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Is Advantage or Skill Better?

A Dungeons and Dragons Math Puzzle

I love tabletop roleplaying games! They are a fun combination of board games, acting, and hanging out with friends. In this article, I’m going to give a simple probability math puzzle based on a common situation that comes up in Dungeons and Dragons, my personal favorite ruleset.

In Dungeons and Dragons, you are frequently rolling a 20-sided die to determine how well you do in an action. Each side of the die is a number 1 through 20. This check could be for anything from attacking a monster, jumping over a chasm, haggling for lower prices, or dodging a boulder. Players have two main ways to improve their rolls.

Modifiers add a fixed value to a roll, so you roll the 20-sided die (denoted as d20), then add that value. They usually represent the character’s innate ability. For example, a character that is physically strong might have a modifier of +3 to strength rolls, while a frail character could have a modifier of -1. Modifiers are always integers. We write this symbolically as follows:

Advantage has you roll two 20-sided dice and use the higher value. This is used to represent situational advantages. For example, if you are trying to hit a monster that is currently stunned, you would get advantage on that roll. In contrast, Disadvantage takes the lower of the…