Let's start with the assumption that by betting every hand or a lot of hands the probability to win after 3 or 4 shoes dealt is minimal.
Of course also the probability to lose all the 3 or 4 shoes is minimal.

Since it's more likely to get a final losing shoe than a winning shoe (and this fact perpetuates infinitely), it should be wise to bet only those hands that seem to get a 'clustered' winning potential.
On the other end we know that even betting every hand or plenty of hands a winning shoe will very likely come out in the same 4-shoe interval.

The 'old' worthless trick to use a strong progression in order to reverse a losing shoe into a winning shoe is the casinos' heaven as it can't be done by any means, yesterday now and in the next few years the human species is entitled to remain in this planet.

Then:

-in 100% of cases, a high frequency betting leads to get more losing shoes than winning shoes;

- there's a very high probability that after a set of 4-shoes one shoe will be a winning one even by betting every hand.

First possible countermeasure.

- Betting fewer hands. That move alone can't reverse the L/W shoes ratio, but surely will lower the HE impact. At the same time helping acute players to realize that things move around 'clusters' of more detectable lenght (see later).

Second possible countermeasure

- probability to get just one winning shoe 'no matter what' are overwhelming the remaining possible set of 4-shoe 16 combinations.
So for example after two losing shoes the probability to get at least one winning shoe in the next two shoes is greater than 25% (naturally to be really valuable our B bets must get at least a 51.3% winning probability and P bets at least a 50.1% winning probability).
The same about experiencing three straight losing shoes, the final fourth shoe will get a better than 50% probability to be a winning shoe. (And the same B 51.3%/ P 50.1% winning ratio applies). 

Obviously after any winning shoe the probability to encounter another winning shoe in the 4-shoe format is reduced, actually this is the only situation where the s.tup.id 'quit when you're ahead' suggestion will be (partially) worth.

The transitory 'lead' should be assessed about how many times a given probability event failed or succeeded to reach its 'average' value (for example a 0.75/0.25  probability model should get a 3:1 winning pace to break even).
Surpassed certain values and according to the expected number of hands left, probability that the 'silent side' will get a substantial lead over the counterpart is very low.

as.

Hi KFB!

Tomorrow I'll respond to you.

Cheers

as.

Hi KFB! Thanks for your interest.

Q1/A1: My thought about baccarat is focused about the 'actual card distribution' and not about B/P patterns.
Well, B/P baccarat streaks are shorter than a random 50/50 proposition and the asymmetrical math force will slightly shift the results, but both features are too whimsically distributed to be exploited.
Therefore, imo, Ws and Ls must be assessed about the 'average' and 'actual' probability of those patterns that are more likely to show up.
Since a perfect 'balanced' patterns world happening at each section of the shoe is out of question, we should investigate when a given pattern will take the transitory 'lead' over the counterpart in either W or L way.
Naturally we can't know precisely how many unbalanced patterns will happen at every shoe dealt, let alone about their lenght.
Yet we may estimate the probability to show up at least one time or, better, the probability to produce an average amount of W situations.
Notice that we do not necessarily need a W>L ratio to be long term winners, just to evaluate when a W cluster is more likely to show up in a way or another. (See later). 

Q2/A2: since baccarat outcomes are more likely distributed along unsteady 'unbalanced' lines, it's quite improbable that after a long losing sequence a specular winning succession will come out.
Tricks to lower such feature by adopting a progressive plan almost always lead to an eventual disaster.

Best way to think that such loss will be balanced by a proportional winning amount is to let many shoes to come out, hoping that a plan will slowly get its due proportional share of wins.
If every HS bac player would adhere to this simple strategy, baccarat wouldn't exist as the idea for such players to stay in the 'losing' side for long cannot be accepted. So forcing the improbable to happen after the 'more likely' had happened.

as.

Clustered destiny

We've already seen that no matter the strategy utilized' long hopping WL lines will be slight less probable than long clustered W or L patterns.
It's true that considering B=W and P=L or vice versa, BP hopping patterns are quite likely to show up, but in some way this is not a pure WL hopping line but just a clustered scenario. (Of course B/P is not a symmetrical probability model).
After all whenever a BP chopping line surpass a cutoff value, all derived roads will present univocal red spot streaks.
Technically and ignoring the very initial part of the shoe, a BP chopping pattern equal or superior than 6 will get ALL derived roads to form red streaks.

Therefore the winning or losing process moves slight more likely around W and L clusters of different lenght.

