks to converge into the same betting spot.

There are many ways to consider the factors influencing the actual patterns. A horizontal way of thinking the results (columns) is an answer as long with a kind of opposite vertical registration (rows).
Then the actual asym/sym hands finite ratio is another factor to consider.
Not mentioning how many high-key cards are live into the deck.
Finally, ties are surely another parameter to look for as shoes particularly rich of ties tend to deny 'normal' statistical deviations as any tie happened seems to 'erase' or lower any back to back expected probability.

To set up a long term winning strategy no need to take care of all those factors, maybe you have to do that whether flat betting maximum limits.
Actually a fair edge comes out whenever an isolated/clustered scenario converging into the same spot must take place at some points of most part of the shoes, as an already asymmetrical math proposition will be enforced by the important asymmetrical card distribution. Happening at unrandom shuffled shoes.

as.

Streaks as a realiable source of asymmetry

The asymmetrical card distribution feature could be exploited by advancing one step further, that is by considering only the streaks of certain lenght.
More precisely by forming 'classes' of streaks of specific lenght.

We well know that per each class of streak we'll get an equal amount of superior streaks, therefore two classes of streaks will fight against another one by a general 0.75 probability.

Say we want to examine 3,4 and 5+ streaks (from now we name them 5). (Of course there are reasons to choose such categories). 

Shoe example #1.  Streaks are: 5, 3, 4, 3, 5, 3, 3, 3, 3.

3 vs superior streaks = 6/3

4 vs sup streaks= 1/2

Since we won't know when a given class of streaks will outnumber a proportional 'homogeneous' distribution, let's try to consider all possible 3-4-5 combinations.

3-4= LWWWLWWWW

3-5= WWLWWWWWW

4-5= WLWLWLLLL

Naturally to try to spot the 'heterogeneous' streak (and more importantly its average impact over the actual distribution) we can always adopt the unb plan #1 guidelines.

Shoe #2. Streaks are: 3, 3, 5, 4, 4, 3, 4, 5, 5.

3-4= WWLWWWWLL

3-5= WWWLLWLWW

4-5= LLWWWLWWW

Shoe #3. Streaks are: 4, 3, 5, 3, 5, 4, 5, 3, 3, 4, 5.

3-4= WWLWLWLWWWL

3-5= LWWWWLWWWLW

4-5= WLWLWWWLLWW

Shoe #4. Streaks are: 3, 3, 5, 4, 3, 3, 4, 3, 5.

3-4= WWLWWWWWL

3-5= WWWLWWLWW

4-5= LLWWLLWLW

Of course and besides of the last part of shoe #1, I have omitted to present shoe examples producing long homogeneous streaks of same lenght as 3, 3, 3, 3, 3, 3, 5, 3, 3, 3. And they are quite often to happen.
I've already named them as 'jackpots' for obvious reasons.
Now:

3-4= WWWWWWLWWW

3-5= WWWWWWWWWW

4-5= LLLLLLWLLL


Notice and obviously that there are no tricks involved about WL percentages, in fact:

shoe #1

3-4= +1
3-5= +5
4-5= -15   

shoe #2

3-4= -3
3-5= -3
4-5= -3   

shoe #3

3-4= -5
3-5= -1
4-5= -5   

shoe #4

3-4= +1
3-5= +1
4-5= -11   

Finally the last 'homogeneous' shoe:

3-4= +6
3-5= +10
4-5= -26   

If we were playing with a team formed by three different players each betting its class (3-4), (3-5) and
(4-5), we eventually got a -48 unit loss (plus vig), a loss accumulated only by the 4-5 player.

Do not be led to think that player wagering the longer streaks (4,5) will be destined to lose heavily most of the time as many shoes will present a lot of 4 streaks with few or no 3s and sometimes shoes are particularly rich of long streaks (5).

