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:
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 | ||||
|---|---|---|---|---|---|---|---|
| 4 | 5 | 6 | 7 | 8 | |||
| 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.