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Adaptive Randomized Bernoulli Cascade System

Hadi

2025-10-21 09:12:41

The Bernoulli Cascade System is an experimental trading framework that integrates randomized trade generation with multi-layer probabilistic validation.
Each batch of trades passes through a cascade of statistical filters — Standard Deviation , Poisson , and Bernoulli distributions — to determine whether the system maintains a statistically acceptable edge.
When performance meets defined probabilistic thresholds, the strategy reinforces itself by adaptively increasing position size.

The approach challenges traditional deterministic system design, positioning itself as a self-adaptive stochastic machine that learns about its statistical consistency directly from live outcomes rather than backtested predictive models.

Conceptual Foundation

The Bernoulli Cascade System begins with a radical assumption:

“If markets are stochastic systems, then an adaptive stochastic participant can statistically evolve toward efficiency.”

Traditional EAs rely on deterministic logic — moving averages, candle formations, or predictive indicators. These methods degrade when market dynamics shift. BCS, instead, treats the trading process as a continuous probabilistic experiment, where every sequence of trades is data to be tested, not trusted.

Each “experiment” (a batch of n trades) is evaluated statistically. If the last batch shows outcomes consistent with a favorable probability distribution, the system permits continuation and scales risk; otherwise, it resets to its baseline.

This structure creates a cascade of mathematical validations — much like a neural filter but grounded in classical statistics.

System Architecture

_Randomized Trade Generation
At a specific daily time (e.g., 10:00 AM server time), the system opens n trades — each randomly assigned as BUY or SELL.
Entries do not depend on any technical indicator, only on random choice governed by a pseudo-random seed.

This randomized input is critical: it prevents curve-fitting, directional bias, and over-optimization.
It turns the market into a sampling space — allowing statistical laws to act as the decision filters.

Each trade has:
- A stop-loss (SL) and take-profit (TP) that can be fixed or randomized within defined pip ranges.
- A base lot size (BaseLots) adjustable by the trader.
- A unique MagicNumber, ensuring historical isolation of trades for evaluation.

_Statistical Evaluation Cascade
After every set of n closed trades, the system collects the net results (profit or loss) and computes three tests sequentially:
- A. Standard Deviation Test
  This test models the distribution of wins in a binomial process with baseline probability p₀ (default 0.5). It calculates the expected mean and standard deviation of wins over n trades:
  
  If the observed number of wins exceeds μ+ kσ (where k is the SDMultiplier ), the performance is considered statistically favorable.
  This acts as the first filter — eliminating random success within expected variance.
- B. Poisson Distribution Test
  For the subset of trades passing the first stage, the count of wins is modeled as a Poisson process with rate λ= n ⋅ p0 .
  The Poisson tail probability:
  
  is then computed.
  If this tail probability exceeds the threshold (PoissonPThreshold), the win frequency is statistically consistent with the desired behavior — indicating the results are not due to rare luck.
- C. Bernoulli Distribution Test
  Finally, the system computes the empirical win rate $\hat{p} = \frac{w}{n}$
  If $\hat{p} \geq \text{BernoulliThreshold}$ , the batch passes the full cascade.
  
  Passing all three layers means the system’s recent performance meets not only expectation but also probabilistic sustainability.

* You can download the EA from the Download Box HERE

Adaptive Reinforcement

When all tests pass:

The system increases its next trade size by a multiplier (LotIncreaseFactor, e.g., 2×).
The increased lot remains active until the next evaluation cycle fails.
If the next cycle fails any test, the system reverts to the base lot size.

This adaptive reinforcement mechanism acts as a feedback loop — statistically successful behavior is rewarded, while poor sequences self-correct by reducing exposure.

Optional Dynamic Risk Control

The MQL4 implementation also supports:

Randomized SL/TP within specified bounds.
Optional trailing stops when using increased lot size.
Isolation of symbols and trade history through a dedicated MagicNumber.

All these parameters are fully configurable via extern variables in the EA.

Implementation Summary (MQL4)

The system is implemented as a pure MQL4 Expert Advisor with no external dependencies. The EA follows this lifecycle:

Initialization:
Seeds the random number generator using system time and an offset.
Trade Trigger:
At a user-defined hour/minute, opens n random trades with chosen SL/TP logic.
Statistical Evaluation:
Once n previous trades are closed, retrieves them from history and performs the three statistical tests in order.
Adaptive Decision:
If all three pass → double next lot size.
If any fail → reset to base lot.
Continuation:
Repeat daily at the specified open time.

This minimal structure allows for easy integration with any broker, symbol, or timeframe, while maintaining complete transparency of logic.

* You can download the EA from the Download Box HERE

Example Scenario

Consider a configuration where:

TradeCountPerDay = 5
baselineProb = 0.5
SDMultiplier = 1.0
PoissonPThreshold = 0.05
BernoulliThreshold = 0.6
LotIncreaseFactor = 2.0

At 10:00 AM each day, five random trades are opened.
After they all close, suppose the system records 4 wins and 1 loss.

Standard Deviation Test:
Mean = 2.5, SD ≈ 1.12, threshold = 3.62 → 4 > 3.62 ✅
Poisson Test:
λ = 2.5, P(X ≥ 4) ≈ 0.24 ≥ 0.05 ✅
Bernoulli Test:
p̂ = 0.8 ≥ 0.6 ✅

All tests pass → lot size doubles for the next session.

