Science collection
Random number generators
Inspect sources, seeds and algorithms. Learn how unbiased bounded integers become valid selections.
Start with Random Number Generators: From Entropy to a Fair Choice, then follow the questions below. Each guide includes a worked explanation, a figure and routes to an experiment or calculator.
Random number generators
Random Number Generators: From Entropy to a Fair Choice
Understand how random number generators combine a source, an algorithm and a mapping—and why each stage matters for fair lottery selections.
3 min read · Formula & figureRandom number generators
Cryptographically Secure Random Numbers: What the Claim Means
Learn why CSPRNGs concern unpredictability, why Math.random is different, and why a secure source still needs unbiased range conversion.
3 min read · Formula & figureRandom number generators
How RoomForChance Generates Random Numbers: An Inspectable Method
An implementation-level explanation of RoomForChance’s browser random source, rejection sampling, partial shuffle and separate simulation methodology.
3 min read · Formula & figureRandom number generators
How to Generate Random Numbers Without Repetition
Learn two fair methods for distinct random numbers, why sorting is safe, and why filtering patterns changes the distribution.
3 min read · Formula & figureRandom number generators
Modulo Bias Explained: Why a Random Byte Makes an Unfair Die
See the exact 256-to-6 mapping behind modulo bias, calculate the imbalance, and understand how rejection sampling removes it.
3 min read · Formula & figureRandom number generators
Rejection Sampling: How Discarding Values Can Preserve Fairness
A practical derivation of rejection sampling for integer ranges and distinct lottery numbers, with efficiency and failure cases explained.
3 min read · Formula & figureRandom number generators
True Random vs Pseudorandom: Which Difference Matters?
Compare physical entropy and deterministic random streams without confusing reproducibility, statistical quality and cryptographic security.
3 min read · Formula & figureRandom number generators
What Is a Random Seed? Reproducing an Experiment Correctly
A random seed is only part of a reproducible simulation. Learn why the algorithm, versions and sequence of calls must also be recorded.
3 min read · Formula & figure