Random Number Generator

Random number generation: Random Integer in [min, max]: random = Math.floor(min + (max - min + 1) × random_float) Where random_float is uniform random in [0, 1) Random Decimal in [min, max]: random = min + (max - min) × random_float Then round to specified decimal places Example: random integer 1-100. Math.random() returns 0.0 to 0.999... × 100 → 0.0 to 99.999... + 1 → 1.0 to 100.999... Math.floor → 1 to 100 ✓ Example: random decimal 0.0-1.0 with 2 decimal places. Math.random() returns 0.0 to 0.999... No multiplication needed Round to 2 decimal: 0.00 to 1.00 Properties of good pseudorandom generators: Uniformity: each value equally likely Independence: no autocorrelation between consecutive values Long period: doesn't repeat for extremely long time Speed: generates fast Reproducibility (when seeded): same seed produces same sequence JavaScript Math.random(): - Implementation varies by browser - Modern browsers use Xorshift128+ or similar (2^128 period) - Suitable for games, testing, simulations - NOT suitable for cryptography, security tokens, password generation For cryptographic randomness, use crypto.getRandomValues() (browser) or platform-specific cryptographic random sources. Random selection from a list: To pick random item from N items: random_index = Math.floor(Math.random() × N) // 0 to N-1 For weighted random selection (some items more likely): Sum weights, random in [0, total weight) Find item where cumulative weight first exceeds random Each item's probability = its weight / total weight For non-replacement (lottery, drawing): Generate random, exclude from future selections Or shuffle entire list and take first N Common applications: Daily decisions: Pick a restaurant from list: random integer 1-N indexes Choose a task to start: random selection from task list Games: Item drop in video game: random 1-100, compare to drop rate Random encounter: random 1-100, compare to threshold Damage rolls: random with modifier Testing: Generate random input data Stress test system with random load patterns Monte Carlo simulations Sampling: Random selection from population Statistical sampling for research Quality control sampling Random numbers in different ranges: For 0-1 (probability): use directly, often used for chance comparison Example: 30% chance event → if Math.random() < 0.30 { event happens } For 1-100 (percentage): random 1-100 Compare to thresholds: 1-30 = 30% chance, 31-70 = 40%, 71-100 = 30% For arbitrary range [a, b]: scale and shift random = a + (b - a) × Math.random() For integers: Math.floor(a + (b - a + 1) × Math.random()) For mean and standard deviation: Box-Muller transform converts uniform random to normal distribution Useful for simulating real-world phenomena (heights, test scores, etc.) True randomness vs. pseudorandom: True random sources: Atmospheric noise (random.org) Radioactive decay Quantum random number generators (QRNG) Thermal noise in electronics Lava lamps (Cloudflare's famous setup) Pseudorandom (PRNG): Mathematical algorithms Deterministic given seed Fast and reproducible Suitable for most applications When to use true randomness: - Cryptographic keys - Password generation for security - Casino regulatory compliance - High-stakes lotteries - Scientific research requiring rigorous randomness When pseudorandom is sufficient: - Game development (most games) - Statistical sampling (typically) - Monte Carlo simulations - Testing - Everyday randomization Reproducibility: PRNG seeded with same value produces identical sequence. Useful for: - Reproducible scientific simulations - Game replays (same seed → same random events) - Debugging (reproduce specific random scenario) - Testing with controlled randomness This calculator regenerates new numbers each time. For reproducibility, would need user-specified seed.