Situations when Player is the best bet to make

1) 'Lucky 6' tables (here any Banker 6 winning point is payed half the bet, so the HE on B bets is 1.46% vs 1.24% at P bets);

2) There is a shortage of naturals related to the average naturals ratio at commission games;

3) Asymmetrical hands actual number related to the average ratio;

4) Asymmetrical hands destiny over the real results;

5) Patterns evaluation on the shoe we're playing at.


1) At Lucky 6 tables and besides of card counting the L6 side bet, best bet to make is Player.
Actually whenever there's a strong shortage of naturals, even betting Banker side could be a sensibile option as there's no commission involved.

2) Naturals have the same probability to appear but at commission games they are asymmetrically payed (1:1 at P side, 0.95:1 at B side).
So whenever we think a natural should come out shortly we have reasons to bet Player and not Banker.
In fact whenever a natural point comes out, our EV at P bets is 0 whereas it's -2.5% at B bets.

3) Asymmetrical hands, those really endorsing a math force at B bets do not come out around the corner. We'll expect them by an average 1/11.62 ratio. So about 10.62 times out of 11.62 we'll play a perfect coin flip game where no side is particularly favored over the opposite.

Obviously and taking the Banker counterpart thought, we have only two ways to get the best of it by always wagering Banker: a) catching above than average asym hands gaps or b) hoping that the shoe we're playing at is richer than expected of such asym hands.

But we need to be a lot more confident (so guessing, that is hoping to be lucky) about the
b) point than the a) point as the latter is more defined by 'more probable' spots.

For example, we have reasons to think that after an asym hand had shown up, a way more symmetrical  spot comes around and such sym hand will be way more clustered than singled.
 
Bac players are too much focused about the real destiny of the hand than about the 'quality' of the hand.
Thus any Player bet not crossing an asym hand is at least an EV=0 proposition, so not conceding any HE.
Conversely any Banker bet NOT crossing through an asym hand is a sure long term ROI (return on investment) loser.

4) Asym hands come out by finite values, it may easily happen that at an asym hand will make the Player to win (for example think when P has 4 and B 5 and the third card is a 2 or a 3, etc). So in this instance we may consider such asym hand as a 'wasted' opportunity to make B more probable to win. And on average it takes quite of space to make another asym hand to come out.

5) Strong polarized shoes, albeit being very rare, tend to remain slightly more polarized than balanced until the end and giving a fk about expected percentages (besides 'naturals' happenings).

Eventually and by assigning a proper value to the above factors, we could build up a 'Player probability score' where we should be inclined to bet or not the Player side. Not necessarily meaning that when such score is negative Banker side will be more probable to happen as the strenght favoring it more often than not is not sufficient to erase and invert the HE.

as.

Coin flip random walk and baccarat random walks

Flip carefully several times a coin and try to guess which side will win.
Itlr you are supposed to break even but at the same time by increasing the number of tosses you'll find yourselves either into the positive field or into the negative one for long (very long) and obviously such probability is 50/50.
Now say that each win is decurted by 1% so when you bet 100 you are payed 99 and when you lose you lose 100.
There is no way that after a large amount of trials you'll be in the positive field even if you are the new genius in town.

Casinos offer baccarat tables for this very reason: as long as we're paying 99 for 100 (or because the probability is somewhat shifted between the two sides) itlr everyone will be in the negative field. Additionally and just in case casinos have other tools at their disposal ('infinite' bankrolls, maximum betting limits, taking advantage of the many gamblers fallacies, etc).

Thus if we are not able to shift the results in our favor at a fair coin flip proposition (other than by chance) and knowing we surely can't win if the coin flip is burdened by 1%, why the hell are we playing baccarat?

To answer this question and as long as we'd think to be smarter than the 'house', we are forced to  think just about two things:

a) baccarat productions could be not perfect randomly offered;

b) baccarat productions are affected by a kind of 'dependence' as a finite number of cards is employed to deal the game (bac rules considered).

In fact those are the main factors that may alter bac successions vs coin flip successions. (Yes, by now we someway disregard the B>P probability).

What is important to say, imo of course, is that such important possible features will work by slight values and many times not presenting by sufficient levels capable to erase the HE.

It's like we're betting at a game where our EV moves from -1.06/-1.24 to +0.50 or +0.80, sometimes and hopefully way more positive than that.
So it could take a relatively long time to get its cumulative full power.

Are there bac random walks better than others?

