Advanced Random Number Generator & Entropy Calculator
Generate cryptographically secure tokens, calculate Shannon entropy bits, run uniformity tests, and compute lottery odds
Number of characters
Generated Cryptographic Token
K9#mP2$vL8!qR4*wX7&yZ3%hF6@bN5#jD1
Cryptographically Secure (Web Crypto API)
Shannon Entropy: 194.2 Bits • Brute-Force Space: 2¹⁹⁴
Character Pool Size (N)
74 chars
Available unique symbols
Entropy per Character
6.21 Bits
log₂(N) randomness density
Total Information Entropy
194.2 Bits
Length × Bits-per-char
Estimated Crack Time (10¹² guesses/sec)
7.4 × 10³⁷ Years
Computationally immutable
Number of integers drawn
Number of discrete integer bins
Chi-Square Test for Randomness (χ²)
χ² = 3.420 (p = 0.490)
Uniform Distribution Confirmed (Pass)
Degrees of Freedom: 4 • No significant bias detected
Bucket (Value)
Observed Count (O)
Expected Count (E)
Deviation (O – E)² / E
e.g., 69 white balls (Powerball)
e.g., 5 numbers drawn
Drawn Quick-Pick Combination
[12, 28, 41, 55, 63]
Exact Combinatorial Odds
Total Combination Combinations C(n, k): 11,238,513
Winning Probability P(E)
1 in 11,238,513
8.899 × 10⁻⁸ probability
Total Combinations C(n, k)
11,238,513
Unordered subset space
Permutations P(n, k)
1,348,621,560
Ordered sequence space
Expected Value Metric
Fair Game Analysis
Evaluates combinatorial odds