The math behind exploding dice rolls
2021/09/19 - Exploding dice is an exciting mechanic that allows a player to reroll any dice that lands on its maximum adding the new roll to the max. In this post, we dig into the math behind that fun system.
Rolling for stats in practice: how bad luck protection inflates ability scores
2021/07/17 - Rolling for stats in DnD 5e always carries the risk of creating a weak character. Many tables offer a player the chance to reroll if bad luck strikes. We show that offering the possibility of a reroll inflates a character's expected stats.
Group checks depend too much on whether you have an odd or even number of players - here's a proposed fix
2021/04/22 - Making group checks requires awkwardly deciding on how to round the required number of successes. Either choice is bad. Here we propose a rule that uses randomization to compromise and give more reasonable results.
Calculating attack damage in DnD 5e
2021/03/29 - A common task when analyzing character builds or theorycrafting in Dungeons and Dragons is mathematically exploring the damage output of various spells and abilities. In this post, we show how to calculate the probability distribution of damage from an attack.
How bad is rolling for health in DnD 5e?
2021/03/08 - DnD 5e provides two rules for gaining health when leveling up: roll for it or take a fixed value. The fixed value is better on average, but by how much?
Deriving the probability distribution for the sum of many dice rolls
2021/02/20 - Rolling one or two dice is simple. Rolling a whole handful is not. In this post, we derive the probability distribution that describes the sum of many dice.
How much is advantage really worth?
2021/02/13 - An often repeated rule of thumb is that advantage is similar to a +5 bonus. How accurate is this? Let's find out.
Expectations and variances of dice rolls
2021/02/07 - "What do I expect?" is a natural question to ask when rolling a dice. Here we dive into expectations and variances of dice rolls and discuss what they help us understand and where they lead us astray.
Some helpful rules of thumb about Advantage and Disadvantage
2021/02/01 - Advantage and Disadvantage significantly change the outcome of dice rolls. Here we state some practical tips that can help us when using these mechanics.
A derivation of the Advantage/Disadvantage probability distributions
2021/01/25 - A derivation of the Advantage/Disadvantage probability distributions and exploration into their properties