Yes, providing we'll make a super selective betting worth of getting rid of the many 'coincidental' results making the recreational players fortune (or misfortune).
And of course providing that the best random walk we could think of is made by the least possible amount of favourable spots, that is 1.

For example say that we have two A and B events (that in no way could be B and P) to choose from and the 'range' of intervention will be 4 event steps.

Per every 4-event step, we'll get 16 possible patterns to face and 14 of them include a kind of consecutive A or B result.
So only ABAB and BABA patterns won't form any consecutive A/B pattern.
It's the old unlikelihood to get multiple 'hopping' events in a row, remember?

Ok, but the above values are taken assuming a 50/50 independent and random game, so we have reasons to think that a kind of dependence and possible unrandomness will slightly shift more such unlikelihood to get ABAB and BABA.
And even if this is not true, at some point those two less likely events must concede the room to the other more likely patterns at the next 4-event steps.

Therefore we do not need to get multiple A or B consecutive patterns, just any AA or BB pattern per any step of any lenght considered (4-event step was just an example).

Ok, per every 4-event step we'll have to make 3 bets to get a consecutive A or B 'run', but we can easily wait to bet after the first or the second betting step that had fictionally failed once or more times.
It's like we are adopting a kind of progressive multilayered plan acting just after some deviations happened so now a flat betting scheme will get the best of it at different levels.
The more we wait for deviated results higher will be our EV, providing to take care of A and B events that may need many hands to be classified.

Fortunately and without waiting too long, it's a piece of cake to understand when A or B will be clustered at least one time, as always it's important not to particularly like A or B as they are the exact opposite sides of the medal.

as.

Hi asym

Nice /thorough essay.

"a) baccarat productions could be not perfect randomly offered;

b) baccarat productions are affected by a kind of 'dependence' as a finite number of cards is employed to deal the game (bac rules considered)."


re: a) I agree, however, the detection early in the "non-random" presentation is often difficult. This nonrandom presentation often is fleeting or short-lived, IMO, at least for me it is difficult to discern in early stages.

re: b) The finiteness of cards and events is IMO what makes Bac a better game vs say craps or blackjack(early shuffles,..etc).



Continued Success,

Thanks KFB for your reply!

About the possible unrandomness of the game I would present this topic:

The wrong player and the right player

Say that anytime we join a table we have two distinct players thinking for us: the player who tries to be right most of the times and a second player hating the first one and liking to counteract his options as he knows that it's impossible to be right most of the times at baccarat.
Obviously the same impossibility to be wrong most of the times will apply for the 'wrong' player.

So we have to decide which one to follow as hands are dealt.

Since we know that the probability to be either right or wrong per each shoe dealt can't be 1 or 0 (providing a fair number of bets made), we could assume that at some stage things will change.
And if things do change, probability to get the right player or the wrong player to win can't be 0 or 1 but must come out by a probability higher or lower than 50%.

Naturally the probability that the right or wrong player will win is in direct relationship of the betting frequency, so the lesser the frequency higher will be the probability that things won't change.

Nonetheless and assuming for example a 1/4 betting frequency (one hand bet per every 4 hands dealt, ties ignored) probability to be always right or always wrong is not zero but very very very unlikely to happen. Actually for a 80-hand resolved shoe, it's like to be right or wrong by crossing a nearly 4.5 sigma probability.

Before crossing such very very very unlikely scenario, more likely patterns will come out at different levels so endorsing the right or wrong player probability to win.

I mean that it's very very very unlikely to get 20 hands shifted toward one wrong or right side, but there's a way greater probability to guess right 20-hands long by 'following' the right player or the wrong player at some point to stop their winning/losing streaks.

The important thing is to reduce (select) the A/B events pace as more hands are needed to form a given pattern higher will be the probability that things will change.
And this is not only a by product of variance but of cards distribution probability.

In a random independent binomial succession 1-steps and 2-steps are equally balanced with superior steps, at baccarat the binomial succession is dependent, finite and asymmetrically placed by the rules, not by an universal strenght but by an 'actual' strenght that must takes into account a volatile degree of likely unrandomness acting at various levels.
So here very often 1-steps and 2-steps are more or less likely than expected.


as.

Right and wrong players work by classes, that is by random walk steps

It's sure as hell that random walks moving at a perfect random environment can't provide detectable points as random world remains random, that is unbeatable.
So here we have strong reasons to think that the right or wrong player will take 'unguessable' lines even though the game is asymmetrical by the rules and somewhat finite.
Thus we don't know when the right or wrong player 'steps' will move forward or to stop then eliciting the opposite player to show up.

