Probability is a field of mathematics that sees extensive use outside of academics. Whether one’s checking the likelihood of rain on a weather app or the odds of winning the lottery, probability is everywhere. My favorite application of probability is dice games like Dungeons and Dragons. The game can be played very simply (choose to attack a monster, roll a 20-sided-die, try to exceed a certain number) or with a complexity that rivals high school math courses. There are spells and abilities that modify one’s dice rolls, such as adding additional rolls to the total or rerolling the die and using the higher result. A good player regularly asks themself when to activate certain buffs and how likely they are to succeed with or without them.
All of these questions boil down to the basics of probability. Things that one learns in an introductory statistics course extend into countless applications. Currently, I’m adding some of that knowledge to the Maple Learn document gallery, and I’m here to give a sneak peek.
First, I’ve built tree diagrams in Maple Learn. Tree diagrams are a way to map probability across multiple events occurring in sequence. Each branching path represents a series of events that have a specified probability of occurring.
Here’s an example: one morning I flip a coin to decide if I buy a lottery ticket. If it’s heads, I do. If I buy the ticket, I have a one in a million chance of winning the cash prize. Drawn as a tree diagram…
I drew this using Maple Learn line, point, and label operations.
My new D&D-themed documents are a bit more exciting. In the first, we explore a tree diagram with variable probabilities. A brave hero makes their way into a dungeon, attacking any random monster they see. How likely are they to land an attack? Adjust the details of the question and watch the diagram change.
In the second, I used Maple program scripting to add a live randomized dice roller. Many probability techniques are at play to analyze which of two buffs will do more good for a dice-rolling adventurer.
I plan on making more documents like these; keep your eyes on the Document Gallery probability collection for updates.