We can 'extremes' such statement by considering that W or L clusters will more likely move around sub classes of Wcl-Wcl classes and Lcl-Lcl classes, each corresponding by a precise value (1, 2, 3 and so on).

The important thing to remember is that itlr WL patterns vs WW or LL patterns are slight less likely to show up in way or another.
I mean that the probability to get, say a 8 WL or LW straight situation, will be slight less likely than to get a straight 8 W or L event.
With all the consequences to get the other 252/256 remaining patterns not belonging to the constant WL or LW or WW or LL lines.

Simplifying, if after 8 wagered hands tha probability to get WWWWWWWW or LLLLLLLL patterns will be slight superior than to face a WLWLWLWL or LWLWLWLW, so the other inferior possible patterns will be somewhat affected by a kind of 'clustering' effect.

Since we are talking about WL events and not necessarily about strict mechanical betting strategies, we may enlarge the field of operations by setting up as 'targets' some other players' destiny.

I know that this could sound as a unscientific strategy, anyway it works wonderfully in practice.

Alrelax is so true about the importance of focusing about actual results and not about 'what should be more likely to happen'.
Furthermore, most bac players like not to 'adhere' about what's happening or hoping too much that a given pattern will stand for long (that is forming long clustered patterns), most of the times when such players are losing so desperately trying to break even shortly.

In some way I'm meaning that individual player's or players' destiny are more likely to follow the above statement (so presenting valuable spots to bet at), no matter how smart and prepared we are.
And of course our personal destiny won't make any exception to that.

Examples.

Probability that a given losing player will get prompt consecutive wins is very low, if such player experienced quite long losing clusters, winning clusters counterpart move more likely about low or moderate clustered patterns at best.
In fact most part of losing players try to break even by forcing W clustered situations to happen shortly.
I'd say that in general circumstances for those losing players the probability to get an immediate four winning pattern is 1:16 but it seems to be quite lower than that.
Notice the adverb 'immediately'.

More intriguing is the probability to encounter a 'targeted' player getting many WL situations that of course cannot last for long, so more likely taking a W or L line.
Naturally even if this relatively improbable WL course seems to act, we'll bet just one hand for any couple of hands are dealt.

Then there are the so called 'lucky players' capable to guess an astounding amount of hands, a class splitted into two categories:

a- players getting the best of those univocal patterns happening (streaky shoes, predominant one-sided shoes), so wagering a lot of hands;

b- players that seem to be right at 'selected' wagered spots. Those are the more interesting to follow, especially if they bet huge amount of money.

Maybe both are getting the best of a fluke, have we reasons to try to stop those flows?

as.

Clusters, clustered patterns and clustered 'destiny'

We can arrange an A/B model into infinite ways then clusters will happen, actually they MUST happen.
And in reality clusters are the reason why we lose, as a constant 'low level' of clustering effect will be easily beatable by progressively wagering toward non clustered results.

But at the same time clusters might be the way to look for in order to win itlr. Again, if clusters would be so constant in their appearance and consistency, baccarat (and some other games) wouldn't exist at all.

Now the problem is: is it better to set up a plan about non clustered or clustered events and what's the level we should start and stop the wagering to get the most profitability (or, at worst, the least negative impact)?

First, a wide definition of 'cluster' is everything that comes out by repeating the already happened same outcome, so we do not need 5, 8 or 15 repetitive events to classify a 'cluster', thus just one back-to-back appearance of the same result or class of results belong to this definition.
Good news is that every shoe dealt in the universe will present several one-level clusters, some 2-level clusters and other relatively less likely superior situations.
For one moment say we are not interested about what should be more likely to happen, just that actual results should take a kind of clustered line at various levels.

Second, some different betting lines could collide into getting opposite clustered (CL) or non clustered (NCL) events, so a searched result could be a winning or a losing one depending upon which line we've decided to take.
Yet, if a given CL line is surely going to happen (always in relationship of its general probability to show up), we can guess that a CL-CL apparition will be slight more likely than a CL-NCL line.
Of course even a NCL line could get its share of clustering effect, again splitted into more likely levels.

Third, virtually there are infinite ways to consider events by CL or NCL situations.
Think about single/double vs 3+ streak successions, unb plan #1 or #2, bac codes and many others strategic plans not presented here.

Not talking about the common three derived roads where a CL effect tends to overcome a NCL factor.

What imo is important to understand is that people making a living at this game will try to get the least level of profitable clustering effect happening along every shoe dealt, that is 1.
Of course after having assessed that such CL effect went 'silent' (so bypassing that 1 cutoff level) for some intervals.