Fortunately, most of the times baccarat shoes won't fit the 'perfect' randomness feature and long term datasets proving otherwise can directly go under the toilet.

Therefore in the vast majority of the times our right and wrong players 'steps' move around way more likely situations. And that means a sensible likelihood that an event A will go forward or to stop by percentages different than expected by a perfect random environment.

But to grasp a probable non randomness of the outcomes we need to consider 'multiple hands' events , that is the total negation of the place selection tool confirming that a given succession should considered really random only whenever every point (whatever taken) will get the same probability to appear and at baccarat this is not the case.

More on that next week, in the meanwhile keep winning as we do. 

as. 

Even though RP (right player) and WP (wrong player) outcomes will deviate from the 0 origin for long, we should understand that every intermediate movement will more likely take short but asymmetrical steps.

First let's consider a perfect random independent binomial model applied to infinite 6-hand patterns. So RP=WP.
Ties ignored, we have 64 possible R/W patterns but only 16 of them will be balanced in terms of an equal number of R and W.
It's like that anytime we attack each 6-hand pattern (whatever taken) the probability to get a kind of 'unbalanced' overall scenario vs a balanced one is 4:1.
Obviously this ratio won't change in relationship of the exact point attacked, as being proportionally placed.

Now let's take a double asymmetrical, finite and way likely not perfect random distribution (baccarat) where R and W  are supposed to get more polarized lines for every 6-hand dealt.
Thus we play (for real or fictionally) a 6-hand range pattern knowing that we are more likely to end it up by a sort of unbalanced ratio.
And what are the most probable unbalanced ratios to look at?
Naturally 4-2, then 5-1 and finally 6-0.

The important fact is that RP and WP do not play simple hands but patterns, so needing a more room to come out (that is more connected hands).

Therefore the RP and the WP are way more probable to form unbalanced short ratios than getting balanced lines for long.
Naturally we can't know exactly when a line will be unbalanced and by how much but surely it will.
Especially after having properly evaluated the previous balanced patterns surpassing some 'more expected' normal values.

After all, whenever we take a univocal betting line (RP) we are missing a lot of valuable opportunities coming around for the WP.
And we need just one step to be ahead or, at worst, to guess at least one winning hand per every two bets made.

Example.

Everybody knows the difficulty to be ahead after two or three or more shoes dealt, and the HE plays a minor role on that.
Obviously as long as the RP wins, we do not have reasons to shift toward the WP betting line.
But such thing happens more infrequently than most players hope for.

Anyway WP has the same identical probability to win and getting the same winning lines, but luckily for casinos nobody is going to someway stop or neglecting a possible unlikely winning line of some kind (so NOT taking the RP part) as the players' aim is to stubbornly get 'sky's the limit' winnings around any corner.

as.

Let's take the casino's counterpart: they serenely accept RP results knowing that sooner or later the WP counterpart will come out. (HE is just an accelerator factor working for the house and not the main tool making us losers).

In fact huge players winnings are asymmetrically produced than huge casino winnings and not by a 1.25% or so HE working for them.

I mean that unless we are able to endure long waiting periods before betting, many times we have to take the part of the WP, that is and taking a forum member words 'playing to miss' instead of constantly looking for favourable opportunities making the RP fortune.

Technically and just to give an example is betting a couple of hands that streaks will stop, or possible starting patterns to stop, or better yet that no common valuable patterns should come along, the right 'hope' (it's a symmetrical expectancy) casinos will rely about.

If you are able to catch the more likely situations where WP will get its share of 'positive' results, you won't concede room to casinos hoping for inevitable strong outcomes changes.

In some sense it's like that nearly 50% of the times we're playing the same side casinos hope for.
And itlr casinos do not lose and more importantly do not win just what math dictates.

Next week I'll elaborate this concept.

as.

Patterns waiting time

Coin flip successions were deeply investigated by many scholars and not only by a strict math/statistical point of view but even about how they are perceveid by humans (Gardner studies for example and many others afterwards).

To cut a long story short, humans tend to get an 'overalternating' perception of random binary outcomes, in poorer words they expect a given winning side to stop soon after a positive run or to think that a streak of certain lenght is less likely than what math really dictates.
It's one example of Gambler's Fallacy.

