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.

Back to the main topic.

Let's pretend as baccarat as a neutral EV game, either side will draw when getting a point from 0 to 5 getting a perfect equal probability to appear and no vig is applied.

Itlr, we'll expect to get the same number of wins than losses, right?

Technically speaking and whether the cards are properly random shuffled, now the game is a finite (312 or 416 cards are employed) and made by independent binomial successions.

The word "independent" must be intended as the previous card distribution can't get an impact toward getting a different than 50% expected probability on the next BP results.
That is any hand should be "new" the same way any roulette spin is perfect independent from the previous spin.
We could compare more precisely those two different games by pretending roulette wheels as "zero free", even though at baccarat a percentage of hands provide no B or P results.

It's obvious to think that as long as bac (or zero-free roulette) results are randomly and independently dealt, our EV will be zero.

Hence and in order to consider a possible positive edge we must work to find ways capable to dispute one or both of such two features: randomness and independence.

Roulette outcomes are disputable just on the perfect randomness being the independence factor irrelevant.
Baccarat outcomes can be assessed by both qualities: a perfect random shuffle acting at 6 or 8 decks is almost not existent, secondly the independence factor cannot be present whenever the probability to get key cards prompting more likely results cannot be equally balanced at the two sides per each shoe dealt.

More on that tomorrow

as. 

Quote from: alrelax on March 22, 2021, 01:14:12 AM
To be clear, I do not concentrate solely on side Wagers but I do like them for certain percentage of my wagers. And when they're hitting, they are hitting and there's no quicker faster way to make some serious money than the side wagers at anywhere up to 200 to 1.

I know.
Casinos can't refrain to deal shoes producing improbable things, actually they like them from one part but they hate them from the other one.

It's not a coincidence that almost every high stakes room in LV offer very few side bets at their tables: tie and pairs. And very few (or none) no-commission tables involving the F-7.
(Only few HS serious people like to play at "Tiger" tables for obvious reasons...)
Casinos do not want to give high bettors the possibility, albeit remote, to recover losses or to get huge wins at few spots.

Despite that, even ties and pairs can seriously (temporarily) harm a casino.
I remember one occasion where a very HS player cleaned up all the "cranberries" ($25.000 denomination chips) present at the entire room. He was allowed to bet up to $80k at B or P and up to $30k at tie and pairs bets.
Magnificent potential house advantage? Sure. But...

This player not only won almost every B or P wagered on the third part of the shoe, he also managed to get a couple of "dreaming scenarios" as winning his P bet with a 4-4 vs a Banker Q-Q and winning a B bet getting 2-2 vs P showing J-J-A (total amount collected, $80k + $330k + $330k = $740k two times, minus $4k on the second hand due to commission); and anytime he would lose the B/P bet, he won a pair bet.

Naturally itlr such a player is destined to lose millions over millions, yet the house wasn't getting a pleasant time to find cranberries to pay him.
Just hoping he would have come back to play at their premise.

Now let's imagine what are the temporary wins a player like this may get at a no-commission table when a shoe produces four or five F-7 spots payed 40:1. Say where the maximum bet allowed is 5k or 10k.

Very unlikely situations? Surely, but when they happen house must pay the customers.

as.

Al, I think yours are points coming from a very experienced player capable to place many bets and many different wagers per shoe.
Quite likely you are one of the best to extract serious money from those rare shoes that come along the way. And knowing when to start or stop the betting, not an easy task when many bets are in order.
That's why I would be glad to play with you. 

Mine is a kind of opposite way to consider the game, I abandoned most side bets a long time ago focusing my attention about BP successions and derived sequences.
Annoyed to hear that baccarat is an unbeatable coin flip game, I devoted a lot of time trying to disprove this (wrong) assumption. Of course not only because a side is more likely than the other one time over 11.62 attempts on average.

Reasons why imo baccarat is a way less random and independent game than what most people think are known.
I'm dead sure others have found the same flaws, of course there's no point to illustrate precisely how to get the best of such flaws.

For that matter, I really do not understand why allegedly winning players like to talk about "discipline".
Either we get a verified edge or we don't, discipline doesn't turn an EV- game into a profitable one.
Probability to win as disciplined players is the same as being undisciplined.
Discipline intended as a way to restrict the field of operation probably helps to lose less but surely doesn't help to win itlr.

I might be the most disciplined poker player on the planet yet I stand no chance to win itlr when playing Phil Ivey.

But if we know to play baccarat with an edge, per every hand played we can toss a dice telling us the amount to bet (from $100 to $600 for example), nothing will change itlr.
It's a whimsical form of flat betting, getting zero impact on long term results. 

I see that some players have the experience to make the proper adjustments according to what the shoe is producing but to test whether they're actually doing right is almost impossible to prove. And anyway difficult to replicate.

Easier to track how given objective betting lines made under specific circumstances will get more wins than losses, that's now that we start to talk about the vulnerability of this game.

as.

Hi KFB!! :-)

Without any shadow of doubt, itlr real results are the by product of key card impact, we could safely assume that bac results are following the general probability propensity to fall here or there and this probability is restricted within finite terms.
There are strong evidences that median values (when properly assessed) of some situations tend to more likely stop after certain values had been reached, despite of the common assumption that every situation will be independent or too slight dependent of the previous one/s.

It's like playing a game where a key card is more likely to fall at a given side, with no guarantees to get a positive outcome, just a greater than expected probability to fall there.
This propensity is more evident at manually shuffled same shoes or SMM shoes, where there's no fkng way to provide a proper random key card distribution.

Worst scenarios come out at HS rooms where any shoe is "fresh".
No worries, even those shoes are producing some exploitable median values, actually there's no way many random walks applied to the BP original sequence will get univocal results for long.
If such thing would happen and considering the average HS player's skills, casinos will go broke very soon.
Fortunately they do not.

as.

Yep, happens so many times but not most of the times. That's why IMO we should make an adjustment at every shoe dealt: is this shoe going to produce an average or higher/lower than average number of  probability spots I'm looking for?

Say we have tested several shoes and the average shifting higher two-card point shows a median=3, that is 3 is the more likely shifting number between two sides (higher two-card points, not final results).
Thus we let go all inferior situations until we'll reach a shifting number of 3.

If the prevalent shifting number is 3 (median) we know that this value will come out more likely in clusters than isolated, there are no other ways around.

Therefore instead of stubbornly hoping that shifting spots will arrest at 3 regardless, we wait until an actual 3 had formed. Then when another shifting spot will reach the 3 value, we bet toward getting another 3.
If we lose we repeat the process, if we win we have to decide what's our goal that is if we want to risk additional money to get subsequent 3s.

Although spotting those shifting spots with a percentage >50% will get us a sure math long term advantage (especially at P side where we need at least 50.1% to win whereas we need at least 51.3% at B side) some problems arise.

The main problem comes out anytime we have made a bet and equal TCPs follow shifting values of 3. Here we are forced to gamble.
Secondly, two-card higher points are cumulatively strong math advantaged to form final winning results but they are susceptible to variance (as Al correctly pointed out in his post).
Third, some profitable opportunities may end up with a tie, thus slowing down further the process.

It's quite interesting to notice that "homogeneous" sources of shuffling (i.e. same shoes shuffled manually or shuffle master machines working at the same deck) tend to provide more constant and regular median values. It's what we name as a "fair or strong" propensity going far from a perfect randomness.

as.