I'm very glad you enjoyed this book.

When talking about gambling I like to hear from the best of the best and in this field Billy is the GOAT!!!

as.

'Runs' are classified by the number of shifts of one side to the another one.
For example a BPBBPPBPPPPPPBB sequence forms 6 runs and the same concept applies to every A/B binomial model where we assign a given status either to A or B.

The average runs number of a given production is one of the simplest way to assess randomness without calculating it by other statistical parameters as by using the chi square test, for example.

The state of art of baccarat has taught us that BP hands are moving around unbeatable values as B and P results are corresponding to a kind of a constant undetectable EV- coin flip succession.
That is a random undetectable world.

That's a complete rattlesnakesh.i.t: if this statement should be true, any bac succession should confirm the perfect place selection independence, in the sense that no matter which spot we select to consider (or bet) outcomes will invariably follow a general (unb) probability line.

To get a better idea of what I'm talking about say we're deadly sure that the card distribution of every shoe dealt will be asymmetrically shaped.

Now the sure asymmetrical card distribution will entice either asym patterns or sym patterns.
And at both categories different densities of those opposite scenarios will reach more probable values.
When some cutoff values are touched, we're not interested to know whether things will change or not, we simply let results to flow without betting a dime. 

Algorithms just exploit the asym/sym various AVERAGE densities happening along any shoe dealt and as already sayed the main algorithm will get the lead over the backup algorithm because A algo will catch a slight more profitable situations than the B algo, as the former consider a slight more complex rhythm than the other one.
For example giving a lesser impact over the moderate homogeneous streaks but relatively suffering of other strong symmetrical but unlikely sequences favoring the B algo wins.

as.   

Differently than black jack where casinos might (but they don't) virtually arrange the decks by not getting any kind of advantage for card counters (as a substantial portion of the cards is cut off from the play), at baccarat everything revolves around the number of 'runs' obvioulsy considered a too volatile value to set up a strategy upon.

Simplifying a lot, players who like to play 'streaky' shoes are hoping to get a relatively low number of runs whereas 'anti streak' players are doing the exact opposite.
Thinking that casinos are adapting their shuffles to the actual players category wagering at their tables is out of question, because itlr the number of runs assume a bell curve (unbeatable) distribution.
Casinos' aim is to get shoes more randomly distributed than they can, period.

The topic why a given shuffle tends to form more predictable patterns needs features overcoming the simple 'runs' factor, that is involving a symmetry/asymmetry parameter enticing the action of so called "limited random walks".

In our opinion there's a delicate balancement between asymmetrical and symmetrical limited random walks that are following diverse lines than expected by a "everytime it's a new independent hand" world and it seems our results are giving us a proof of such "weird" theory.

More on that later

as.

Basically casinos offer three kind of shoe shuffling:

a- manually

b- shuffling machines (the most utilized is the Shuffle Master and its variations)

c- preordered shuffle (HS rooms for example)

We have a strong belief that the 'cut' doesn't significantly change the "natural" flow of the outcomes for the already mentioned "alignment" factor. At least for our algos prediction.

Long term studies made on large samples of distinct categories enticed us to think that one algorithm performs significantly better at machines shuffled shoes, meaning that to get a substantial edge over the house just one algorithm random walk will get the best of it, so capable to nimbly overcome the natural negative deviations.

On the other end, manually shuffled and (at a lesser level) preordered shuffled shoes sometimes might pose a serious threat on the main algorithm action so luring the back-up alg to work. Hence complicating things a bit.

Don't worry: casinos do not give a lesser damn about this, they know that more shoes are offering in very restricted times, greater will be their probability to get profits.
And shuffling machines will perfectly fit this task.
Since players' aim isn't certified by math we're sure machines are making unbeatable our main algorithm and I'm not joking about this.