Again we are jumping back to the same old concept that it's not possible to beat the game by a strict mechanical betting unless we're considering a kind of 'biased' card distribution happening along any shoe dealt negating a perfect random unbeatable world.
And few spots are really worthwhile to be wagered at.

Therefore there will be 'math' probabilities to get B after A and there are statistical and actual probabilities to get B after A as at baccarat no hand is completely independent from the previous one, especially whether we have reasons to think the actual shoe is not perfect randomly shuffled.

Always realizing that such slight propensity will act under insignficant variance values just at very selected spots.

as. 

Think that any shoe dealt in the universe will be affected by a kind of sure 'asymmetrical' bias as key cards cannot be proportionally distributed along any shoe.

The 'average' card distribution will help us to define what will be the more likely patterns that can't avoid to suffer natural short term negative fluctuations, but surely getting a long term profitability.

For example and neglecting a key flat betting strategy, set your random walk at an X more probable event (unb plan #1, #2 or code). Do not give a fkn fk about short term deviations. Dayly sessions are losers stuff.

Martingale your setted event by a progressive betting up you'll erase any previous deficit.
At any loss you'll stay at the same level, at any win you'll raise your bet.

Since we know that a chopping WL long scenario is less likely to happen than streaky negative or positive situations, a simple progressive plan will get the best of it as we won't raise our wagers unless a W came out and whenever a L shows up we'll stay at the same level.

The power of such strategy is that in any instance three different strategic plans will simultaneously get strong negative deviations on all lines.

And, btw, in any instance you'll get your bankroll crushed as a symmetrical losing world cannot happen for long at any single plan.

More on that tomorrow.

as.   

Without any doubt statistical signicance is the best tool to try to beat BP results.
So we must ask ourselves 'how large should be the testing sample to know if a strategy is really good?"

The larger=the better of course, then we must compute the average betting frequency per shoe and the actual source of outcomes.

Simply put, we have to test until natural strong 'negative' deviations will happen (as heavy positive fluctuations are more expected) in relationship of the number of bets considered and then evaluating their impact on our strategy.

After all if we've chosen to set up our main plan on 'averages', we should be ready to face any strong negative unlikely deviation the course of action will produce along the way. And those unfortunate situations will come out proportionally with the number of shoes tested.
Trivial considerations, I know.

For example, say we have found a method capable to survive after a 4 sigma negative situation (e.g. losing 16 hands in a row or other situations like that).
More or less it's like facing a negative 16 B or P streak that will put a harsh or fatal dent to our bankroll.
At a 50/50 proposition and discounting neutral ties, odds that we'll face this event are 1:65.536.

So, on average, assuming to play nearly 65 resolved hands per shoe, we need 1000 shoes to face this possibility.

At the same token, by betting just 6.5 average hands per shoe we'll need more than 10.000 shoes to get a 4 sigma.

Hence we shouldn't fool ourselves by thinking that a 'diluted' betting plan alone will get better odds unless a proper proportional amount of shoes were tested. (Of course betting by a 10 times less frequency leads to a minor vig impact). 
This trick was (and is) currently used by 'magic system sellers' that (and I'm taking into account the 'fair' part of them) had tested an insignicant amount of shoes when related to the actual betting frequency.
Even worse are the people keep thinking and claiming that simple key trigger mechanical situations happening on average 1 or 2 times per shoe will get 'em a long term profit.
Now they'd need at least a 32.500 or 65.000 shoe sample to verify their claimings.

And we know the importance to ONLY register real phisically shuffled shoes, better whether considered under the more homogeneously factors we can think about.
So it's very very unlikely that a player or a team of players will possede such a large sample, so such claimings will directly go into the toilet.

But now let's say that after a fair amount of tested shoes in relationship of a shoe's average bet frequency, per every strong negative deviation happening (where we can't do anything) we'll get an unproportional amount of strong positive deviations, that is a number higher than 1.
If this number is substantially higher than 1, we might overcome the HE even knowing that our general math expectancy will be negative but our actual probability of success will go beyond the expected values.