It's like that no matter the bet selection, a 0 level of CL factor (no clustered patterns) cannot act for long independently of how's 'more likely' some patterns should be generally prevalent over the counterpart.

Think about this: a HS player will hope that CL events will happen for long by a 'sky's the limit' feature.
Nothing wrong about that, unfortunately this is just a short term hope.
Another HS player will hope that CL events will happen more frequently by whimsical levels but by a degree different than 0, in a word hoping that certain events will be clustered by a level greater than 0 and up to 1, so they need just one positive step to be right.

Math edge and the 'rule' is to expect both players to be broke, in reality the second player will constantly make a 'unnoticed' small dent at casinos' bankroll, mostly as he/she's willing to  bet a way lesser amount of wagered hands, then by knowing precisely what to look for.
Many times getting valuable hints by simply evaluating the first players betting destiny, being invariably oriented toward a losing line more often than not.
A thing we'll see in a couple of days.

as.

Not all A/B patterns are equal

We know that without an edge of some kind we are not going anywhere; an infinite bankroll could dilute or getting no effect on the risk of ruin, anyway we're not going to win.
But since we play to win (thus we have verified a possible edge working for us) we should assess how much we want to risk, that is how long our strategy could endure the inevitable losing situations happening along the way, at the same maximizing at most our probability of winning.

Value of the positive edge assessed, there are some formulas dictating the best fractions of our bankroll to be bet, yet baccarat is a very volatile game mainly as, imo, many shoes are not properly shuffled.

We have learnt that on average baccarat is a 'biased' world performing various and heterogeneous levels of 'confidence'.

We have taken for grant that if A=B, A1>B1 and A2>B2 (and so on but the probability that A3, A4... isn't practically exploitable), meaning that superior than A levels of probability follow values not belonging to a normal distribution curve, simply put that itlr some patterns are slight more likely than others. (A thing not belonging to the mere Banker math propensity of course).

So an A or B betting model is unbeatable by definition, only A1 and A2 models could be beaten as itlr both are getting more wins than the B1 and B2 respective counterparts.

Now a question should arise: is it better to bet toward A1 vs B1 or A2 vs B2 (or both)? What about our betting amount?

It's obvious that per every shoe dealt a bias cannot constantly act at both more probable lines, one line will be more favoured to get clustered wins than the counterpart. Not mentioning that A2 line (albeit being more 'precise') needs more room to come out.
And in fact and even knowing that both lines will get a EV+ play itlr, long term data show that whenever one line will get a fair amount of winning spots, the other favourable line will present more losses than wins or at best an equal W/L ratio. (And vice versa).
The old as the hills 'clustering effect' working.

Say one shoe is:

A1, A1, A1, A3, A1, A1.

By applying the well known 1:3 ratio, wagering the A1 line will get +2 units (before vig) and wagering the A2 line will get 3 units loss.
I mean that A2 line bettors will need three subsequent wins (A2, A2, A2) to balance the previous deficit.
By betting both A1 and A2 lines we'll get a cumulative  -1 unit loss.

Now a shoe went as:

A2, A1, A2, A1, A1.

Now A1 line bettors got a -3 unit loss but A2 bettors got a +2 profit (minus vig).
Overall both lines produced a -1 unit loss (plus vig).

Of course there will be 'unlikely' shoes like this:

A1, A3, A3, A1.

A1 betting line got -4 unit loss and A2 betting line a -6 unit loss. A 'disaster' cumulative -10 unit loss.

So it's just about the general probability to face such shoes, notice that by considering a 'clustering effect' the last horrible shoe got one loss at A1 betting line and zero losses at A2 line. That is a cumulative -3 unit loss (way better than a -10 unit loss).

You can argue about those other events not belonging to A1, A2 and A3 scenarios.
Good news is that all those events are winning situations, so different than A but not sufficient to belong to A1 category. (say we name them as A-x).

Since it's very very unlikely to face a shoe producing more than two A3 situations, we know that most bac results belong to the A-x, A1 and A2 situations with some rare A3 spots happening along the way. And obviously not proportionally distributed by the A-x + A1 + A2 = A3 equation.

Actually when testing your shoes you'll be somewhat bored to look for the A3-A3 distribution that you begin to think as them as 'very unlikely scenarios'.

After all at baccarat there no other ways to look other than for more probable lines to be clustered or happening after a single opposite less likely situation happened.

as.