Generally speaking, manually shuffled shoes considered under our main algorithm lens could be a heaven or a hell as more likely affected by a moderate or strong unrandomness tending to provide longer positive or negative streaks than expected.
Good news is that the backup algorithm is able to catch a slight greater amount of positive than negative situations (at the cost that the main alg had to previously lose some spots before we consider to utilize the B plan).

Preordered shuffles where most money is wagered upon are a bit more intricated to be assessed as we do not know the visual source of shuffling.
Anyway we have reasons to think that casinos' goal is to offer shoes as perfectly random distributed as they can, well knowing that math edge + randomness = 100% unbeatability.

Actually a strong 'seemingly' randomness is what the main algorithm looks for: in fact an optimal randomness is unbeatable only when a perfect independent production source is acting per every hand dealt, thus giving a fkng damn about the average key cards impact and/or the natural math asymmetrical features happening along the way. Moreover giving a lesser damn about the "density" of the asymmetrical and symmetrical outcomes.
But all those parameters are considered irrelevant (besides the obvious B long term propensity) by our math and gambling expert fkng losers.
But not by our long term winning algorithms.

Naturally and to state that, we know how machines shuffle the cards and obviously we know by a fair degree of precision that preordered shoes are coming out from machine shufflers.

So as long as a machine is involved to provide outcomes, long term probability to make our main algorithm to lose will be very close to 0.

When manually shuffled shoes seem to get unprofitable the main algorithm random walk's action, it's time to utilize the backup algorithm. Or, naturally, to consider as unplayable that shoe.

Problem is that without using an illegal software, riding two different algos will easily lead to a lot of mistakes as the different algos' rhythms need plenty of attention to be properly registered.
This is the only downside of such long term EV+ plan.

Algorithms do not guess or hope for anything, they just suggest to bet EV+ spots.

Of course we're just clowns, baccarat remains an unbeatable game.
In the meanwhile we collect the short term positive variance (LOL)

as.

Very soon a brief discussion about how much the baccarat 'source' (SM machines, manual shuffling, etc) has a sensibile impact over the outcomes.

as. 

 

Ahahahhahah they've chosen the wrong number "four minutes"....
Maybe it would have been better a "....-learn in less than six (or) eight minutes"

as.

 

Hi KFB!

Excellent points. No jokes.

Again I stress about the importance of R. von Mises definition of randomness and Smoluchowski probability after effects concept, clearly and undoubtedly confirming that at baccarat most successions are unrandomly or partially unrandom distributed.

There's no way to beat a perfect random world for long, but there are several ways to exploit unrandomness itlr even though we do not know the precise direction the unrandomness will take at any shoe dealt.
Obviously and as you correctly sayed in your post, the unrandomness could lead to terrific spots or to terrible situations, so enticing the betting action or not by assessing, shoe per shoe, simple statistical standards.

Smooth operators

Algorithms act like the Sade 'Smooth operator' song words: "No place for beginners or sensitive hearts".
The final betting process is made after considering several parameters, so they'll do what they are instructed to do: That is suggesting the more probable spots, shoe per shoe, giving a lesser damn about the actual conditions or long term probabilities that sometimes could lead to bet the opposite side.

Algos do not guess anything: They just know that when betting Banker they need at least a 51.3% to succeed, or when betting Player they need at least a 50.1% winning probability.
That's where the edge comes from.
Whenever such cutoff values are surpassed too much, they simply stop or moderate their action as they "know" that a kind of too deviated situation is happening.
When a strong deviation happens, half of the times will go to our favor but the other half will be harmful and obviously both parts are asymmetrically ROI (return on investment) shaped for the natural EV- feature.

It's the rhythm of presentation that counts and fortunately one of the two algorithms is entitled to catch a "more expected" course of action by a degree of precision touching the 100% value.
So in some sense it's very very unlikely both algos will get the same long positive streaks for long.

as.

