Actual distributions of the outcomes

Imo winning by flat betting means that after long trials our strategy got more winning clusters than expected and not because the strategy tried to contain in some way the losing clusters' counterpart, even though the latter could be inferior in number.

Therefore our long samples should have provided us more W doubles than W singles, more W triples than W doubles, more W 4+ streaks than W triples and so on.
Despite that, it happens that baccarat outcomes whatever considered but filtered by a strategy dictating to bet very few hands per shoe and not per every shoe, will show two very different profitable peaks: the double W clusters opposed to single W spots and multiple long W clusters often prolonging up to the end of the (playable) shoe.

Now we should choose either about the larger probability and less affected by variance probability to get more W doubles (WW) than WL spots or to play a kind of "sky's the limit" approach hoping that sooner or later we will catch the shoe forming a univocal series of winning spots.
Of course as long as we've ascertained that the number of shoes getting this "all winning succession" feature will outclass the WL or L counterpart considered at various levels.

In other words, do we prefer to get more stable wins or to go for the all wins "jackpot"?
Or maybe a mix of two, thus lowering a lot the standard bet and making progressive bets after a first win was secured?

We see that in either scenarios we are not risking much money per each shoe played as after losing the first step we're not interested to prolong our action. That's why a sudden losing spot or losing stop needs several hands to form another possible profitable opportunity. Surely denying the "all winning situation" already depicted.

How many hands should we play per shoe to get the most of the above features?

Of course the "shoe presenting all winning spots" must be restricted within a relatively short bets amount, we've found out that on average one hand per every ten hands dealt are a good approximated ratio to look for.
That is 7-8 bets per playable shoe, of course this being an expression of average outcomes' distribution.
Naturally more often than not we need just one betting spot to be ahead when searching at a simple WW spot.
Losing spots coming out along the way (especially at the very first situation considered) reduce such ratio up to the point that we can simply get rid of that shoe without losing a dime.

Think that if a given strategy can get 7-8 consecutive wins after 70-75 resolved hands, such strategy can't start with a L.
After all gambling world is made by streaks whatever considered.

Btw, when talking about baccarat do not trust so called "math experts" by any means, they do not know a fkng nothing about this game other than B and P long term probability.
Kashiwagi was stopped to play after a bad losing sequence but being in the positive field nonetheless, why stopping a super HS player knowing he was math entitled to lose huge sums?

Whenever huge sums are allowed to be wagered and smart players are betting, no casino is so sure about the math edge they're taking advantage of. Even after dozens and dozens of shoes played.

as.

BTW, it seems that some so called "math experts" do not like to have people posting that bac could be beatable, labelling them as "spammers".

Let's see how this stuff evolves, it could happen I have some stories to tell about them. Specifically regarding Vegas/Henderson (NV) areas.

as.

Quote from: argalim147 on April 19, 2021, 04:19:34 PM
Hello, AsymBacGuy!

You said you are strict flat betting.  Give, please, an advice in which direction need to think to create a winning flat betting scheme.  You are long term winning flat bettor, yes?

Hi argalim!!

The reasons why only a flat betting approach should get a long term advantage are quite simple to understand.

- any bet is supposed to be EV-, thus no matter how deep we make progressive bets our EV will be negative.
For that matter, let experts to show me how to beat even a fair 50/50 game as a classic coin flip succession is.

- if progressive betting aficionados think that at certain points something must be more likely than the opposite situation, why not focusing the action about those (maybe rare) spots without risking money previously?

- EV- or EV neutral games applied to a random source cannot be beaten itlr by any means.   
Fortunately baccarat is not so randomly placed and/or so independently dealt as math 'experts' keep to say.

Now let's see the reasons why this game could be beatable by flat betting (for the good peace of mind of those who cannot think this is possibile):

- most part of shoes are not properly shuffled, meaning that key cards are more or less concentrated at some parts of the shoe way higher than what a perfect shuffling will do.
Whenever key cards are quite concentrated along some portions of the shoe, more likely outcomes come out even in term of whimsical actual results.
We play probabilities and not short term actual results.

