## Sunday, November 12, 2017

### Giant Hit Points

To get the hit points of a monster with a lot of hit dice, you have to roll the d8—or d6 if playing the old way—repeatedly and add them up.

This is similar to rolling fireball damage. An earlier post shows how to approximate the results of fireball damage using just two d6 rolls. The goal in the earlier post was to reduce the amount of calculation while preserving the original distribution.

The same could be done for hit dice. But do we want to preserve the original distribution? As noted in the previous post the result will usually be within 5 hit points of the mean. If a more uniform distribution is desired, we could replace an nd8 roll with an (n-1)×d8 + d8 roll.

Here are the distributions for a hill giant using 8d8 and 7×d8+d8:

A few values: 15, 22, 29, 36, 43, 50, and 57, are twice as likely as the others. If we were using 8×d8+d8 to roll hit points for a stone giant the distribution would be perfectly uniform.

When n is greater than 9, some values have a probability of zero. We could use an (n–2)×d8+2d8 roll so that all values are still possible, at least as long as n isn't greater than 17. Here is a comparison of using 15d8 and 13×d8+2d8 for storm giant hit points:
You might ask how hit points are distributed in the old modules. Let's take a look at the adult male hill giants in the steading:

Also see an earlier post for the distribution of goblin hit points in Little Keep on the Borderlands.