Al wrote The limitations are within each person playing.

This statement is very interesting to be commented, we'll see it in a couple of days.

as.

Thanks Al for your reply.
You gave me the input to expand my idea. 

First, we should ask to ourselves whether baccarat is a completely random independent succession, I mean random outcomes without any possible bias we could exploit in some manner.
If the answer is YES, we better change the game to play at.

In fact those thinking that progressive plans alone will make the best of it at a pure random succession (even if it would be a fair 1:1 proposition as a coin flip is) are just fooling themselves and giving false hopes.
The only possible exception to think that a random game would be beatable in some way is whenever long term data had shown that some selected events wagered have produced low sd values, so possibly attackable by a careful progressive multilayered scheme.
By statistical terms, it's like that instead of getting a classical normal distribution we have found a kind of Cauchy distribution.

So if the sample examined is quite large, it's 1 quadrillion percent certain that pure random successions cannot give the player any minuscule probability to get the best of it.
If anyone thinks otherwise he/she should be entitled to present his/her strategic plan to MIT. 
Notice that some progressive plans (but also flat betting strategies) could shape positive lines for 'long', but this is just a temporary 'random' coincidence as even at random events the improbable will happen.

Second, if baccarat outcomes are not so 'randomly' and 'independently' dealt (and this is the only fkng option we could rely upon in order to beat the game itlr), that is a kind of exploitable bias happens, we must choose what will be the best course of action to take.

a) Trying to adhere at most at what the 'biased' shoe is presenting, a wonderful theorical thing to look at.
After all the vast majority of bac players adopt this strategy (and filling the casinos pockets).
Unfortunately most bac players haven't measured their EV, because it's just sufficient to check few hundreds of shoes to understand that under normal circumstances this strategy is a sure loser.
In reality and whenever a player likes to bet many bets per shoe (by the fear of missing something 'good'), just a 3-4 shoe mere sample confirms the low probability to be ahead.
Of course 'progressive plans' dilute the problem not solving it.
Nevertheless we can't rule out the (distant) possibility that 'experienced players' or keen scholars have found out that a low amount of bets made on supposedly favourable situations will get them the best of it.   


b) Every bac shoe dealt is affected by a kind of bias cumulatively merging into univocal 'mechanically devised' patterns giving distribution curves progressively shifted to one direction that has nothing to share with the B>P propensity.
Those are 'limited random walks' that without any doubt and giving the lesser sh.it about B>P asymmetry will get more probable lines than what a 50.68/49.32 strict model will dictate.

In reality such 'more probable' lines (so giving an edge by a mere flat betting scheme, the only one to guarantee a long term advantage) will be whimsically distributed as we cannot know the actual 'bias' level acting at our shoe.
Anyway a possible bias must act well more likely at consecutive (0-gap) or 1-gap or 2-gap situations; anytime those cutoff values are surpassed, we are simply not interested to chase it.

c) a mix of the above two approaches.

If it's proven to be worthless a kind of 'adhering strategy', it'll be more dangerous to set up a strategy oriented to stop given lines happening at the actual shoe, even if they are strongly disappointing your long term data.
Imo the better approach stays in the middle.

For example and simplyfing the issue a lot, only an id.io.t could hope to get a P 3+ streak after a shoe presented only P singles and doubles, after a quite amount of shoes all presenting only P singles and doubles happen quite often.
At the same token, it's a kind of bighorn.sh.it strategy to hope that B side will get some B streaks after many B singles happened.

oOoOo

There's no way to beat this game by betting many bets per shoe, anyway I've collected different strategies of serious HS players wagering a lot of hands, so next week I'll try to condense such different ways of thought into an univocal line by considering a hand-by-hand process made at real live HS shoes.

as.

Thanks for this post Alrelax.

I pause at your final passage:
Unlike the ability to measure a curve to see what fraction of an area between start and midpoint and points in-between will become finite in their outcomes, the baccarat shoe cannot be measured in the same way or any other way that will allow you with finite guaranteed wins.


For most part this reasoning is correct but we know that some statistical limitations continuosly work at baccarat shoes.
The same way it's virually impossible to get 37 different numbers after a 37 spin cycle at roulette, we can safely discard from the baccarat possibilities many patterns or situations.

This thing becomes more important, imo, whether we've decided to collect into the same category different classes of results.
So 1 remains 1, 2 remains 2 but 3 could be 3, 7, 26 or a greater number, yet it should be still considered as a 3.
Naturally there's a different impact over the expected probabilities if in the actual shoe a streak of 10 or 15 had shown up as it 'consumes' quite space to get other more likely patterns to happen.

