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.

Welcome back.

You are not losing anything by not attending other forums, that's for granted....

as.

Very interesting and valuable thread Al!

as.

Thanks again KFB!

There are several experiments to make, one of them is to compare the flow of two-card initial situations with the corresponding flow of actual final results.

From a strict math point of view each hand's winning probability is polarized at the start, only few hands will be affected by the third card/s impact, namely two-card situations being equal and both needing the third card (asym hand rules besides, of course).

Thus we should focus our attention about how many times higher two-card points on the same side will come out in a row on average.
The fact that many two-card higher points won't produce the math results we're looking for shouldn't bother us at all: as long as we are able to catch a superior than expected amount of those spots, itlr the probability to get more W than L is sure as hell.

I mean that we do not want to be right at single spots, just adopting a bet selection at spots where the probability to be right is cumulatively enlarged.
A necessary condition that cannot be applied at every shoe dealt.

In some way after having placed our bet at a given side, we should consider W and L just in terms of superior or inferior two-card point, regardless of the real outcome.


But it's about your second quoted "sentence" that baccarat is scientifically beatable.

A random succession cannot be beaten by any means, there's no fkng way to do it.
Successful long term bac players do not need luck, actually they hate it. And of course recreational players and "I know to win" claimers need it and like it.

The game is beatable as each possible betting spot does not correspond to the expected probability dictating that each hand is independently and randomly placed. (that is EV-)

Simplifying, some portions of most part of the shoes (not every shoe) provides unrandom sequences at different levels. Not every unrandom sequence will get the player a profitable level.
This feature is more evident when considering multiple random walks running on the two-card higher point probability.
Normal players are focused about BP real outcomes, strong bac players do not give a fk about those results, they are willing to risk their money about the probability that something "favourable" is going to happen again or is going to shift. And those probabilties are restricted about finite numbers.

Tomorrow our "bac walker" example.

as.

Without any doubt itlr we'll win because the side we have chosen to bet presents more two-card initial points higher than the opposite side.
Although it happens frequently that third card/s will invert this strong advantage, hoping to be ahead for long by guessing repeatedly that the unfavorite side will win is pure illusion.

For example, if we had bet Player getting 2-K and Banker shows 3-T, third card to the Player is a picture and Banker catches a 7 we win the hand but actually we have lost from the start.

Third card/s, besides the important asymmetrical hand factor, are just there for entertainment and to confuse things.
Naturally there are some equal two-card initial points that may need the third card draw, in these situations no one side is advantaged from the start (again besides the asym factor when working).

In the vast majority of the times any new hand dealt in form of two initial cards on each side will entice the formation of very different probabilities: cumulatively the higher two-card points will be almost 2:1 favorite to win the hand. It's like playing two dozens vs one dozen at roulette but by wagering just one unit and being payed 1:1 or 0.95:1 and not 0.5:1.

If we're here is because we are trying to dispute the randomness of the card distributions or any other bac feature that might get us a kind of an edge.
Surely we can't dispute math situations once they have appeared.

Hence a long term winning player is anyone capable to get a greater share of two-card initial points at the right side. Real outcomes are just a by product of such strong math propensity.
On the same token, we know that certain higher points will be so favorite to win up to the point they're eventually unbeatable (natural 9s) and going down with other high points.

It remains to define whether a supposedly random but surely finite card distribution will provide valuable betting spots by taking the problem by two different way of thoughts that actually constitute the same issue.

a- average lenght of uniformed one side favorite segments;

b- average number of gaps between favorite situations happening at the two opposite sides.

Obviously greater is the lenght of uniformed one side situations lower will be the number of gaps and vice versa.

Nonetheless we ought to remember that not everytime a favorite side is going to win the hand, but we have to accept this kind of error as any situation getting nearly 2:1 cumulative odds to win must eventually get a double number of wins than losses.
That means that we're allowed to get a fair amount of wrong "guessing" that we could easily reduce by selecting at most our action.

So a shoe is going to produce several "favorite initial two card states" at various degrees, try to register those situations regardless of the final outcomes.
To get precise registrations, deal the hands as bac rules dictate, nothing will change itlr.

Now in order to find out our possible long term edge we need a further adjustment, that is comparing what could happen more likely in relationship of what really happened in the past taken at different paces.

