## Posts

Showing posts from June, 2017

### A hypercube full of rooms

While I'm on the subject of Dungeons & Dragons (see my previous post on ability score probabilities), I recall something I did involving a tesseract way back in 2007 and posted on the community forum of Wizards of the Coast. WOTC took down their forum in 2015, but fortunately the Wayback Machine has an archived copy. Imagine a cubical room. It has four walls, a ceiling, and a floor (six faces). Each face has a door or opening, to allow you to pass through to the next room. Each cubical room connects to six other rooms — but there are eight rooms interconnected this way.This isn't possible to draw in 3 dimensions without distorting some of the rooms. Imagine a central room with a room connected to each face. So you have the center room, the north, south, east, and west rooms, and the top and bottom rooms. That takes care of seven rooms. The eighth room, we'll call it the "outer" room, is connected to those six rooms surrounding the center. Designating the room…

### Most probable array of D&D ability scores

There's an element to the game Dungeons & Dragons that lends itself to a numerical analysis: the initial array of ability scores assigned to a character. Some background: A character in the game has scores assigned to each of six abilities (strength, dexterity, constitution, intelligence, wisdom, and charisma). The first step in creating a character is to generate an array of six numbers by rolling dice, using a method known as "4d6 drop lowest". This means, roll four six-sided dice, remove the lowest value, then add the remaining three dice together (the result ranges from 3 to 18). Do this six times to generate an array of six values, then assign these values to your character's abilities as appropriate for the character's role (fighter, cleric, wizard, etc.).The problemThe question I want to answer here is: What does a "typical" array look like? More importantly, how would I know if the array I end up with is better or worse than average?Each res…