Going back to my last post, say we are driving a car capable to overcome with agility 1 and 2 steps but someway 'crashing' whenever a 3 step shows up. The aim is to run as far as possibile at the same time losing the least amount of cars.
In fact we have numerous cars to travel with, of course not knowing precisely how many 1,2 and 3 steps will present our road (shoe).

So before making such hazardous trip (or better sayed, a kind of 'infinite' series of those trips) we need to somewhat estimate   how many 1,2,3 steps any road will present on average, so influencing either the number of cars we should utilize and the average lenght of our 'safe' drives getting the least possible amount of 'crashed' cars.

Actually it would be a child's play to make assessments if itlr 1+2 steps >3 steps, unfortunately 1+2=3.

But since 3 is a three times more unlikely scenario than 1+2, we better focus about the 3 average probability distribution as people making a living about numbers rely upon the probability that something less likely won't happen for long. Of course also knowing that sooner or later unlikely scenarios will surely happen.

Now we have two different opposite options to set up our plan about:

- hoping that sooner or later a relative high unlikely scenario will happen;

- hoping that a relative low unlikely scenario (3s) remains as silent as possibile.

Both options surely follow a kind of 'clustered'/'diluted' strenght as a card distribution cannot be symmetrically placed by any means.

First let's examine the 'low unlikely scenario', that is 3s happening on average about any shoe dealt.
At 8-deck shoes the average probability 3s will show up is around 9.5 per shoe.
If we'd assume that any shoe dealt will produce an average number of 28-30 columns, we'll see that the 1:3 general percentage is respected. More importantly, relative sd values will be way more restricted than at a pure independent symmetrical game.

I mean that under certain conditions, along any shoe dealt the probabiilty to get a more probable class of events is very very close to 1. That is the almost absolute certainty that a given event will happen.
After all and assuming 28-30 columns, a 0.25 probability cannot happen clustered for long and consecutively and at the same time not giving the proper room to get 0.75 probability events to show up clustered at some level (or, in the most very unfortunate scenario, to show up at least once after a 'fresh' new 3 had come out).

'Relatively high unlikely scenario' wonderfully perform at some side bets plays.

Say you want to play at the Dragon Bonus bet where a given gap of winning points matters (being payed 1:1, 2:1, 4:1, 6:1, 8:1, 10:1 and 30:1).
Of course only an id.iot would bet the Banker side Dragon Bonus (sadly too many players like to bet this side), thus only Player side DB should be wagered.
Classifiy Player winning results under the 1-2-3 gap point classes vs superior gap points (those getting a DB win), ignoring naturals (half of them will be winners anyway).
After a given series of 'isolated' DB Player results, progressively bet toward getting 'clustered' DB events, providing you think that for some reasons Player side will be more entitled to win.
It's not a coincidence that at HS rooms such side bet isn't offered at all.

Tiger bet

No commission tables where B winning hands by a 6 point are payed 1:2 are faster to be dealt and the HE raises from 1.06/1.24% to 1.46%/1.24%. (So the less worse bet at those tables is wagering P).
Notice that as long as B won't show an initial 6 point, betting Banker will get the player an enormous math advantage.
Of course a relatively small portion of hands not belonging to an initial two-card B 6 point and getting B side to win by a final 6 point will lower such possible advantage.

Anyway, at a 8-deck shoe on average Tiger bet will show up nearly 5 times. Two card B winning 6 points are payed 12:1 and three card B winning 6 points are payed 20:1.
This bet is so relatively probable that we could even make a kind of 'sky's the limit' side approach.
Anytime a Tiger bet shows up, we could just bet three times to get the same Tiger bet to appear again by adopting a progressive plan.
I know it's a unsound math move, but I'll invite you to test your shoes and see what happens.

as.

Patterns

The baccarat invulnerability relies upon the fact that it's impossible to 'restrict' the variance terms of the results, meaning that anything could happen anytime and anywhere.
In statistical terms this means that the 'improbable', even though being carefully calculated, will surely happen providing to get a fair amount of trials.
So after an 'infinite' amount of shoes we'll surely face an all B or P hand shoe or a whole BP chopping shoe or, well more likely, a whole 'streaky' shoe without any single showing up. (Btw, we have crossed through this last situation more than once). 

