Random Number Generator

Random Number Generator (RNG) is a tool that produces numbers where no pattern is predictable. Each number has an equal probability of being selected within the specified range.

Types of Randomness

True Random:

• Based on unpredictable physical phenomena
• Atmospheric noise, radioactive decay, thermal noise
• Completely unpredictable
• Used for cryptography and security

Pseudo-Random:

• Generated by computer algorithms
• Deterministic but appears random
• Sufficient for most applications
• Repeats eventually (very long cycle)

Why Use a Random Number Generator?

• Games & Contests: Fair winner selection
• Statistics: Random sampling
• Decision Making: Unbiased choices
• Simulations: Monte Carlo methods
• Cryptography: Security and encryption
• Education: Teaching probability and statistics
• Lotteries & Raffles: Random draws

Pseudo-Random Number Generators (PRNG)

Common Algorithms:

Linear Congruential Generator:

X(n+1) = (a × X(n) + c) mod m

• Fast and simple
• Not suitable for cryptography
• Used in basic applications

Mersenne Twister:

• Very long period (2^19937-1)
• High-quality randomness
• Default in many programming languages
• Not suitable for cryptography

Cryptographically Secure PRNG:

• Based on cryptographic algorithms
• Unpredictable output
• Used for security applications
• Slower but more secure

Seeding

What is a Seed?

• Starting value for PRNG
• Same seed = same sequence
• Different seed = different sequence

Common Seeds:

• System time (most common)
• User input
• Hardware entropy
• Atmospheric noise

Example:

Integers (Whole Numbers)

Definition:

• Numbers without fractional parts
• Can be positive or negative
• Example: -5, 0, 42, 100

Common Uses:

• Dice rolls (1-6)
• Card draws (1-52)
• Random selection from list
• Lottery numbers

Example:

Decimals (Floating-Point)

Definition:

• Numbers with fractional parts
• Can specify decimal precision
• Example: 3.14, -2.5, 0.001

Common Uses:

• Scientific measurements
• Financial calculations
• Statistical sampling
• Simulations

Example:

Sequences

Unique Numbers (No Repeats):

• Each number appears only once
• Useful for sampling without replacement
• Limited by range size

With Duplicates (Repeats Allowed):

• Numbers can repeat
• Independent selections
• No limit on quantity

Example Comparison:

Dice & Games

Standard 6-Sided Die:

Multiple Dice:

RPG Dice:

• d4: Range 1-4
• d8: Range 1-8
• d10: Range 1-10
• d12: Range 1-12
• d20: Range 1-20
• d100: Range 1-100

Card Draws

Standard Deck (52 cards):

Example:

Random Selection

From a List:

1. Number list items 1 to N
2. Generate random number: 1 to N
3. Select corresponding item

Example:

Multiple Selections:

Lottery Numbers

Powerball-Style:

Statistical Sampling

Simple Random Sample:

Common Ranges

0-1:

• Probability calculations
• Percentages (0% to 100%)
• Normalized values

1-6:

• Dice rolls
• Simple games
• Quick decisions

1-10:

• Rating scales
• Quick decisions
• Simple selections

1-100:

• Percentages
• Temperature (Celsius)
• Common measurements

1-1000:

• Larger ranges
• More variety
• Fine granularity

Negative Numbers

Including Negative Values:

Applications:

• Temperature (Fahrenheit)
• Coordinates
• Mathematical operations
• Financial (profit/loss)

What Makes a Good RNG?

Characteristics:

• Uniformity: Each number has equal probability
• Unpredictability: Can't guess next number
• Long Period: Doesn't repeat quickly
• Speed: Generates numbers quickly
• Reproducibility: Can reproduce sequence with same seed

Testing Randomness

Visual Tests:

• Scatter plots should show uniform distribution
• No visible patterns
• Fills range evenly

Statistical Tests:

• Chi-square test
• Kolmogorov-Smirnov test
• Runs test
• Autocorrelation test

Fairness in Games

Ensuring Fair Play:

• Use cryptographically secure RNG
• Prevent manipulation
• Document RNG method
• Allow verification if possible

Example (Online Casino):

• Provably fair systems
• Published algorithms
• Third-party auditing
• Player verification

Sorting Results

Ascending Order:

Descending Order:

Use Cases:

• Ranked selections
• Organized lists
• Easier analysis

Filtering

Even Numbers Only:

Odd Numbers Only:

Multiples of N:

Custom Distributions

Non-Uniform Distributions:

Normal Distribution (Bell Curve):

Weighted Random:

When to Use Cryptographically Secure RNG

Use Cases:

• Password generation
• Encryption keys
• Security tokens
• Authentication codes
• Financial transactions

Not Necessary For:

• Games and entertainment
• Statistical sampling
• Simulations
• Random selections (non-security)

Preventing Manipulation

Client-Side Generation:

• Runs in user's browser
• Server doesn't know results
• User can verify fairness

Server-Side Generation:

• Controlled by service provider
• Can be audited
• Prevents client manipulation

Best Practice:

• Document RNG method
• Use proven algorithms
• Allow third-party verification
• Implement safeguards

Example 1: Dice Roll Simulation

Settings:

• Type: Integer
• Range: 1 to 6
• Quantity: 3
• Allow duplicates: Yes

Generated:

Interpretation: Rolled 4, 2, and 5 on three dice

Example 2: Random Sample

Settings:

• Type: Integer
• Range: 1 to 100
• Quantity: 10
• Unique only: Yes
• Sort: Yes

Generated:

Use Case: Select 10 random items from 100