At a given binomial succession, one of the simpler ways to ascertain randomness is to register the number of "runs", that is how many times a given side will shift to the opposite one.
If the production source is constant and completely independent for each outcome, there are no valuable strategies to detect when the runs number may enlarge, decrease or stay at 'average' values. Any hand is a new hand, period.

Therefore after 100 hands, 25% of total outcomes will be singles (enlarging the runs number) and the remaining part belonging to various streaks (25% of doubles and 50% of superior streaks) that tend to decrease the runs number.
Do not confuse the number of total hands with the patterns shape (obviously itlr singles=streaks, doubles=superior streaks, etc)

But at baccarat we have reasons to think that the production  may be affected by a partial (volatile) unrandomness and anyway cards cannot be uniformly distributed, especially for the fact that some ranks will get a different weight over the final outcomes (key cards).
Now and for obvious reasons, the number of runs is a too simple tool to rely upon as being too sensitive of the volatile actual card distribution.
We'll never know precisely and even by considering single outcomes by "ranges" the key card falling and their impact over the final results.

Thus we could face the issue by a different angle, that is considering outcomes under the asymmetry or symmetry lens so considering diverse classes of results more probable to converge toward specific situations.

Our algorithms do not give a damn about actual strong (profitable or not) deviations and let alone about the B math advantage. They simply do their best to assess the various levels of natural asymmetry and the temporarily (less probable) symmetrical situations any shoe in the universe will be more likely to produce.
When both events tend to be silent (thus the asymmetry is not present or showing up by very low values and, more importantly, the less likely symmetry takes an improbable strong lead), our algos will lose.
Actually whenever the main algorithm seems to get unplayable spots for "long" or collecting more losses than wins, the back-up algorithm will get a slighter amount of favourable situations than not.

It's because we set up both algos not by a kind of opposite triggers applied to the same succession, just by a different constant rhythm that tries to get the best of the more likely card distribution.

as.

Into a true random environment where each result is fresh and completely independent from the previous one(s), the average card distribution concept cannot exist so the algorithms can't rely upon nothing as every outcome and every class of outcomes will belong to the same (unbeatable) world, so forming the old fkng Bell curve.

Thus the pivotal average card distribution (no matter how whimsical are the card combinations producing the actual results) should be entitled to make more asymmetrical events than symmetrical situations and of course we're just interested about one side of the asymmetrical operations (the positive side).

Consider an A/B succession produced by a random source where (p)A is 0.52 and (p)B is 0.48. (For example a roulette wheel having 52 black slots and 48 red slots).
Itlr and sure as hell we'll expect to get univocal situations privileging A streaks and B singles as every spin will more likely fall into the greater number of slots.

Say that even at baccarat we have found betting paces capable to get similar probabilities itlr, so we have reasons to dispute the perfect randomness of the source; in addition we may infer a kind of dependent back-to-back probability up to the point that the "natural" expected POSITIVE asymmetry could be erased or even inversed at a substantial portion of the shoes dealt.

Since any shoe is a new world (albeit being slight more likely to follow some pattern lines), distributions deviating too much from the "average" could be a perfect heaven or a terrible hell and we don't need deep thoughts to ascertain that.

In fact when the more probable average card distribution shows up, the positive expectancy is more likely to be clustered and clustered for long or to be isolated for very short terms, but when card distributions deviate too much from the average CD, we'll get a half probability to encounter deeper favourable events than average or, sigh, a half probability to get a sort of nightmare.

In some sense, we have 2 out of 3 occurences to rely upon:

1) Average card distribution (working at both algos)

2) Positive deviated card distribution (working at one alg, we do not know which)

3) Negative deviated card distribution (working at one alg, we do not know which)

Fortunately and differently than derived roads successions, per every shoe dealt both algorithms are able to spot more likely situations by taking care of a higher amount of volatility.

It's like that by riding both algos not a single shoe is unplayable and that's a decisive finding to not waste time by waiting an average card distribution or positive deviated CD to happen.
Anyway and without a software help, it's very very harsh to manually classify both algos at the same time, not mentioning the difficulty to know what to bet when one (or both) algos dictates so.