Anyway to get an idea about how's unlikely to get some 'negative' patterns for long, consider this simple mechanical and progressive betting plan.

Notice that we're not saying it's a sure way to beat baccarat, just that these random walks will disrespect the unbeatable features belonging to a typical random walk as they are more prone to roam around the 0 point or taking a given univocal direction (no matter which side we'll bet at).

Our random walk #1 will bet toward singles and doubles after any 3+ streak happened (that is any 3 or 3+ streak happening at either side), so 'hoping' that such streak will come out more isolated than clustered or that 'isolated' streaks will come out more clustered than isolated (see later).
If any 3+ streak comes out clustered (back-to-back) we simply stop our betting, waiting for another 3+ streak occurrence.

Beside the obvious first-step progressive betting scheme after a single apparition was missed (otherwise a second winning Banker bet would get us losers for the vig), we'll raise our standard bet in two occasions:
- after a winning bet in either one of the two steps (at least up to the point to erase a previous deficit) and
- after a single losing two-step bet.

No need to try to erase a previous deficit too fast, it's casinos' hope to know that sometimes sh.i.t happens for long (in either way), let shoes to be dealt and those random walks cannot get negative values too distant from the 0 point.
Obviously we should consider that every bet will be burdened by a math EV- return.

Then our random walk #2 is more patient as it'll act just when two 3+ consecutive streaks had happened, the same target being singles and/or doubles.
Same progressive features to be utilized.

Actual long term results of such plan at real live shoes

Both random walks #1 and #2 get a common 'enemy': that is series of three or more consecutive 3+ streaks.
Actually those situations will surely come out but they cannot neglect for long the more likely propensity to show up as isolated as an average live card distribution (being dependent of the previous results and surely finite) will make some limits over their back-to-back apparition at the same shoe.

If you'd test a relatively large sample of live shoes, you'll see that, more often than not, just one of the two random walks will take a decisive positive line as 'complex' patterns will take a huge amount of trials to show up a possible propensity working at both random walks.

Is this big.horn.stuff stuff as many fkng mathematicians will surely bet their as..ses upon?

Ok, so let's take the casino's part.

A sky's the limit progressive player will first bet that A (a+b) will be more likely than B (c) by wagering that A-A and B-A will be more likely to show up than A-B and B-B. (Of course from a theorical point of view a+b=c).
So casino must hope results will take a c clustered line.

But say the same player had noticed that A is more likely to come out by rarer B clusters of two that seem to be prevalent than isolated B (so c>a+b but c-c<a+b) , so now casino must hope to get c-c-c clustered patterns than c-c spots distributed by more likely lines.
Hence this player wouldn't give a fk about random walk #1, just more focusing about his/her higher bets by following random walk #2. 

Now this casino should hope to deal shoes presenting a lot of either A-B or B-B spots (r.w. #1) or B-B-B spots in a row not intervaled by more likely B-B-A patterns (r.w. #2).

BTW, it's a sure long term finding that the more 3+s streaks are clustered, better are the odds to cross through single/double patterns in the remaining part of the shoe.

A thing we'll look at the next week.

as.

In this interesting paper the only (partial) positive conclusion for bac players is restricted into this passage:
The only possible winning strategy is to catch the trend(either the Player or the Banker) and to bet on that side.

Next let's see this passage:  This implies almost independence of the game in
probability. Therefore the previous outcomes have no effect to the next outcome. In theory, it is
meaningless to decide which side to bet on according to the outcome sheet.

Another passage I've found interesting is this:
The simulation results are shown in Table 9. Compare Plan 4 with Plan 3, we note that the 'follow'
method seems to be better than the 'alternative' method, because all the losing game probabilities are
relatively smaller for the 'follow' method.


Then this: Note that the random walk is a typical nonstationary stochastic process. Every random walk
wanders away from the origin and is never guaranteed to return to the origin.


Our comments.

Not surprisingly this paper confirms that baccarat is an EV- game for players. Nonetheless authors have found that some strategies are less worse than others beside the fkng old 'better betting B than P' statement, also leaving a potential minuscule possibility to set up a strategy based upon exploitable 'trends' of some kind. 

We hugely respect such statistical experts, yet as pure empirical 'practitioners' we dare to make some considerations.

First important feature to look at is that such paper was based upon 'simulated' results and not over real ones.
Naturally we can't take only the possible minuscule good parts of this study and ignoring and just arguing about the global negative conclusion.
Anyway we've seen that at simulated 'random shoes' the 'follow method' tend to performs better than the 'alternative method'.
Notice that this finding totally collides with the old and verified very slight propensity to get the opposite outcome already happened.     
In our opinion the truth stays in the middle, not necessarily merging into a 'neutral' zone. (see later).

