1. Roulette and Randomness: The Imbalance BehaviorRoulette outcomes are statistically independent—each spin is not influenced by the previous one. Despite this, over short periods of time, streaks and imbalances are entirely possible, simply due to the nature of randomness.Imbalance Growth:

   
In roulette, imbalances can theoretically continue to grow, but there are practical boundaries. The idea of an imbalance continuing forever is unlikely due to the law of large numbers. The longer you observe, the more likely it is for the results to approach the theoretical expectation (e.g., 50/50 distribution for black and red outcomes).
Small Sample Sizes: In smaller windows or sub-windows, streaks and significant imbalances are more common because there is less time for randomness to average out.
Large Sample Sizes: As the number of spins increases, it becomes more likely that the results will converge toward the expected average (e.g., roughly half red and half black outcomes).
2. What is Most Likely to Happen After an Imbalance?If you observe an imbalance that meets a strong threshold in a given sub-window, the most statistically likely outcome is that over time:

   
The imbalance will eventually correct itself.
This is not guaranteed immediately after the imbalance is detected, but rather over the long term.
The mean reversion effect indicates that the probabilities for underrepresented and overrepresented sides will stay the same for each subsequent spin (i.e., still 50/50 for black or red, regardless of the previous streak).
However, because you are focusing on a specific sub-window and aiming to identify mean reversion within the next window of the same size, what happens next is driven by a few important points:

   
Immediate Correction: Statistically, once an imbalance has been detected, the system may be more likely to see events favoring the underrepresented side, simply because the event itself (e.g., more reds than blacks) is currently underrepresented. This is not a rule but rather a statistical trend when considered over time.
Continued Imbalance: It's also possible for the imbalance to continue growing further before correction occurs. Sometimes, randomness favors streaks of one side (e.g., reds) beyond what you might expect. This is often called positive autocorrelation—one streak leads to more of the same in the short term.
3. Practical Limits on Imbalances: Can They Grow to Infinity?In theory:

   
An imbalance can continue growing indefinitely in a purely random system since there is no inherent memory and each spin is independent.
In practice:

   
The Law of Large Numbers: Over a very large number of spins, the imbalance tends to even out, and deviations decrease in proportion to the total number of spins. The average difference between the actual outcomes and expected outcomes converges to zero.
Gaussian Distribution: For sufficiently large spin counts, the outcomes tend to fall into a normal distribution, meaning extreme imbalances (more than ±4 or ±5 standard deviations from the mean) become extremely rare.
4. Likelyhood Limits: Observations and Real-World RecordsThe concept of how far an imbalance can go is crucial, and there are some real-world scenarios and records to consider:

   
Roulette Records: Observations from real casinos have shown that streaks of the same color can sometimes reach 15-20 consecutive spins. The probability of getting 20 consecutive reds or blacks is approximately 1 in 1,048,576 (since (1/2)20(1/2)^{20}(1/2)20). However, this can happen and has been observed. Even streaks of 24 consecutive reds or blacks have been reported.
Famous Example: One well-known anecdote took place at a casino in Monte Carlo in 1913, where black came up 26 times in a row. This event was so notable that it led to a psychological effect called the Gambler's Fallacy, where people assumed that red was "due" and bet heavily on red, leading to massive losses.
Practical Imbalance Limits:

     
In practice, when looking at smaller sub-windows (e.g., 25 spins), it's rare for an imbalance to grow beyond ±5 in terms of standard deviations.
Typically, if you measure écart as the difference between occurrences divided by the square root of the total number of spins in the sub-window, an imbalance of ±3.0 or more already indicates a significant deviation, which would suggest a high likelihood for a reversion or correction.
5. Implications for Betting Strategy: What Should You Expect After an Imbalance?

   
Imbalance Limits: While an imbalance can theoretically grow indefinitely, it's practically limited by the behavior of randomness, which tends to revert to the mean over time.
Correction Expectation: After detecting an imbalance, the most probable event is that the system will move toward correction. This doesn't mean an immediate correction will happen in the next few spins, but statistically, the longer the imbalance exists, the more likely it is to revert.
Considerations for Strategy:

   
Threshold for Action: Once an imbalance is measured above ±3.0, the expectation is that a correction is more likely than a continued imbalance growth. Thus, betting in favor of the underrepresented side could be a reasonable approach.
Record Limits: Given that extreme imbalances are observed but rare, the strategy could include watching for thresholds such as ±5.0 before betting aggressively, considering that these situations are less likely to persist.
Summary:

   
Imbalances Can Grow: Imbalances can grow to surprising extents but are practically limited by the nature of randomness in large numbers.
Return to the Mean is Probable: After a significant imbalance is detected, a return to the mean is statistically more likely over time.
Real-World Imbalance Limits: Observations in real casinos show that extreme streaks (e.g., 20+ consecutive outcomes) are possible, but very rare.
Strategy Implication: If you detect an imbalance above ±3.0 in a sub-window, it's generally more likely that a correction will follow rather than the imbalance growing further without limits.

day2, 20 triggers. 132 units profit.

you know it is good if it comes from me. Also, it is clear and explanatory.
...and free.

day 1. 13 triggers. 90 units profit.