And this possible feature must show up unproportionally at each class of favourable or unfavourable streaks lenght.

For example: say that after 1000 hands placed and assuming to bet a 50/50 percentage of BP hands, we've set up a strategy where our profitable winning rate must be at least 50.7%.
Thus we need to win at least 507 hands, so losing hands account as 493.
It's a 1.4% cutoff edge, the minimum value to beat the HE when considering a 50/50 BP percentage average betting frequency.

Now let's dissect such values in terms of patterns.

Step #1

W singles must be lower than W clusters of any lenght;

L singles must be superior than L streaks of any lenght.

Step #2

W doubles must be inferior than superior winning streaks;

L doubles must be superior than superior losing streaks.

Step #3

W 3+ streaks must be superior than triple W streaks;

L triple streaks must be superior than 3+ losing streaks.

And so on.

Each class fights constantly against the opposite counterpart, so itlr a powerful strategy must get every class to outnumber the same opposite class by an ascending line.

It's the average card distribution that beats the house.

as.

8OR9: good points.
BTW, "happy wife (or happy husband) = happy life" 

There's a big difference between baccarat testing and black jack testing:
At black jack we are just interested about high/low card concentration/dilution, being high cards favourable and low cards unfavourable, anytime anywhere and anyhow. So pc simulated shoes are really worthwhile to test.
In a word, one sided deviation (deck portions rich of high cards and aces) will be the only guideline to follow in order to get a math edge.

At baccarat the main factor polarizing the results will be the average key card distribution, but we do not know how much and how long a side will be kissed by such key card falling.
Moreover many 'whimsical' results produce 'prolonging' or 'stopping' patterns where math apparently can't do anything about that other that in the very long run.
That is there are so many actual variables to consider that we should just rely upon the king/queen tool of statistical evidence: the frequentist approach.

So, for example, never assume that after tossing a given dice a '6' will show up by a 1/6 'expected' probability unless you have collected data capable to confirm that (sd is the watchdog of randomness).
Now it's clear that pc simulated shoes are not performing the same qualities any physically shuffled shoe dealt will get as many different than 'high/low' variables come in order.

Consider a Shuffle Master Machine shuffling two different shoes alternatively.
The probability a fresh shuffled shoe will break ALL coupled (back-to-back) cards happened at the same dealt shoe is literally zero. And many times even three (or more) cards won't be broken in their old sequence.
You can argue that this thing doesn't make a side more likely than the other one, yet this is a strong proof that shoes are not so 'randomly' shuffled as people would think of.

There are additional examples to make not involving SM machines that for obvious reasons I do not want to expose here.

Anyway think that in the vast majority of the times, physically shuffled shoes can't simulate a pc card distribution as a kind of bias is acting along the way at some point.
So testing a strategy on pc bac shoes is a fruitless task.
After all we won't bet our money at pc simulated shoes.

as.

At baccarat the only thing we should look for is the 'Probability World', I mean the real situations bac tables are going to produce endlessly.

We won't give a lesser cottontail rabbitsh.it about math laws as those belong to an 'ideal' world where each hand is completely independent from the previous one and the source of results will be perfect randomly distributed.
Therefore do not insult your intelligence by thinking that baccarat cannot be beaten as math dictates so.

Anyway it can't be beaten as well without having measured your results by testing a very large LIVE shoes sample.

After having tested a lot of real live shoes and knowing what to look for, it's quite easy to find out that potential math probability has nothing to share with actual probability, especially whether we're considering series of limited events.

That means that itlr the probability to get an 'average card distribution' shoe will overcome any other scenario and whenever an average shoe will happen we're strongly favored to win.

as.

Quote from: alrelax on February 01, 2022, 02:30:34 AM

However the problem once a player wins using it, is his psychological end which falls subconsciously to greed (big time) and then the recklessness begins. 

I have written extensively about that. 

Being successful at baccarat involves numerous things to be conscious about and employ at the table.