Secondly, this study examined just B and P successions, not classified by more 'complex' patterns, especially into the back-to-back form.

Third, we've collected valid reasons to doubt that in every scenario previous outcomes won't affect in some way the next results. At least such negation of 'place selection' supposedly indipendence works at live shoes data.

Fourth, we totally disagree about this study's conclusion:

'Every random walk wanders away from the origin and is never guaranteed to return to the origin.

That's true only whenever we're considering an independent and random source of results or at least over a simple BP successions examined at both simulated and real live shoes samples, but not at more complex baccarat patterns happening at real live situations.

Imo, it's the main mistake almost every scientist had made when studying baccarat (along with the fatal error to consider simulated shoes as the same as real live shoes).

Average shoe's card distribution is way more sensitive about 'complex patterns' successions than about mere B or P hands.

Theoretically complex patterns still belong to the 'random walks' category but in reality they work under a sort of 'conditional probability' where (depending upon the bet selection utilized) they either are proved to roam around the 0 cutoff or even better to take a long term univocal direction being well greater than the common B>P math propensity.

Main answers to that assumption?

First, the average key cards distribution being surely asymmetrical up to some level and for some sections of the shoe.

Second lower level, math two-card advantaged situations not involving key cards but getting an edge more often than not.  And of course even such feature will be asymmetrically placed. Up to a point.

Third level, asym hands math favoring B side. Differently to the two above factors, we know that on average this parameter will strongly shift the results just 8.6% of the times.

If we'd assemble such factors into a whole scheme, we'll see that itlr 'complex' patterns will tend to follow more probable back-to-back values.

After all, we can't think about a card distribution placing ALL key cards to one side for the etnire lenght of the shoe, not mentionting that such key cards must combine with valuable cards to provide a worth result (most of the times a zero value card).

Then it's impossible that a shoe will present univocal winning long streaks of two-card math favored higher points.

Finally, asym hands apparition per each shoe is well restricted into finite terms and of course very few shoes will get ALL asym hands to win after a third card is dealt to the Player side.

as.

Thanks klw!

Here's the link I was referring to:


https://www.koreascience.or.kr/article/JAKO201208040009207.pdf?msclkid=7a459b53ac4011ec901c1c5de08abc42


as.

Here another real live shoes data regarding the same plan I was referring to in my above posts.

First order cluster spots got 1974 winning situations and 632 losing spots (632 x 3 = 1896) that is a 1.04 WL ratio.
Again a too tiny shifted ratio to get the best of it.

Second order cluster spots got 445 winning spots and 103 losing spots (103x3=309) that is a 1.44 W/L ratio.

Even though such samples are quite small under the 'math' lens, definitely and so far there's a strong 'relative' propensity that second order cluster spots move around a kind of a way better probability of success not following general values applied to a coin flip model (we did bet B or P regardless of the B general math edge).

In some way we may conclude that the more we are waiting for certain 'more probable' patterns to show up, greater will be our probability of success capable to erase and invert to our favor the EV.

Btw, WARS ARE PROVED TO NEVER EVER BE AN ANSWER TO SOLVE PROBLEMS. MOST OF THE TIMES WARS BACKFIRE TO THOSE STARTING THEM.


as.

If we want to test the effectiveness of our idea, we should make a lot of experiments.
The purpose of experimentation is not to convince other people but first to convince ourselves. (Galileo).

I'll meekly add to that: 'providing we make experiments under the most replicable conditions we'll meet at the real tables'.

Dice controllers do not test their ability by tossing cubes into a 3 ft felt (al least not eventually) or using Monopoly dice.
Even at black jack some literature has shown that the mere 'high/low cards' parameter could be misleading, so more depending upon how are really shuffled the cards.

Imo, before testing several thoughts should be made when thinking to try to beat baccarat.

1- beside side bets and anyway with many caveats, pc simulated shoes are worthless. We need real phisically shuffled shoes to test our ideas.
I know it's a way faster process to collect data from pc than from a real source, but we have to understand that we'll risk our money at real tables and not at 'simulated' situations, no matter how's sophisticated the software employed.

