My weekend D&D group has a different way of rolling attributes for characters, and it’s probability has been bothering me mathematically for a couple of weeks now. First, I should show how the regular rolls work for comparison.

Normally when you create a D&D character, you roll 3 six-sided dice (also known as 3d6) and add them up to get a total. You do this 6 times and apply each totaled value to one of six character attributes.

A higher character attribute is better. 10 is average, while 18 is the best you can roll. Anything below a 9 is below-average for a human, so a character with an intelligence of 6 isn’t so great.

The numbers in each attribute are used to determine attribute bonuses. Attribute bonuses are used inthe game to affect certain skills. For example, a character with an Intelligence rating of 18 receives a bonus of +4 to all skills related to intelligence. A character with a Strength of 18 receives a bonus of +4 to all melee attacks and to damage. This factors into the game significantly.

For every two points in an attribute, the bonus changes by one. A single bonus point is an effective 5% bump in chance to succeed. So a character with a Strength of 18 has a 5% better chance of hitting a creature than a character with a Strength of 16, and the stronger character also does at least one more point of damage when he hits.

Ok, so now I will describe our in-house rolling system, and you can see how horribly broken it is.

The extra little bit that we’ve added is to re-roll 1s and 2s. So if you rolled 1-2-3-4, you would roll those two dice again until they were not a 1 or a 2. The possible range of the roll is now from 9 to 18, since you can’t roll 1s or 2s to bring the total lower. See what’s going on here?

Essentially, that reduces the number of possible roll combinations to 256. 7 in every 20 rolls will result in an attribute bonus of +3 or higher - that’s 35% of all rolls, meaning two of your six attributes will have +3 or greater bonuses. 72% of all rolls will result in at least a +2 bonus. So with this rolling method, you’ve basically got a character that is usually at least 10% better at every skill than the baseline, and probably 15%-20% better at what he specializes in than an average character specializing in the same thing. Statistically it’s extremely improbable (1 in 24 million rolls) that your character will have a +0 in all attributes - an average character.

Now when you factor in that all monsters challenge ratings are based on being fought by a party of average characters, you start to see real cracks in this rolling method. Mind that it’s not even just one character having a 10% advantage, it’s a whole party of superior characters.

The solution is certainly not to employ more difficult monsters or adjust challenge ratings. The solution is to use a normal method for rolling attributes that celebrates extraordinary character abilities. Alternatively, setting character attributes diretly based on a point system would also work. I would suggest starting all six character attributes at 8, and then letting players allocate 14 points to any attributes they choose.