- at real live baccarat shoes, the sym/asym (91.4/8.6) ratio produces sd values quite different than at a random and perfect independent model.

- no way each bac hand is dealt by the common 50.68/49.32 percentage (ties ignored). BP hands probability moves from 0.5/0.5 (sym hands) to 0.5793/0.4207 (average asym strenght hands), thus our bets will get either a neutral (and fair) EV or a strong positive or strong negative EV.
Of course such discrepancy definitely will happen more likely when key cards are more diluted than concentrated.

Practical issues

The probability to be right or wrong moves around the actual key cards distribution.
Very slight key card concentrations will make the game quite unbeatable, as hands are more likely to form whimsical results as few hands are strongly favorite at the start to win the final hand.
We do not need to classify key cards, itlr most shoes will form patterns eliciting more likely patterns, especially when considering outcomes at different paces.

For example, consider the three derived roads making an univocal red or blue outcome. Those are rare situations, mostly when long hopping lines or long consecutive streaks or back to back streaks happen.
Classify them and try to figure out how many times r or b streaks will stand or shift to the opposite situation per any shoe played and per each level considered.

as.

Quote from: KungFuBac on April 19, 2021, 04:16:22 PM

Asym: "...Obviously when considering an odd number of patterns, most winning situations come out after knowing the very first W or L result nature as there are more winning patterns starting with a W than the opposite situation..."

     *Im not sure what you mean by this phrase.

Hi KFB!

You are right, I've badly expressed my point.

At 7-tier betting cycles, the break even final result cannot happen, we'll get +1, +3, +5 and +7 and the specular losing counterpart.
Whenever a new 7-tier cycle begins with a W, odds are more favourable to get a final result presenting more Ws than Ls. Meaning that this specific cycle itlr will produce a positive situation, an important issue to be considered when adopting this system or some strategies derivating from it.

Itlr and without a proper advantage, 7-tier final cycles will end up equally between winning cycles and losing cycles.
It's intuitive to think that when a cycle starts with a L, we'll need a higher amount of Ws than Ls to finish a cycle as a winning one.
In some way this system focus about the probability to get a W at the very first hand of a new cycle.
If we're adopting a less aggressive procedure, this feature is even more important as at some time we need winning final cycles to quickly or slowly cancel the previous deficit.

I hope to have explained better the issue.

Take care

as. 

Time to play some baccarat in LV Al!

No jokes

as.

Very good post.

as.

Thanks KFB for your comments!

Only a team could approach the 7-tier system in the original aggressive version having a "leader" instructing when to bet and sharing an enormous bankroll.
Such a team work very well at online sites where different result lines are put together in order to get supposedly "more likely" betting spots (by a pc software, of course).

Even tough bets can theorically (and practically) reach huge values, this system is mathematically sound as per every 7-tier played the math probability to win is 72.66%.

I do not use this system as I'm a strict flat betting aficionado and HS live player (and mentor), anyway the 7-tier concept is quite interesting as it doesn't take into account single results but successions of 7-hand outcomes attacked by the same bet amount.

We know that itlr among the 128 possible WL patterns, each of them will present sooner or later, besides a "general" math probability to succeed it's just the relative frequency of every single WL pattern that cares.

There are several steps to assess whether we're doing good for a reason or by luck.

Best example is to estimate the most deviated 2/128 WL patterns, that is WWWWWWW and LLLLLLL patterns.
If after a given amount of shoes tested the former number will overcome the latter, we got a sure sign that the probability to be right is more significant than otherwise.

The same about less deviated patterns as those containing 6 W or L and specular 1 L or W and so on.

Obviously when considering an odd number of patterns, most winning situations come out after knowing the very first W or L result nature as there are more winning patterns starting with a W than the opposite situation.
If we'd think to get a long term winning system we should put a lot of emphasis about this very first bet.

Now say that we do not want to set up or belong to a team but trying to get the best of it by not  risking a lot of money.

