# Hellcats Dice Mechanics

In Hellcats & Hockeysticks, you take the highest of a number of d6s, but you also have a choice. You can choose to reduce your dice pool by 3d6 to get a +1 on your end result. This means there is a choice. A simple rule of thumb to follow is this:

• If it's a contest (i.e. you want to get as high possible), don't roll less than 2 dice or more than 4 dice.
• If it's a fixed difficulty, don't roll less than 3 dice or more than 5 dice unless you have to.

In other words, suppose that you have 7 dice. To get the highest roll, you want to change 3 of those for a +1, so you're rolling 4d with +1 result. You don't want to go lower than that, though.

The logic behind this is in the probability distribution, which I include in a table below:

Effective Skill # of dice Chance at Difficulty Avg
456 78
0 1d 50.0% 33.3% 16.7% 0.0% 0.0% 3.50
1 2d 75.0% 55.6% 30.6% 0.0% 0.0% 4.47
2 3d 87.5% 70.4% 42.1% 0.0% 0.0% 4.96
3 4d 93.8% 80.2% 51.8% 0.0% 0.0% 5.24
1d/+1 66.7% 50.0% 33.3% 16.7% 0.0% 4.50
4 5d 96.9% 86.8% 59.8% 0.0% 0.0% 5.43
2d/+1 88.9% 75.0% 55.6% 30.6% 0.0% 5.47
5 6d 98.4% 91.2% 66.5% 0.0% 0.0% 5.56
3d/+1 96.3% 87.5% 70.4% 42.1% 0.0% 5.96
6 7d 99.2% 94.1% 72.1% 0.0% 0.0% 5.65
4d/+1 98.8% 93.8% 80.2% 51.8% 0.0% 6.24
1d/+2 83.3% 66.7% 50.0% 33.3% 16.7% 5.50
7 8d 99.6% 96.1% 76.7% 0.0% 0.0% 5.72
5d/+1 99.6% 96.9% 86.8% 59.8% 0.0% 6.43
2d/+2 97.2% 88.9% 75.0% 55.6% 30.6% 6.47
8 9d 99.8% 97.4% 80.5% 0.0% 0.0% 5.78
6d/+1 99.9% 98.4% 91.2% 66.5% 0.0% 6.56
3d/+2 99.5% 96.3% 87.5% 70.4% 42.1% 6.96

The rule of thumb for fixed difficulty doesn't really work perfectly, but it's close enough for most purposes.

John H. Kim <jhkim-at-darkshire-dot-net>