I don't engage in these or study these types of questions.  But I like the gist of the 'adventure'.

Thanks for posting, hopefully you get some productive answers.

we are looking for imbalance situation where singles are overrepresented. we expect in the future series of length 2 or 3 at least to be formed. Progression is designed to capture those.

hello.
i have 6000 units. I want to get some profit out of them. this is money i can afford to loose.
How far can i go? how much can i take out of it?
So lets go. 300 spins a day.
I have 464 vitual players, each one tracking an even chance.
2 standard players (Red/Black and Odd/Even)

462 complementary street‑pair players (derived from 924 street combinations grouped into 462 complementary pairs).

Base bet is 6 units. Maximum Loss at each Tier is 62*6 units: -372 units.


Step   Bet (units)   On Win   On Loss
1   1           END+1   3
2   1           END+2   1
3   1           1   5
4   2           END+2   5
5   2           1   7
6   2           END+2   5
7   2           8   9
8   4           END+2   9
9   4           10   11
10   4           END+2   9
11   4           12   13
12   8           END+2   13
13   8           14   15
14   8           END+2   13
15   8           16   17
16   16           END+2   17
17   16           18   19
18   16           END+2   17
19   16           20   BUST
20   32           END+2   BUST
Notes:

END+1 means end the progression with a profit of +1 unit.

END+2 means end the progression with a profit of +2 units.

BUST means the progression ends with a loss equal to the total amount risked.

BAC is a game where we all receive a unique set of unexpected limitations with variables in a shoe of approximately 80 hands, eight decks of cards, making up 4-6 card presentments.  The question is, how will you decide which hands to respond to that are about to be dealt? You can either totally focus on your three bad habits which we all have, or you can empower yourself to play the game of BAC resourcefully and profitably making the very best of each group of limitations you wager correctly upon.

The bottom line is, while you cannot totally control what is happening, or about to happen in front of you, you must control yourself by the way you respond to what is happening or just happened. And you do exactly that by managing your habits of mind. Yes, much easier said than done.  However, because it is hard to change the thinking habits we all have developed as they are mostly at a subconscious level. We, you, everyone can get better by bringing the awareness as to what each of us are doing when we are in that seat at the BAC table with our hands placing those wagers. Bad habits of drain us. Plain and simple. Bad energy removes good things from each of us, you cannot change that. And if you let it happen you are doomed.

1). The Habit of Expecting Things to be a Certain Way

All of us have it to some degree. Some all the time, others at certain times. Without realizing it and being conscious of it, expecting things in BAC to be presented a certain way will definitely kill you.

Leave the expectations at the door before you buy-in at the table. Realize you do not know and at the same time, you do not expect to know what is going to happen and how it will be presented. (Oh, that will be ultra hard for the egotistical player, buy hey-it's your money my friends). Be totally impartial with total openness and that will in most cases, keep you away from expecting things to be a certain way. Because if you fall into the latter as I said in the first paragraph above, you will kill your buy-in, each and every time.

Have no habit of expectations. Period. Recognize the habit with your consciousness and awareness as you play by saying repeatedly to yourself, "I have no expectation of any certain way".

Try what I laid out, probably a new experience for yourself but all you are doing is setting your mind free of expectations that probably would not have occurred anyways. 

Here is the bottom line of your habit of expecting things to be a certain way. If you approach the BAC table with expectations of how it should be, or how it has to be in order to meet your expectations, they will almost every single time fail to come together and match you. And you will be stuck in a habitual cycle and probably will not even notice the damage you are doing to your gaming results most every time you play.

2). The Habit of Your Inner Resistance

In so many words, your fear and procrastination rolled up into one. Causes hesitation and avoidance of most things you desire. What is better at the BAC table, fear and procrastination or desires? One thing for sure and I welcome challenge, is when the group of clumping of any type is present, only unadulterated desire will allow you the guts and balls to wager on it for some handsome wins! And after all isn't that what gambling is all about getting some decent return on the money that we risk?

