I've done something similar, 1d20 + Ability score, target 20+ yields success, 30+ great success. Way back in the day, we used 4d6 < Ability for checks, 3d6 for easy and 5d6 for hard. Your thoughts are interesting with a high but not over roll. Thanks for the idea!
- Ability checks (including what are in 5e skills, tools, etc) are NOT 1d20 higher is better. Instead you want to roll as high as possible while still not exceeding the ability score you are checking against. [not necessarily 1d20, either.]
I like this combination! Once you suss out the AC, you can figure out if you need to take extra care with your technique (first), or just wollop them to ring their bell (second).
- After rolling to hit, but before you know the result, you can add your battle die to that attack roll.
- When you miss with an attack, you can deal your battle die in damage to one target.
Level Up: When you finish a level of fighter (i.e., if the class you took most recently upon leveling up was fighter), you can choose one of the following options, with an ability score needing 10 advancement points to increase one full point:
- Your Str, Dex, or Con gains 1d6 advancement points.
- Another ability score of your choice gains 1d4 advancement points.