Next week an explanation about how different levels of asymmetry or temporarily symmetry will affect each algorithm.
Then I'll shut up.

as.

Hi Al: yep, we can't know exactly when things happen, we're forced to move around probability ranges and IMO some ranges are more reliable than others.

Hi KFB!

Stadium bac live dealer games are quite good for this strategy but only tracking one table at a time. It's very easy to make mistakes and as already sayed this is the main problem of the algos action. (More inputs on that privately)

About the early detection of 'streaks': obviously an above than average profitable shoe must start  'positive' at the first steps rather than starting bad and suddendly producing a long positive streak. It's what we name as "positive recency" that tends to get a much more important impact than the "negative recency" counterpart on the betting frequency.

If a positive streak shows up we could think of it as a natural situation or a biased event, in any instance we have no reasons to stop the action, sometimes up to the end of the shoe (due to the relative rarity of the betting frequency).
Of course if we win itlr it means that most shoes are somewhat 'biased', in our case because they belong to the "average card distribution" category that most of the times produce expected result ranges.

Most shoes doesn't mean "all shoes" so we have to think what to do when the 'bias' seems not to be working.
Have to run, see you later

as. 

For a moment say that the 'average card distribution' is an insane thought, that is just bighorn.sh.it.
So let's compare baccarat with the math beatable black jack.

Ask any serious bj card counting player how many profitable shoes, on average, he/she is going to expect along the way.
Moreover ask the same players whether a strong negative count happening on the initial-intermediate portions of the shoe will provide next favourable positive situations at the same shoe.

Probable answers are in the 12-16% field for the first question and a kind of "very close to zero" about the second one.

So and assuming a fair shuffling, 84%-88% of total shoes distributed produce both an 'average' card distribution or a "negative" unprofitable deviation.
That means that 24%-32% of total shoes are NOT roaming around averages where half of those deviations are profitable and the rest is EV-.

In a word and simplifying the issue, 76%-68% of total shoes are following a low deviation probability that we can condense into the 'average distribution' category.

At baccarat the 'average card distribution' concept still stands even though it's more intricated to be grasped as being a by product of both math and statistical features. 
In some sense algorithms follow what is more likely to happen at that 68%-76% portion of the shoes dealt, at the same time conceding a "possible" valuable room to that half part of 32%-24% deviated distributions not belonging to the average class. Anyway fearing at most negative streaks up to the point that even a single negative spot makes them to stop their action.

Therefore whereas there's a point to bet toward a positive streak as the main goal is always oriented to achieve a homogeneous winning streak per shoe, there are no reasons to 'limit' a negative occurence of any kind.
Actually it's just the (slight less likely) clustering negative appearances that makes this plan profitable.

No precise patterns will make the algorithms to start or stop their action, it's just the actual results pace to make the job and we have two different paces to rely upon.

Algorithms don't guess anything, they just select the spots where more probable sums are formed by adding a previous pattern value with the next unknown pattern value and fortunately they are more right than wrong.

as.

IMO, more parameters we're inserting in the algorithms and greater will be the probability to get a poor prediction as the baccarat variables are so many that we risk to sink in the undetectable ocean where casinos take their huge profits.

For practical reasons, we've chosen to set up both algorithms in the simplest way and obviously 'training data' take care of the old 'average card distribution' that cannot be disregarded for long.
As already sayed, when an actual card distribution tends to deviate from the 'average', algorithms stop their action even if they have collected a temporary loss.

Good news is that when both algorithms are in action, in the vast majority of the times the positive clustering effect of one al. will overwhelm the other performing bad and not by a kind of 'opposite' way of considering things.

After all predictions are made upon a very restricted field of operation where the main goal is to  get all winnings along the shoe dealt.
Remaining situations, albeit producing more wins than losses at the end of the shoe, are very welcome but considered by the algorithms just as 'incidents'.