The aspect of your inner resistance is, that it is an invisible and negative force that will govern you because we all have common tendency to submit to our vulnerability and fear of failure. You generally feed into it with anxiety and distraction over the loss of your buy-in funds.

You must find what it is you fear that causes your inner resistance. Start by complete acknowledgment of your wagering fears, once you discover, you can then begin moving towards some type of insight to overcome the fears that hold you down in gaming. Most all of us will say, I don't have any fears or inner resistance. And those classifying all losses as uncaptured variables and unplayable shoes have some type of negative inner resistance.

No matter what happens, post each wager, you must face every wager with no tension and with more conscious presence.  That is an ABSOLUTE MUST.  The PRESENCE put you in neutrality and focus that are huge advantages. You will then be able to change your mode from struggling with harmful inner resistance to a beautiful one of flow and acceptance no matter what happens with the hand.

3). The Habit of Focusing Only on What Is/Was Wrong

The greatest thing about BAC is that almost every situation one can imagine has hidden beauty in it, if we are only willing to focus on what is actually happening. Of course that is much easier said than accomplished. Try putting aside the term, "difficult" at the table. Try the best you can to forget all the "wrong" that was or is at the table in past hands or in the current hand.

BAC is playable. And it's very playable and it's winnable. The biggest problem is we are all attempting a rocksolid approach to a "most likely win guaranteed" to be in our favor situation. Like I said in the first sentence of this section, every situation usually happens.  Those are or can be, chop, doubles, triples, ones and twos, ones and threes, streaks long and short, naturals cut, ties cut, ties stick, naturals stick, etc., etc., etc.  Problem being, you cannot follow only one because if you do, then you lose when the 'cut' happens and you become frustrated and emotional.  Because the biggest problem being, when you bet, it changes up. Simple. So simple it is so overlooked by people, because they just don't understand how simple it really is.

So, that is why I say we are in the habit of focusing on what is/was wrong with our decisions. I am not going to sit here and write, our wagers are all controllable and in perfect sync with the presentments that we are betting on. However, if you can always remind yourself that your wager is more powerful than the perfect present circumstance finding some type of inner peace, controlling the situation as it unfolds without any frustration whatsoever.  You will have to be in total consciousness of not allowing yourself to fall back into old habits of 'mind supply', that focus on what you have done wrong. Because you cannot move forward if you keep going back.  (Mind Supply: A person's attention. A person's memory. A person identified with their intellectual faculties. A desire or inclination that occupies one's thoughts.)

Summation

It's totally up to you and you alone. I know at the BAC table, I have won a great deal of wagers 'easier' when I was in a total oblivious state to my past bad habits as well as being in my current win state with total consciousness of neutrality. Likewise, I know I have lost a lot of wagers in sessions because I was stuck consciously within my bad habits. I admit it here, unlike many forums with countless members that write about how they all have their "unpublished——secret and never to be disclosed" protocols for winning all their hands for fear of casinos learning.  In so many words, their precious and golden Holy Grails.  ROMAFL! 

Myself, I found that writing, expressing and discovering my thoughts, play and related have led me to a much better understanding of the game, the people playing it and how psychologically our brain functions play a much larger part of wagering and interpreting the baccarat shoe and its presentments than most can ever imagine.

I am well aware how most all of us will go to a casino, walk up to a BAC table and our mind goes basically blank. We will remember our last couple of losses and possibly our wins easily, but as far as the things I brought out here, confusion surrounds us how to remember them as we play. All you have to do is write some small reminders on the BAC card, as you were allowed to have scorecards in front of you at all the properties I have ever been to in the USA. They are as follows.

"Do not expect things a certain way"

"No inner resistance at all"

"Ignore everything wrong, what Was/Is'

As the old saying goes, the balls in your court.

I pretty much explained in post #4 how I play. 

I do not have any kind of mechanical or pre-planned structured betting regime.  I wager a base unit (usually). Until I begin to win a few.  Then I parlay 1x or 2x's as I have described numerous times.

Parlaying does work for me with my winnings.  If I lose my parlay wagers, they are not from my buy-in risk capital, at least greater than my 1 unit base bet.

My buy-ins are roughly 10% of my bank roll at most.  If I lose a session or two or three, no big deal.  When I win, the first thing I do, is replenish my bank roll back to norm.  I have also detailed that out numerous times in my MMM articles. 

I am full prepared to face harsh sessions with my win money parlays, however if the session is harsh, I would have lost the session with single wagered base units anyways, IMO.

I do see your point in playing every hand, shoe after shoe.  But that is not the way I play the game.

new pm for you asym! good idea probably