I was thinking of designing a new die system, too, just for fun. If anyone feels like using this, go right ahead.
XdYdZ: Where Z is the character's skill level, Y is it's equipment bonuses, and X is the energy spent on it.
If 3 energy is gained per turn (And only a maximum of 5 can be stored), and without equipment Y is 1, and can go to 5 with really, really good equipment (generally 3), and finally the skill level ranges from 2 to 8:
The average of the first roll (XdY) should be derived from it's average variables: X should average 2.5, and Y should average 3. We know that the average of 1d3 is 2, 2d3 is 4, etc, so 2.5d3 should be 5. On average, XdY should be 5, though it can range all the way up to 5d5, with an average of 15 and maximum of 25. So, we have (1-5-25)dZ. Since Z ranges from 2 to 8, that average is 5 again. So the average roll should be 15, with some really high rolls on occasion and low ones slightly more commonly.
The equipment roll where no equipment is nessesary or needed (looking to the horizon for ships, general luck, or winning a chess match) should be the average, instead of the minimum: 3. For when Equipment is useful (blocking an attack, making an attack, or pole vaulting), it should start at 1, go to 2 for damaged equipment, 3 for average, 4 for very exceptional, and 5 for legendary equipment.
The difficulty values for actions may vary, but should be around 10. This should make most actions easy. For doubling the difficulty, a critical success should be achieved, and for tripling it an overshot should be produced. Failing is getting above half the difficulty but not reaching it, and fumbling is less than half. Of course opposed rolls exist, where the "difficulty" is your opponent's roll. This makes it so when one succeeds, the other fails - and when one crits, the other fumbles. And vice versa.
Of course, medium difficulty actions (stuff that may actually require skill, like taking apart a computer) that aren't an opposed roll are difficulty 20, a difficult one should be 40, and an impossible one 100; since the highest possible roll is 200, if you save up enough energy for it and maxed out your stat and have the best equipment, it's still possible to critically succeed on an impossible task - if you're extremely lucky.
As I said, feel free to use this if you're feeling gutsy. I actually have no intention of using this system.