You are absolutely correct!!

Probably the quote Hoping for the best but expecting the worst best illustrates the concept.

Even playing by a math edge (or an advantage of some kind) we must 'hope' that things will go in our favor in a decent amount of time; in the meanwhile we must expect the worst.

Sometimes even casinos rely upon that adage.
Think how glad pitbosses stare at an occasional super high stakes player finding endless winning streaks with no guarantees he/she will return to play there.   

Sayed that, I'm pretty certain that baccarat is a scientifically beatable game, actually the best game to play at any casino.
It will be a time when casinos will use CSM at their bac tables, erasing any possible 'card distribution' study and finiteness of the shoe, neutralizing random defects and of course any side bets card counting.
Or maybe not as 99.9% of bac players (a real optimistic percentage) keep staying at the 'ignorant' side of the things, so continuing to fill casinos' pockets. 

Finally, but we should know that very well, itlr the probability to win mathematically at a math EV- game is zero.

But 1+1=2 only when 1 is a real 1; maybe in the real world 0.9+1.1=2 and it's now that things could change.

as

This new derived road will take care of the 'predominant' red or blue global propensity (2/3 or 3/3) happening at any shoe dealt.
If 2/3 or 3/3 of all three DRs dictate to get a red spot and the next hand will be a red spot we'll sign a red spot otherwise we write down a blue spot.

Of course this new line will get the same identical properties of any other registration, confirming that baccarat shoes are not so randomly produced as general probabilities dictate.

It's now that we should understand the important fact that some hands cannot belong to our registration by any means as they simply had surpassed our cutoff points of interest.

Since bac shoes are finite by definition, we know that the probability to get this or that will be proportionally related about how many times such cutoff points will be surpassed.

We can't control every outcome, let alone the majority of outcomes, we could just control the propensities of an average (then more likely) card distribution.

In other words, our strategy should rely upon a 'limited random walk'.

We can do that as any card distribution of the universe cannot deviate from more likely occurences for long, otherwise casinos would be thrown out of business by offering bac tables.

So 'easy detectable trends' will be less and less probable as long as shoes are dealt whereas the 'more likely world' must happen very soon than later.

Math expectation and statistical expectation

Mathematics cannot be disputed but the environment where math should be working should.

There's no one serious statistical evidence proving that live baccarat shoes are randomly produced, and we can't give a lesser fk whether itlr B will approach more and more the 50.68% winning probability.
For that matter ask the math geniuses what will be the more likely pattern coming up at both sides and such fkng 'experts' have to run simulated shoes to provide an answer.
As no math formula will help them.

In any instance simulated shoes are belonging to an 'ideal' world as cards are not physically shuffled with all the consequent random limitations.

We can guess that a profitable strategy relies upon the actual probability to get a more likely average card distribution than a deviated card distribution as we've tested that the former category will overcome the latter category itlr.
So in some way we must get the lesser impact of natural deviated situations over the more likely normal lines, a principle perfectly opposed as to what many bac players will try to take advantage from.

And the answer is by assessing clustered and isolated events.

as.

At gambling (and at real world for that matter) it's very unlikely that authors and works of the past won't be of any help for actual scholars.
You know that on my pages I've stressed a lot about the cleverness of derived roads (DR) Macau inventors in the 70s: even though it's probable their main aim was different than ours, derived roads remain the best indicator that baccarat could be beatable.

Why casinos that are so smart in extracting money from their customers keep presenting derived roads on their displays?
I do not know, probably as math gurus had instructed them to think that more derived lines are showing up higher will be the confusing world players must face. Or in any case that DRs won't hurt the house.   

Notice that baccarat literature remains focused about B and P hands (mainly by fruitless card counting techniques) or side bets card counting but nobody has ever mentioned DR features.
Along with other features. Fortunately for us.

Of course to be worthwhile DR probabilities must follow a kind of 'biased' original BP sequence, so if we win at DR we'll win at Big Road too. And vice versa.