More later

as.

BTW, next week we'll talk about the 'overfitting' problem. 

as.

The algorithms are built after having tested thousands and thousands of real shoes coming from various sources:

- Manually shuffled shoes

- Shuffle Master Machine shoes

- Preshuffled shoes (typical of HS rooms)

- Different mix of the above procedures

Results and profitability are the same, there are no significant statistical values favoring one or another method of shuffling.

Therefore we have thought that the partial unrandomness or the nearly perfect randomness of card shuffles won't make a role in determining the excellent alg's prediction.
That tends to collide with our past hypothesis that only a defect of randomness could make a game beatable.

Since we are not so naive to think that we were up on something without a reason, we thought that the old key cards asymmetrical distribution makes an important role about the results, moreover reinforced by what we name as "average card distribution" where alg A put the most emphasis on.
At the relatively less likely occurences where the 'average' seems to fail privileging the outliers and despite of a huge betting selection, the alg A stops its action conceding room to the alg B, but this is just a back-up less important move as more shoes we'll play more consistent will be the probability to exploit our EV+.

For sure there will be better algorithms to beat the game, yet we have tested an unbelievable number of different possibilities and so far those are the best.

The decisive factor, in our opinion, was to get a possible long term 'optimal play' based by comparing expected math and statistical features with the actual results, so even density and rhythm of presentation are both valuable tools to instruct the algorithm to make a proper job.

As already sayed, an ironic aspect to consider is that a same pattern (commonly considered as a single or a double, etc) could be a losing or a winning spot in relationship of when the alg decides to act.

To make a simple counter intuitive example, alg A may easily suggest to bet P after PP or PPP, or to bet P after B as those are the slight more likely occurrences related to the actual distribution.   

Obviously and to make the already complicated concepts simpler and to implement the authors ideas, the algorithms consider BP results as 50/50 spread, thus having the expected same probability to appear.
So in the process and while betting P side, we're conceding a general (but volatile) -0.18% math edge to the house.
Actually the algorithms are capable to catch situations where P probability is way over than 50% whereas B side gets more difficulty to spot situations surpassing easily and safely the 51.3% profitability cutoff point.

But this is a well known baccarat problem while betting B side: Either we're rarely astoundingly right (8.6%) or absurdly consistently wrong (91.4%).

See you next week

as.

Derived roads vs algorithms

Everybody knows that a given plan performing bad at a given derived road very often will form opposite situations at one or both other roads, so enticing us to change the succession to be followed, with the hope that things keep staying in the 'good' territory.

Sometimes the 'trick' works and other times does not and of course most of the times the probability to succeed is 50%. So worthless.
 
The derived roads invention was a brilliant accomplishment made by some Macau colleagues in the 70s (there are some statistical features to exploit by playing them) but somewhat flawed from the start.

The main problem of the DRs is that they are geometrically produced like bricks forming walls of different height, so 'too much' affected by the actual card distribution without giving a proper  role to the decisive math features.

In fact, whereas natural difficult situations arise at both DRs and algorithms and for different reasons, DRs do not give us the luxury to rely upon a 'well calibrated and controllable' scenario, the paramount condition to set up serenely a profitable plan itlr.

In truth, each DR is capable to provide longer positive situations than our algorithms but with the fatal downside to make more probable long negative sequences to happen.
A thing that we must avoid at all costs.

Obviously the same problem applies to the Big Road but at least here we possibly get additional factors to rely upon (see 'codes' plan for example).

But the most interesting thing we've found is that DRs are providing 'symmetrical' events, in the sense that every road will whimsically present good or bad situations in relationship of the actual distribution without any link between the three lines, whereas alg A when seems to fail makes alg B to get a more normal 'course of action'.

Despite of being both algorithms built with the same math and actual distribution issues, the alg A always takes the lead over the alg B as this one is considered just a back-up (still very profitable) plan. 

More later

as.