Even Chances made of 6 Streets

[albertojonas]

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.

[albertojonas]

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.

[alrelax]

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.

[albertojonas]

day 1. 13 triggers. 90 units profit.

[albertojonas]

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

[albertojonas]

day2, 20 triggers. 132 units profit.

[albertojonas]

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.