On the other hand, after years of playing this game, I've found that most part of baccarat players tend to assign too much emphasis to the opposite feature, that is looking for the 'streaky' part of the game and neglecting the 'alternating' one.
Obviously and differently to a coin flip succession where H and T are continuously showing up, bac players add some (basic) considerations to the 'streaky/alternating' ratio, for example considering singles vs doubles, or double vs 3+s, long streaks, etc.
In any instance most players constantly hope to get streaky situations of some kind to show up as it's the easiest situation not needing much thought to accumulate winnings.

See you later

as.

So we are 'genetically oriented' to think that random successions are somewhat more limited than real, but all of a sudden while playing baccarat we are completely distorting such predisposition thus hoping for endless streaky situations of any kind.

The difference between the two different ways of thinking 'outcomes' is that whereas our ancestors would have starved for long when they didn't find any food (so fearing at most long no-food runs), at baccarat we can serenely wait the possible favourable opportunities without consuming a lot (or any) of our resources by exploiting the most likely situations that must happen sooner or later even if they don't show up around any corner.
Furthermore and even considering a 'unbeatable' random world, some patterns that mathematically have the same probability to appear will show up sooner than others.

Example.

Say that at a random coin flip succession you have to choose from one of those HTHHTT or HHHHHH pattern coming out first.
All intermediate patterns do not count, so you will win or lose just when one of the two patterns will show up first.
Different studies, albeit being made on different patterns lenght, have demonstrated that the former HTHHTT pattern will show up by a lesser 'waiting time' than the HHHHHH pattern, despite of having the same probability to appear.

So we do not know about all other patterns coming out, but we do know that we're favorite to first cross the HTHHTT pattern than the HHHHHH pattern, so in some way the 'waiting time' matters.

Obviously this finding doesn't directly help us to predict bac outcomes (random independent propositions are unbeatable by definition), but maybe luring us to think about the importance that    some events, albeit getting the same probability to appear, will feature different 'waiting times'.

Fortunately for us, baccarat is not a perfect random proposition and not even a perfect symmetrical 'fight' (as B>P), yet the aforementioned findings still get a huge role in determining  why 'complex' events (e.g. HTHHTT) should show up first before some other 'equal probability' counterparts will do.
Therefore in some sense attributing a decisive role to the 'waiting time' gaps.

See you next week.

as.

AsymBacGuy above in post #773.

"...Say that at a random coin flip succession you have to choose from one of those HTHHTT or HHHHHH pattern coming out first.
All intermediate patterns do not count, so you will win or lose just when one of the two patterns will show up first.
Different studies, albeit being made on different patterns lenght, have demonstrated that the former HTHHTT pattern will show up by a lesser 'waiting time' than the HHHHHH pattern, despite of having the same probability to appear.

So we do not know about all other patterns coming out, but we do know that we're favorite to first cross the HTHHTT pattern than the HHHHHH pattern, so in some way the 'waiting time' matters. ..."

I agree Asym and wait-time distance between shorter patterns are even more important IMO(as related to Bac). With that said I also think we need to be cautious when comparing a coin toss vs a near-5050 proposition such as so called even-chance games like Bac. Due mainly to how the casino treats a Push and Tie results, which obviously a coin toss has neither.


In my opinion one of the best pieces of research on coin tosses and similar probability events was written by a Dr. R.S. Nickerson back in early 2000s I believe. In part below (I will post whole article once we have capability to upload pics and such).


Reasoning about probabilities can be tricky. Some probability problems
are notoriously opaque, even occasionally for people well-versed in prob␂ability theory. Examples include
• the three-doors or car-or-goat problem ("the Monty Hall problem") [Vos
Savant 1990a; 1990b],
• the sibling-gender problem [Bar-Hillel and Falk 1982],
• the condemned-prisoner problem [Gardner 1961, 226–232],
• Bertrand's paradox [Nickerson 2005], and
• the exchange paradox (two-envelope problem) [Nickerson and Falk 2006].



The UMAP Journal 28 (4) (2007) 503–532. ␂c Copyright 2007 by COMAP, Inc. All rights reserved.
Permission to make digital or hard copies of part or all of this work for personal or classroom use
is granted without fee provided that copies are not made or distributed for profit or commercial
advantage and that copies bear this notice.

Excellent point KFB!!

Casinos do not give a lesser fk about probability in decline, RVM definition of randomness, Marian V. Smoluchoswki probability after effect concept and many others studies conclusions, as whenever a math edge is shifted at their side, well, the remaining stuff is just bighorn.sh.it.
Good for us.