Whenever the 7-tier system will dictate to bet a progressive X amount, we'll reduce it by a 5:1 scale.
Therefore after the first 7-tier betting series, we'll get those scenarios:

-1 unit loss= next betting amount 1

-3 unit loss= next betting amount 1

- 5 unit loss= nerxt betting amount 1.1

- 7 unit loss = next betting amount 1.4

It's true that now a very first bet (and other profitable conditions) won't erase the deficit by just a +1 W step over a L counterpart at any degree considered, but it's altogether true that mathematically we'll need a way lesser amount of profitable patterns to get the same erasing deficit.

Say tonight we're not guessing a fkng nothing, thus getting 5 more losses at 1.4 betting amount level.
Overall we got 2 wins and 12 losses (7 L and 0 W at 1 unit level and 2 W and 5 L at 1.4 unit level).
Thus we are behind 7 units plus 1.4 x 3 units = 7 + 4.2 units = 11.2 units.

Next bet will be 11.2 : 0.5 = 2.24 unit.

We see that even after a very unlikely 2:12 WL ratio our next bet will be just set up at 2.24 unit.

Now we need just a lesser amount of WL patterns than math expected to erase the deficit (even adding up the vig impact to losses), actually a wise flat betting approach cannot reach strong LW deviations by any means.

Nonetheless, even a "I do not care about what the shoe is producing" strategy (not recommended) will get a proper math advnantage itlr.

as.

KFB and Rickk,
if you wish to expand your thoughts here you are very welcome! 

Have a nice day!

as.

Quote from: RickK on April 06, 2021, 03:56:52 PM

So in the first 7 hand sequence you have a 5 net L (6L-1W) @ 1 unit bets = 5 unit Loss.
The next 7 hand sequence goes to 6 units per hand ? and with 3 net L (5L-2W) = 18 unit loss?
Then the bets go to 24 units per hand for the next 7 hand sequence ?

Rick

Basically you flat bet 7 hands cycles, as long as you get a profit the betting unit remains 1.
Whether after flat betting 7 hands at the end you are behind of 1, 3, 5 or 7 units, you increase the bet on the next 7-hand cycle by adding 1 unit to the previous deficit until you recover everything (so you stop to bet the entire cycle then restarting to bet 1 unit 7 times.

In the example, after the first cycle you are losing 5 bets, so on the next cycle you'll bet 6 units each hand until you recover the previous deficit.
Unluckily we got more losses than wins (5L and 2W) totalling 3 x 6 unit = 18 unit loss, so next bet will be (5 + 18 + 1 = 24 betting unit). Yes, we'll stay at this 24 unit level until we'll be ahead of just one hand capable to recover all the losses accumulated at every previous cycles. 
And so on.

The beauty of this system is that you can win even at a percentage of losing cycles adding to your 50% a 22.66%.
In fact losing sequences as WLLLLLL or WLWLLLL or LLWWWLL and some others become winning sequences.

In the example we played 14 hands, getting 3 W and 11 L, not an awesome flat betting strategy (lol) but we know it could happen.

Let's imagine a very bad scenario.

First cycle (1 unit) = 7 L  0 W  unit loss: 7; next bet 8 unit (7 + 1)

Second cycle (8 unit) = 6 L  1 W unit loss: 40; next bet 49 (8 + 40 + 1)

Third cycle (49 unit) = 6 L 1 W  unit loss: 245; next bet 294 (8 + 40 + 245 + 1)

After having played 21 hands, we got 19 L and just 2 W (I discarded the lucky scenario where second and third cycles may get a W as first hand totally erasing the deficit). Our unit increased almost 300 times...
A 4.12 sigma is quite uncommon to cross but it may happen. Not mentioning that half bets are made on B side, thus we need to increase the bets by adding some units to cover the vig.

To reduce the progressive betting impact, we might start the real betting after any losing cycle or even after two consecutive losing cycles, for example.

It's quite interesting to notice that 3 players betting simultaneously the three derived roads in selective situations can't reach huge negative deviations as the possible deficit is spread between them.
Situations where all three roads provide simultaneously many univocal lines (yet assuming them as negative) are very rare, if not anybody would be millionaire very fast.

