Not the most exciting subject possible, but bear with me.
Barring any major change in my attitudes between now and probably mid next-week when the basic rules are written in their semi-permanent form, ONI PUNCHER is going to be resolved in a roll-over with 2d6 type way.
Couple of big reasons:
1) 2d6 has a brief and easy-to-comprehend bell curve on it. It's extremely predictable, and helps granularity around the middle while reducing it at the ends. Let's say that the average number you're aiming for is 7 or higher (because it is, by default in ONI PUNCHER). With no bonus, you have a 58% chance of succeeding. If you have a +1 bonus, your chance jumps to 77%. With a +2 bonus, your chance is at 83%. +3 is the mighty 91%. It's actually more likely for you to succeed than to fail. And I like that. I like that a lot! It gives me some design wiggle room and lets me keep mental math to a minimum while still keeping the world in a "human scale". I'll explain what I mean by that later.
2) Everybody has 2d6- bust open your Monopoly game, or run down to the grocery store and pick some up, right next to the packs of cards. You don't have to look around for weird dice or anything. Plus, you can use those little bitty wargaming dice that I love so much.
3) Small bonuses have weight and large bonuses are relatively less useful. Your +1 rocks, and the fact that an Oni could have +5 might doesn't mean that you'll necessarily lose in an arm-wrestling contest, since the highest result you can get is 12. If you roll a 12 and he rolls a 7, you win, because natural 12s always win. Congratulations- it's now possible for you to do the impossible.
4) I don't know where the rest of my dice are right now (WHOOPSIE).
5) I like rolling boxes.