Random Millionaire for Life Number Generator

// Millionaire for Life number generation algorithm
Algorithm: Dual-Pool Secure Random Sampling with Millionaire Ball

For each ticket:
  1. Main Numbers Selection (5 unique numbers from 1-58):
     - Initialize empty set S for main numbers
     - While |S| < 5:
       - Generate random number n ∈ [1, 58] using CSPRNG
       - If n ∉ S: add n to S
     - Sort S in ascending order (display preference)

  2. Millionaire Ball Selection (1 number from 1-5):
     - Generate random number m ∈ [1, 5] using CSPRNG
     - Millionaire Ball drawn independently (can match main number)
     - Note: 1-5 range gives 20% probability per number

  3. Quality Assurance:
     - Verify exactly 5 main numbers selected
     - Verify all main numbers ∈ [1, 58] and unique
     - Verify Millionaire Ball ∈ [1, 5]
     - Apply Fisher-Yates shuffle to eliminate positional bias

  4. Output Format:
     - Display: "7, 15, 29, 44, 58 + Millionaire Ball: 3"
     - Main numbers sorted in ascending order
     - Millionaire Ball clearly separated with label

Security Properties:
• Uniform Distribution: Each main number [1-58] has exactly 1/58 probability
• Millionaire Ball Distribution: Each Millionaire Ball [1-5] has exactly 1/5 = 20% probability
• Statistical Independence: Each draw is independent of previous draws
• Cryptographic Strength: Uses OS-level entropy sources (e.g., /dev/urandom)
• No Predictability: Impossible to predict future outputs from past results

Probability Analysis:
• Total possible combinations: C(58,5) × 5 = 22,910,580
• Odds of matching all 5 + Millionaire Ball: 1 in 22,910,580
• Odds of matching all 5 numbers: 1 in 4,582,116
• Overall odds of any prize: approximately 1 in 8.47