Take care!

as.

Thanks KFB for your explanation.

I'll try to simplify the issue.
What are the original BP sequences capable to get long and univocal both original and derived outcomes per every shoe dealt?

Just two.

Long BP chops and long consecutive streaks, both being quite unlikely to happen.

We need just a single hand at various degrees not belonging to those patterns to get a long term edge and at the same time we'll fear that just that hand will be unlikely prolong an already unlikely pattern to get us losers.

Long term data show that the probability to get ITCPs or key cards falling at the same side for long are surpassed by the opposite probability.
The only reason that come off of our minds is that itlr both key cards and non key cards privilege a kind of chopping probability.

Thus imo it's not about how much the chopping propensity come out but about how many times it will come out per every shoe played.

@Rickk: I'll reply you tomorrow.

as.

Hi KFB!

As Key cards I'm referring to 9s, 8s, 7s and 6s.

.Whenever no key cards are involved in the process, the propensity to get higher ITCPs remain the same at different degrees..."

I mean that if many key cards are removed from the deck or not available for the moment, the average card distribution slight privileges ITCPs streaks of given lenght, even though card combinations are virtually "infinite".
It's a concept very difficult to be grasped by common players, way too focused about the actual outcome and not about the overall probability's plan.
Not mentioning that quite often key cards are interfering with this propensity, we have 4 classes of key cards and 5 classes of non key cards (zero value cards considered as neutral cards).

Btw, I'm interested to know your opinion about this, thanks in advance!

as.

Mathematical system to get a sure edge over the house

For a moment forget the importance to get an edge by flat betting, let's try to implement a MM capable to get the best of it without crossing the unfavourable circumstance to lose our entire bankroll.

We consider our action restricted within a virtually endless series of seven separated betting cycles, getting each a given amount of profit or loss units. Ties are considered neutral.
Every 7-hand cycle step is made by betting the same amount (flat betting), meaning there are no bet increases before each cycle ended up.

Thus we start the first 7 cycle bet by wagering one unit by flat betting, at the end we'll get:

- 7 units won (7 W and 0 L)

- 5 units won (6 W and 1 L)

- 3 units won (5 W and 2 L)

- 1 unit won (4 W and 3 L)

- 1 unit lost  (4 L and 3 W)

- 3 units lost (5 L and 2 W)

- 5 units lost (6 L and 1 W)

- 7 units lost (7 L and 0 W)

Naturally those W/L percentages are the same per every 7 hand betting cycle, regardeless of how much we bet (obviously)

If after the first 7 bets cycle we'll get a profit, we repeat the process by wagering the same initial amount and so on.
Whether we are losing from 1 to 7 bets (meaning we got more Ls than Ws at various degrees) we'll set up our new standard bet by adding one unit to the overall deficit.
For example, if we had lost 5 bets, our new bet will be 6 units employed in the new 7-hand cycle until we'll get a one unit profit within the same 7 betting range.
If we have the misfortune to not be able to recover previous losses, for the next 7 hand cycle we'll add one unit to the new deficit.

Say after our first 5 L situation we bet 6 units getting another 3 L, thus we'll be behind of 5 units plus 6x3=18 units totalling a -23 units deficit. Thus now our new bet for the next 7 hand cycle will be 24 units.
And so on. Up to the point that we'll be sure to recover ALL previous losses and getting one unit profit.

Math aspects

Even though we could be the worst bac guessers in the universe, per every 7-hand cycle bet our winning probability will be 72.66% as among the possible 128 WL patterns, 93 of them will be winners and just 35 losers (as we'd stop the betting after getting a W amount overcoming Ls).

Notice that differently to a common martingale, those bets are less susceptible to the negative variance and table limits, as they are assessed by 7-hand same amount steps.

This system is so powerful and math wise that just 2 or 3 people playing as a team will get enormous profits, after all itlr a 72.66% probability cannot be wrong for long.