2- Live shoes are surely affected by a 'bias' of some kind. Even if we do not know the precise directions this bias will take (almost always splitted into sub sequences), such factor will produce a sort of 'asymmetrical' world where a number of some 'expected' situations will come out unproportionally with the number of 'unexpected' events.
Sh.i.t (or heaven) comes in clusters, therefore as long term winning players we must rely upon the remaining non sh.i.t or non heaven world constituting the vast majority of the outcomes.
We already know the importance of setting up numerous 'limited random walks' to bypass such problem.

3- A 'simple' pattern as one single or a double or a 11 streak means nothing.
Instead, we should be interested about the back-to-back probability of getting something, being more expected or not by assessing the actual 'cluster' ratio that will be surely unbalanced in some sections of the shoe.
Sometimes the 'unbalancement' patterns ratio will be too tiny to be exploited but this is the exception and not the rule.
After all gambling is just a 'streaks' issue otherwise progressive plans would have destroyed it the day after its invention.

4- Derived roads do confirm the non real randomness of the bac outcomes (or at least they tend to amplify the baccarat flaws we're talking about), so I'll invite you to register each live shoe under the common four registration lines (BR, byb, sr and cr).
Just the BR must be classified as to instanly get all derived roads you could use a free software by googling 'baccarat scoreboard' working very well on your cell phones.

Notice that no one registration line will be superior to another one (albeit giving slight different long term results), yet by examining four different lines we're simply amplifying the number of betting spots (with the downside of crossing through some colliding spots).

oOoOo

In some way we should compare baccarat to black jack with important favourable features working for us:

- no need to bet anything (or worth) unless we'd think to be advantaged;

- black jack is a one-side bettable game but baccarat is a two-side bettable game;

- the 'no entry at mid shoe' rule doesn't apply at baccarat;

- baccarat scholars are considered by both mathematicians and casinos as pure clowns, that is sure losers.

It's funny that casinos are more worried by facing a sudden $60 bj bet placed by a $20 standard player than a $10.000 occasional wager made by a railbird fellow.

as.

Thanks KFB!


Same plan applied to a different live shoes sample

The beauty of playing baccarat worldwide is that sometimes you meet interesting people wishing to share some ideas about the game.
I'm particularly attracted by players that like to write down and collect the shoes they've played at, on one occasion I've encountered a couple of guys realizing the importance to consider only real live shoes and when they told me they got a fair amount of them I've invited them to share their data with ours.

We completely agreed that while considering live shoes a 'perfect random shuffle' is just a coincidence and not the rule.

So they sent me their live shoes sample that's even greater than ours (by a nearly 50% more amplitude).
We run the same plan as seen as above and here are the results:

First order cluster spots W/L ratio was very close to 1 (1:1), meaning no significant deviations went on either side.
Since we are constantly obsessed by a bet selection capable to get more wins than losses, we took this result as a kind of normal 'losing' situation to look for.
Therefore we are not so interested about a possible leptokurtic curve, the best to set up a progressive plan upon.
 
Second order cluster spots W/L ratio got more 'comfortable' results as the W/L ratio was 1.31:1, that is a well higher value than it was at our sample, more proportionally 'balanced' toward first and second degree cluster spots.

There are some possible answers to that, the most important is that whenever we are considering a supposedly clusters propensity by 'general quality' and not by 'strict quantity', some deviations may easily happen for the actual 'volatility' of streaks lenght.
Anyway if we'd think that along any shoe dealt 'things must change after a X cutoff point' or 'remain at a steady level up to a Y value' (all due to the average card distribution factor), it seems that the more we're restricting the field of operations higher should be our probability of success. Up the point that we will surely invariably get a fkng edge over the house.

Many could ask: "ok, given the relative rarity of bettable possible EV+ opportunities, a 25k live shoes data study means nothing to me. Show me such possible propensity on several hundreds of thousands of shoes or, better, on millions of live shoes dealt".

Even assuming that we're betting an average amount of one hand per shoe, the probability to be ahead after 25k shoes dealt will be zero unless we've found out that a kind of propensity belonging to an average card distribution should work.
Hence after any 25k shoes sample considered, any bet selection capable to get an edge after the vig impact is a sure EV+ recipe.   

Moreover, if an original result succession is asymmetrically affected by reasons going beyond the natural math propensity and binomial features, every sub succession originated from it will follow the same principles as the card distribution 'bias' cannot be altered by different 'pace selections' outcomes.

That means that what happens at the original succession will present the same properties at derived situations.
For now we've just considered Big Road successions (second degree cluster steps > than higher counterparts), what about common derived road lines?

What about other betting plans?

as.