At their bac tables casinos should print in bold those words: "players should be warned that we try to deal random successions, actually it's very likely we don't"

as.

As alrelax has mentioned the Tote Board is a great invention and designed to make players focus on the wrong type of outcomes: streaks. Red vs Blue, same-side streaks vs opps,...etc. Even the rectangular shape was clever.

I frequently have friends across the country that are well versed in games such as Texas Holdem, Poker-type games, Miss Stud,....etc. They have little knowledge of Bac but will walk through a table pit and snap a pic of a Bac Tote Board and send it to me and say something like: Mr Fu you would have scored a homerun on this streak.

The streak will always be a same-side streak or Opp streak. One in particular recently sent a
long P-streak of 12. However, what he didn't see was a perfect 3-1 streak(BBB P BBB P BBB P BBB) of 15 just before that and it was one that was easy to see at the beginning(if one was looking for a streak different than same-side or opps).


Continued Success,

Lol, I like 'Mr Fu'...I guess Fu stands for 'luck' isn't it?

Yep, that succession was awesome and of course scientifically unsound (actually it's not strictly speaking), yet I guess most bac players would have collected many wins from that.

Is it rare to happen? Sure!
Are there other ways than following it in order to get multiple back-to-back winnings? Nope.

Independence

The notion of independence, which is, in a way, the heart of randomness, presents a major psychological obstacle.
This obstacle involves severe fallacies concerning random walks (Falk).

We have seen that 'normal' people tend to assign (improperly) a too much 'overalternating' strenght at random binary successions whereas bac players tend to do the opposite, that is hoping that random binary sequences will get homogeneous situations of many kind around any corner.

Obviously as long as the baccarat production is really random, both different ways of thinking 'probability' doesn't lead to nowhere as random=unbeatable.

More on that later

as.

Postulating that bac shoes are not randomly shuffled doesn't mean that streaks of 'specific' something all of the time will take a univocal direction longer than expected, it would be too easy to exploit the game.
In fact we can't know what will be more likely to happen per every shoe dealt as things continuously change so not privileging one side or the other one of the operating world.

That's why the only tool we can rely upon is the watchdog of randomness: standard deviation values.

Beyond any doubt bac shoes are not perfect randomly shuffled but it's very likely they are offered quite close to that, so we should learn to distinguish when and how much the unrandom world will take a practically exploitable lead over the unbeatable random world.

Therefore we should think of our bets in terms of winning 'ranges' where most part of them will fall into the random EV- proposition but some of them do incorporate a greater than expected winning probability capable to erase and invert the HE working at all other bets.

It's the same math concept why Banker wagers are less worse than Player bets: most of the times they don't, all of a sudden they strongly are.

Then it's intuitive to think that the 'independence' factor cannot work at baccarat as unrandom shoes sooner or later will feature a kind of dependence more likely showing up at sensibile levels after the formation of certain 'complex' events that tend to restrict the power of randomness.

In a nutshell and differently to any other gambling game, at baccarat each shoe is a world apart where most outcomes are randomly offered but some events (due to the unrandom shuffling nature) are way more likely to happen than what a pure random world dictates (e.g. sensible lower sd values).

Our advantage comes right by selecting 'probability' ranges where one or more bets should involve a strong EV+ capable to proportionally erase and invert all the other wagers made on that betting range (where half are lost and half are won by chance), the same way why itlr B>P.

Fortunately for us, regarding baccarat mathematicians and gambling 'experts' have made two fatal mistakes:

a) Taking for grant that bac shoes are really randomly offered;

b) It's the corollary of the above point, that is considering baccarat as any other gambling game where the 'whole' findings (infinite shoes) matter instead of focusing about 'single shoe' dependent features and properties.

Baccarat works the same way as poker: it's better to appear stu.p.i.d than smart but with a substantial difference: itlr at poker some players are detected smarter than others, at baccarat we are all stu.pi.d.s with no exception.

as.

At baccarat there are sure indeniable bet selections getting a slight edge over the house (after vig, of course) so bac results are affected by a kind of dependency neglecting a perfect unbeatable randomness.

The problem is that such 'slight' edge is quite dispersed within the various successions, needing some 'room' to show up.

Tomorrow I'll present many real examples of that, maybe it would be helpful to understand that a lot of times baccarat is more a silly than wonderful game even though we're playing with a verified edge.
 
as.