Anyway most players like to play on their own and it's easy to assume that this system could get the bets so high to make in jeopardy everyone's bankroll and peace of mind.

Therefore we want to introduce the "scale reduction" factor, an important strategic tool capable to control the variance and at the same time keeping the benefit of a math advantage.

as.

Run several shoes and register how many times ITCPs will come out in a row and by which degree.
No matter how many cards you'll burn after each hand (as from 0 to 2 additional cards are whimsically employed per each hand dealt in the real world), itlr some values will be more likely than others.

After spotting what's more likely to happen, don't give a fk about real results as itlr math advantaged situations must overcome the underdog counterpart.

Therefore we shuldn't be interested about REAL outcomes but just about the potential math power average distribution.

as. 

Hi KFB!!

Each bac shoe presents several different multistep math probabilities.
Of course itlr what is math advantaged will overcome what it does not.

If those math advantaged situations will be proportionally placed or, even worse, whether we'd think they are, we're not going to anywhere.

We can beat baccarat consistently only whether math advantaged situations are not fitting to the common independent and random probability provided by the general probability.

The main factor (first step) directing results is the initial two-card point (ITCP): the side getting the higher point will cumulatively get nearly 2:1 odds to win the hand eventually.
A percentage of hands won't get such feature, getting an equal point at both sides.
No worries, itlr such hands will get an almost neutral impact over our results.

Normally card distributions will produce "more likely" back to back ITCPs, as the average key card distribution itlr will make a huge impact over the final two-card point results (not final results!).
It's true that key cards could easily combine with a second low or worthless card, anyway itlr it's way more likely to get a winning point whenever a key card had fallen on that side than to face the opposite situation.
Whenever no key cards are involved in the process, the propensity to get higher ITCPs remain the same at different degrees, meaning it's restricted within measurable (then exploitable) terms.

Thus and from a strict math point of view, whenever we find a better than 50% betting rate of ITCPs we'll get a sure undeniable edge over the house.

After all we just need a better than 50% statistical probability to be "probably" right getting after that a close to 0.65% mathematical probability to be surely right.
And this parameter is measurable.

Say we have found a "decline in probability" factor, meaning that ITCPs streaks are measurable and thus getting finite values well lower than what general probability dictates. (So it would be way more sensible to bet that something will stop than hoping the opposite situation will stand for long).
 
Now let's pretend casinos are aware of that, trying to voluntarily mix cards in order to get long clustered ITCPs not fitting a more likely natural course.

Really?

First, most HS players do not follow a given strategy, they just like to bet univocal betting lines and long ITCPs situations endorse such probability. Hence such shoes will get a greater damage for the casinos than normal distributed shoes.

Secondly, HS bac players and amateurs are more likely to be thrilled by third card impact than what serious players are, forgetting that what is underdog remains underdog.

Knowing that ITCPs pace is following precise lines, it's time to consider third card impact random walks.

as.

At baccarat the probability to get something is partially dependent by the previous situations providing we've properly evaluated the cumulative effect already happened with the general probability.

More deeply we're investigating the process, higher will be our positive expectancy.
Think about 8s and 9s falling pace or valuable third card falling pace going to the Player side.
Naturally and obviously being forced to consider real outcomes, a lot of variance will act along the way.

So it may easily happen that our 9 will combine with an ace or a deuce on the first two cards and that a valuable 6 or 7 as third Player card will produce a worthless point.

Of course itlr such 9s or 6s and 7s as third P card are going to form valuable points.

Actually we shouldn't give a lesser fk about short term less likely situations, even knowing that they could go in our favor despite their "unlikelihood".

What we're really interested about is the estimation of the "paces" involved of such situations, at the same time trying to restrict them as a "whole" as no way 8s and 9s are falling equally on both sides and no way valuable P third cards are constantly falling as fifth card. With every other card situation falling in between.

We've seen that depending upon the random walk applied, the actual card impact over results assumes several different shapes up to the point where univocal albeit unlikely patterns will get the same picture at multiple r.w.'s.

it's about this probability that imo we should set up our strategy.

as.