That's why RVM theories and Smoluchoswki studies help us to 'solve' baccarat.
Any random succession must provide independent results on every step of the original sequence and on every other possible subsequence derived from the original one, that is for each step whatever considered and for every random walk considered a x result will be proportionally equal to the expected probability.

Expected probability? Rattlesnakesh.i.t from the start.

as.

That's good KFB! :-)

Think as baccarat as a game of a slight biased 12-face tossing dice getting 6 B faces and 5 P faces where the remaining 1/12 side prompts the toss of a further hypothetical dice getting 7 B faces and 3 P faces.

If each one-step or two-step toss will be independent from the previous ones, no way a profitable strategy could be applied as the asymmetrical probability will come out proportionally as expected.

I mean that 11 out of 12 possible first dice toss outcomes are differently payed, one side getting 0.95:1 payment and the other one 1:1 payment.
It's just about that nearly 1:12 odds probability that things substantially change by math terms.

Thus Banker bettors will be hugely right just one time over 12 attempts and Player bettors will be hugely wrong just one time over the same 12 hands range.

In a sense Banker bettors are hugely right rarely and Player bettors are hugely wrong rarely.
At the same token, Banker winners are more likely id.iot 5% contributors, whereas Player bettors feel as idi.o.ts just one time over 12 bets. 

The common suggestion dictating to wager B side in order to lower the HE is completely unsound as long as we decide to select at most our bets.
Following this "B always betting" strategy, we see most B bets are hugely unfavorite as the asym strenght happens rarely, mainly as they are not taking into account the whimsical finite key cards impact.

It's interesting to notice that a careful selected betting plan will get more profitable opportunities at Player side than at Banker side, meaning that a 1:1 payment will crush a supposedly 0.95:1 payment diluted at more likely expected math B spots.

Remember that we just need a 50.1% probability on our P bets to get a long term edge.
We shouldn't care less whether we could find ourselves in those rare 42.07%/57.93% disadvantaged asym spots, consider them as a kind of zero happening at roulette now getting a substantial degree of success.

After all it's only the key card distribution who cares itlr, isn't it?

as.

So our goal is to get one of these precise B patterns: 1-1, 1-2, 2-1 and 2-2.
Of course we start the betting when a 1 or a 2 happen.
Since we utilize a mini progression as 1-2 or 100-150 or 100-120, etc. to be ahead of something we need to win right at the first attempt; if we lose this very first attenpt, odds are strongly shifted toward NOT getting any kind of profit as the average number of the searched patterns is four.
(for example, after a L we can only break even with a subsequent WWW sequence)

Nonetheless, we can choose to make our first bet right on the second searched pattern when the first pattern produced a loss, that is betting to get a LW situation.

Since itlr the overall number of L outweigh the number of W (in term of units won/lost), we could test large datasets to see what's the most likely losing pattern distribution.
After all, Banker 3+s are more likely because asym hands come out in finite numbers, mostly clustered.
Hence we do not want to fall into the trap of looking for a positive pattern whenever the first two patterns are LL or risking to cross an unfavourable WL spot.
This is not a stop loss or stop win concept, just a cumulative study on what are our best chances to win at EV- propositions.

After all we can't win less than one unit (or a portion of it) and since we're flat betting we do not want to chase losses when the actual shoe had shown a "negative" propensity from the start. (As we need at least a triple number of W to balance a single L)

On average and choosing to adopt a super selected strategy (waiting shoes forming a first L), we are going to bet nearly 25% of the total shoes dealt.
Moreover, not every shoe will form a four (or greater) WL pattern, some of them stops at two and three (and sometimes only one W or L situation arises).

Why such strategy should enhance our probability to win?

Like other binomial games, most part of bac results are formed by singles and doubles, In three hands dealt, only two patterns over eight form triples (odds 2:8.), the remaining part includes singles and doubles.
Bac rules from one part raise the probability to form 3+s (Banker) and the opposite is true at Player side favoring singles and doubles.
Anyway, this math propensity comes out just one time over 11,62 hands dealt and sometimes it will shift the results very slightly. Not mentioning that some card distributions favor Player side even in asym spots.

Many bac players tend to emphasize too much the less worse 0.18% Banker return, this simple strategy (along with some additional adjustments I do not want to discuss here) shows that we can concede the house the higher advantage; let the house hope everytime we'll make a rare bet an asym hand will come out precisely on that spot.

as.