How To Use Anydice

How to Use AnyDice: A Comprehensive Guide for Dice Roll Simulation

AnyDice is a powerful free online tool that allows you to simulate dice rolls and analyze probability distributions. Whether you're a tabletop game designer, a mathematician exploring probability, or simply curious about the odds of rolling a specific combination, AnyDice can help you. This guide will walk you through the basics and some more advanced techniques.

Understanding AnyDice's Syntax

AnyDice uses a unique programming language based on descriptive dice notation. The core concept revolves around defining dice and then performing operations on them.

Defining Dice

• Simple Dice: The most basic form is d<number>, representing a single die with <number> sides. For example, d6 is a six-sided die, d20 is a twenty-sided die.

• Multiple Dice: To simulate rolling multiple dice, simply use the number before the d. 3d6 represents rolling three six-sided dice.

• Custom Dice: You can create dice with arbitrary sides using curly braces {}. For example, {1, 2, 2, 3, 3, 3} creates a die with sides 1, 2 (twice), 3 (thrice). This is useful for simulating dice with unusual distributions.

Dice Operations

• Addition: Use the + operator to add dice rolls. 2d6 + 1 simulates rolling two six-sided dice and adding 1 to the total.

• Subtraction: Use the - operator for subtraction. d20 - 5 subtracts 5 from a d20 roll.

• Multiplication: Use the * operator for multiplication. 2 * d6 doubles the result of a six-sided die roll.

• Output Modifiers: AnyDice provides various functions to analyze the results. output displays the results, while output [sum of 3d6] specifies you want the sum of three six-sided dice.

Example Programs

Let's look at some practical examples:

Example 1: Simulating a Single d20 Roll

output d20

This simple program simulates a single roll of a twenty-sided die and displays the probability distribution of each outcome.

Example 2: Calculating the Average of 3d6

output [sum of 3d6]

This will show you the probability distribution of the sum of three six-sided dice. Notice the use of square brackets [] which calculate the sum before displaying the distribution.

Example 3: Comparing Two Dice Pools

Let's say you want to compare the odds of rolling higher with 3d6 versus 2d8.

output 3d6 > 2d8

This will give you the probability that the sum of 3d6 is greater than the sum of 2d8.

Example 4: Custom Dice & Conditional Logic

This example shows the use of custom dice and a conditional statement to calculate the probability of exceeding a threshold:

DICE: {1, 2, 2, 3, 3, 3}
output [if DICE > 2 {1} else {0}]

This code defines a custom die and checks if a roll exceeds 2, assigning 1 for success and 0 for failure.

Advanced Techniques

AnyDice supports loops, functions, and more advanced probability analysis. Explore the AnyDice documentation for a deeper dive into its capabilities. Remember to use descriptive variable names to make your code easier to understand.

Tips for Effective Use

• Start Simple: Begin with basic programs to understand the syntax. Gradually increase the complexity.
• Read the Documentation: The AnyDice documentation is a valuable resource for learning advanced features.
• Experiment: Try different programs and explore how different dice combinations affect probability distributions.
• Break Down Complex Problems: Divide complex simulations into smaller, manageable parts.

By mastering AnyDice, you can greatly enhance your understanding of probability and design more balanced and engaging games. Remember, practice makes perfect!