Technically this thing is possible only when disputing the real randomness of the sample (card distribution) by place selection and probability after effects tools.
Or that baccarat was beatable at the start but 'experts' hadn't find a decisive tool to look for as stubbornly oriented about math probabilities.

Building a fourth derived road

This is not the magic potion to look for, just an accelerating and additional tool to assess in order to get more likely patterns along any shoe dealt. A further proof that the random world won't be so random.

Say we call it 'asymbac' road as I strongly think to be the first to publicly present this idea.

In a nutshell, we are simultaneously registering all 3 DR (byb, sr and cr) in form of blue or red dots by this rule: whenever 2/3 or 3/3 DR will converge toward a specific color (blue or red) we will write a blue or red spot in one separated line accordingly to the actual red or blue outcome.

Since any hand is good to provide a shifted red or blue spot as 2/3 oriented no matter what, we can assess an additional 'predominant' red or blue line considered by 'codes' and each having a more likely  lenght.

Example.

Shoe went as

PPP
BB
P
BBBB
PP
BBB
PPPP
B
PP
BBB
PPPP
B
P
BB
PP
B
PP
BB
P
BB
PP
BBB
P
B
P
BBB
PPP
B

The actual 'asym DR' went as:

rrr
b
r
b
rr
b
rrr
bb
r
b
rr
b
rrr
bbbbbbbb
rrrr
b
rrrrr
bbbb
r
b
r
bb
r
b

Let's add byb and small road lines:

byb:

r
bbb
rr
b
r
b
r
bb
rr
bbbbb
r
bb
rr
bbb
r
bb
rr
bbb
rr
bbb
rrr
bbb
rr
b
r
b
rrr

and sr:

b
r
b
r
bbb
rr
b
r
b
r
bb
r
bb
r
b
r
b
r
bbbbbbbb
rr
bbb
rr
bb
r
bbbb
r
b
r
bb
r
b

If we were to assess the most likely card distribution this shoe presents, we see there are good opportunities to look for, sometimes so polarized a child would get the best of, others more intricated but in any way 'codes' are way more restricted than what a unbeatable random world dictates.

More on that tomorrow.

as. 

Quote from: klw on January 26, 2022, 08:00:17 PM
Cogratuations AsymBacGuy . It truly is 1 of the best threads ever. Full of information and very helpful. I am using your information as a base for my Bac. journey. A problem I am encountering is that I am trying to observe and note hand histories from live play. I can't seem to find a free play Bac. table and when I observe my online casino tables you get disconnected pretty quickly if you don't place a bet and I don't want the added pressure of placing bets while studying what's going on.

Any ideas how I get round this ?

Cheers.

Thanks klw!

Yep, it's quite difficult to play at online casinos and one of the reasons is just the disconnection issue.
For that matter I know some people experiencing many disconnections even though a lot of real bets were placed but a more fearsome issue to face is that some bets are 'returned' without any sensible reason (as they were placed on time and connection was good).
Finally, too many cards are burnt at the end of the shoe (for obvious reasons) erasing some profitable opportunities to bet.
However, a strong pro about online play is that you won't catch Covid by any means 

I'd suggest to manually shuffle and deal shoes for yourself, tracking the results by a free software that takes care of all roads.
A further (but quite costly) improvement is to purchase a Shuffle Master machine (identical to those working at live casinos) where you can get a new fresh shoe ready to use after the first one was dealt.
Now you can compare the same shoe results coming out alternatively.

as.

I have to thank you all as this thread got 100k views, it's a nice accomplishment I'm very proud of!

Special thanks to Alrelax, the owner of this site. Then thanks to Kungfubac, klw and many others.

On one occasion I've heard a bac manager of one high end casino saying "not every baccarat player is a loser".
Good news. We suspect he was right. 

Next week I'll present a class of additional derived roads to look for.

Take care.

as.