1. The Validation Principle

A statistical tool is only as good as its ability to detect the truth. To validate the Lucky Picks Fairness Score, we don’t just run it on real lotteries—we run it on synthetic lotteries where we control the truth.

We developed a simulation engine (trust-score-experiment.js) that generates thousands of draws under specific, “rigged” conditions to prove that our algorithm correctly identifies them.

2. Stress Test Scenarios & Results (v3.1)

We subjected the updated Fairness Score algorithm (v3.1) to a comprehensive stress test suite. This version enforces the strict “Weakest Link” policy, ensuring that a failure in any single component (like a biased bonus ball or temporal anomaly) caps the entire score.

For a full breakdown of the v3.1 algorithm, please read our Methodology Report.

Each scenario consisted of 1,000 draws repeated over 10 iterations.

Scenario A: The Control Group (Fair Game)

  • Setup: Pure Math.random() generation for all numbers.
  • Expected Result: Pass (Score 95-100).
  • Observed Score: 99.1
  • Verdict: ✅ VALID. The system correctly identifies a fair game.

Scenario B: The “Hot Number” (Biased Main Drum)

  • Setup: One specific number in the main drum is 3x more likely to be drawn than others.
  • Expected Result: Fail (Score < 20).
  • Observed Score: 10.0
  • Verdict: ✅ VALID. The system detects the frequency anomaly immediately.

Scenario C: The “Hot Bonus” (Biased Bonus Drum)

  • Setup: The main numbers are fair, but the Bonus Ball (e.g., Powerball) is 5x more likely to be a specific number.
  • Expected Result: Fail (Score < 20).
  • Observed Score: 10.0
  • Verdict: ✅ VALID. See Section 3 for details.

Scenario D: Pattern Bias

  • Setup: The numbers are technically uniform, but the machine is forced to pick Even Numbers 80% of the time.
  • Expected Result: Fail (Score < 50).
  • Observed Score: 44.4
  • Verdict: ✅ VALID. The Pattern Analysis module correctly flags the combinatorial impossibility.

Scenario E: Seasonal Parity Shift (Temporal Scan)

  • Setup: We forced “Even” numbers to appear 80% of the time, but only in December.
  • Expected Result: Fail (Score < 50).
  • Observed Score: 32.6
  • Verdict: ✅ VALID. The new Scan Statistic correctly identified the localized December anomaly, which previous global tests missed.

Scenario F: False Alarm Stress Test (FWER)

  • Setup: We ran 1,000 perfectly fair simulations. In a standard system, ~50 would fail due to random chance (p=0.05).
  • Expected Result: 0 False Positives.
  • Observed Result: 0 False Positives.
  • Verdict: ✅ VALID. The Permutation Test successfully prevented false alarms.

Scenario G: The “Subtle Nudge” (Sensitivity Limit)

  • Setup: We increased the frequency of a single number by just 20% (vs 300% in Scenario B).
  • Expected Result: Monitor (Score 60-80).
  • Observed Score: 73.8
  • Verdict: ✅ VALID. This confirms our system is tuned to ignore minor statistical noise, focusing only on “Meaningful Impact” (Effect Size).

Scenario H: Extreme Pattern (Consecutive)

  • Setup: We forced the machine to pick consecutive numbers (e.g., 1-2-3-4-5) 50% of the time.
  • Expected Result: Fail (Score < 50).
  • Observed Score: 20.0
  • Verdict: ✅ VALID. The system correctly identified the impossible frequency of consecutive patterns.

Scenario J: The “Eddie Tipton” (Sniper Attack)

  • Setup: We simulated the famous “Hot Lotto” fraud, where the RNG was rigged to produce specific numbers on 3 specific days per year.
  • Expected Result: Fail (Score < 60).
  • Observed Score: 54.0
  • Verdict: ✅ DETECTED. The new Collision Test flagged the impossible duplicate draws immediately, triggering a critical penalty.

3. Case Study: The “Hot Bonus” Fix

During our internal auditing of Version 2.0, we discovered a vulnerability. In Scenario C (Hot Bonus), the algorithm originally returned a score of ~79/100.

Why? The Main Drum (5 balls) was perfect. The Temporal stats were perfect. The Patterns were perfect. The only flaw was the Bonus Ball. A simple weighted average allowed the “good” data to dilute the “bad” data.

The Fix (v3.1) We implemented the Component-Based Integrity Check. Now, the algorithm treats the Main Drum and Bonus Drum as critical dependencies. If either fails, the score is capped.

Result: The score for Scenario C dropped from 79.2 (Passing) to 20.0 (Critical Failure). This proves the system can no longer be “gamed” by a lottery that is partially fair but critically flawed.

4. Reproducibility

We believe in open verification. The core statistical libraries used in our analysis are standard, open-source packages:

  • chi-squared: For goodness-of-fit testing.
  • jstat: For distribution analysis.

The simulation parameters described above can be replicated by any researcher to verify our findings.