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. Checks:
     - exactly 5 main numbers, all different, all in [1, 58]
     - Millionaire Ball in [1, 5]

  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
• Source: PHP random_int(), backed by the OS cryptographic RNG

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 5 numbers without the Millionaire Ball: 1 in 5,727,645
• Overall odds of any prize: approximately 1 in 8.47