If subsequent performance falls below thresholds, the system automatically reverts to the base size, effectively forming a self-dampening risk control.

Philosophical Interpretation

The Bernoulli Cascade System isn’t designed to predict price direction — it’s designed to probe the market’s randomness.

Where traditional systems fail under regime change, The Bernoulli Cascade System adapts by redefining what “success” means statistically.
Its power lies in separating random success from probabilistic persistence.

The cascade of tests ensures:

Standard Deviation layer: filters normal noise.
Poisson layer: checks rarity vs. expectation.
Bernoulli layer: validates sustained success.

Together, these form a three-dimensional quality gate for any performance streak — enabling adaptive exposure without prediction bias.

Strengths and Limitations

Strengths:

✅ Immune to overfitting — no indicator tuning required.
✅ Fully interpretable statistical framework.
✅ Works as a self-learning reinforcement mechanism.
✅ Can be combined with any other trading logic as a meta-filter.

Limitations:

⚠️ Requires a sufficient number of trades for statistical significance.
⚠️ Random entry may lead to long drawdowns in trending markets.
⚠️ Statistical tests assume independence between trades.
⚠️ Position sizing growth should be capped to prevent compounding risk under variance clusters.

Practical Extensions

Future developments could include:

Sliding-window analysis: apply the cascade over multiple batches to detect long-term bias.
Volatility weighting: adjust SL/TP dynamically based on ATR or realized volatility.
Meta reinforcement: allow multiple EAs to share a central statistical state, creating a multi-agent Bernoulli network.
Hybridization: combine BCS with a predictive signal (e.g., neural net output) where prediction controls direction but BCS controls risk scaling.

* Leave a comment below if you’d like these features added. Scroll To Comments

Backtest Results by MetaBacktest
We ran multiple backtests of the MQL4 Expert Advisor using MetaBacktest to ensure fair and transparent results.

Test Parameters:

Instrument : EURUSD
Timeframe : M1
Period : Aug 2024 – Aug 2025
ExTradeCountPerDay: 9
OpenHour : 18
OpenMinute : 0
RandomizeDirections: True
BaseLots : 0.01
UseFixedSLTP : False
RandomSL_MinPips : 20
RandomSL_MaxPips: 30
RandomTP_MinPips : 20
RandomTP_MaxPips : 500
baselineProb: 0.05
SDMultiplier : 1.0
PoissonPThreshold : 0.0011
BernoulliThreshold : 0.1
LotIncreaseFactor : 10.0
HistoryTradesToCheck: 30
UseRandomSLTPSeed : True
RandomSeedOffset: 10
UseTrailingOnIncrease : False

* You can download the EA and setting file from the Download Box HERE

Process time: 0:00:34.250
Adaptive Randomized Bernoulli Cascade System EURUSD-M1 - MetaBacktest

Key Results:
Adaptive Randomized Bernoulli Cascade System EURUSD-M1 - MetaBacktest

Conclusion

The Bernoulli Cascade System demonstrates a new paradigm in algorithmic design — one that replaces market prediction with statistical validation.
By structuring a random process and evaluating its outputs through mathematically sound filters, The Bernoulli Cascade System turns randomness itself into a tool of adaptation.

While unconventional, its beauty lies in its simplicity:

“Trade randomly, validate probabilistically, scale adaptively.”

In an era dominated by overfit predictive models, the Bernoulli Cascade System reminds us that sometimes, the purest edge isn’t found in the signal — it’s found in the statistics of our own outcomes.


Bernoulli-Cascade-System_MetaBacktest.ex4
Bernoulli-Cascade-System_MetaBacktest.mq4 
Bernoulli-Cascade-System-Set1.set 



Report-Bernoulli-Cascade-System-EURUSD-M1_MetaBacktest 



 



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Comments

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EA_Mastermind 2025-10-22 09:47:20

The Standard Deviation test checks if the number of wins deviates significantly from the expected mean. The Poisson test assesses the likelihood of observing the number of wins by chance. The Bernoulli test evaluates if the win rate is consistent with the desired probability.

SmartMoneyFX 2025-10-22 07:06:23

Can this system be combined with other trading strategies or indicators?

MetaBacktest 2025-10-22 07:06:23

Yes, the Bernoulli Cascade System can serve as a meta-filter, allowing you to combine it with other strategies to enhance overall performance.

Pip_collector 2025-10-22 05:22:53

Opening trades at a specific time with random buy/sell decisions seems unconventional. How does this randomness contribute to the system's effectiveness?

MetaBacktest 2025-10-22 06:42:41

The randomness prevents the system from becoming too tailored to past data, reducing the risk of overfitting. It treats the market as a sampling space, allowing statistical laws to guide decisions.

marketHawk 2025-10-22 01:26:03

Could someone explain how the cascade of statistical filters works in layman's terms? I'm familiar with basic trading strategies but not with this approach.

trendsurfer 2025-10-22 03:06:23

Sure! Think of it as a multi-step quality check. After each batch of trades, the system evaluates the results using three statistical tests: Standard Deviation, Poisson, and Bernoulli distributions. If the results pass all tests, the system increases the trade size. If not, it resets.