I was once again thinking about how one might add more of a bell curve to a d20 system, and specifically the problems associated with doing so for 13th Age. I often mentally reference two articles from the Gaming Security Agency when I'm thinking such thoughts - Die, d20 die! and Extreme Makeover, d20ish Edition. If these sound familiar, it's because I referenced them in a previous post about revising d20, a post that specifically addressed the problems associated with increasing the maximum value via large modifiers, especially in Pathfinder where such modifiers get really out of hand (and where skills you don't invest resources into don't automatically advance, increasing the "skill disparity" even more as you level).
While the comments of that post did touch on whether or not this is as much of a problem in 13th Age (compared with Pathfinder, it's not), there's still a lot to be said for trading in the uniform distribution of a d20 for the bell curve of 2d10. But in 13th Age this makes characters with flexible attacks, like Fighters and Bards, problematic. Even if you don't have those classes in your game, the GM will still have to worry about this issue since most monsters have triggers based on the natural result of the d20 roll. So how can you get around this?
The solution I came up with (which is very much theoretical) requires differentiated d10s. Different color dice will work, but considering that your standard set of dice already includes differentiated d10s to be used as percentile dice, it's not much of an issue. You designate one d10 as the primary die, and the other as the secondary. The primary die alone can handle a lot of the more common natural die roll triggers. A natural even or odd result works just fine with the same probability as a d20 roll. But what about a natural 16+, which has a 25% chance of occurring on a d20 roll? Or for that matter, critical hits that normally have a 5% chance of triggering (usually on a natural 20)? Critical hits are important for some classes, like Fighters (most of which pick up Carve an Opening since it's a rare odd-roll trigger) and Rangers.
I think a viable solution for such scenarios that would preserve their relative probabilities would be to combine the result on the primary d10 with a high/low (coin flip) on the secondary die. In other words, a result of 10 on the primary die would count as a natural 20 if the secondary die is 6 or greater, or a 19 if the secondary die is less than 6. A natural 9 would count as an 18 if the secondary die is greater than 6, and so on. Of course the secondary die doesn't necessarily have to use a high/low dichotomy (evens or odds would work just fine, too).
To use another example, a natural 16+ would include a natural 9 or 10 on the primary die, but also a natural 8 if the secondary die is "high." Therefore while you're totaling 2d10 for the purposes of determining success/failure, any given roll can also generate natural result triggers in 5% increments just like a d20 roll. Granted it's not the most elegant or intuitive fix, but for those who dislike the probability of a d20 roll and would prefer a dice pool mechanic to get more of a bell curve, it might be a tradeoff worth making without changing how specific options in the system work.
The GSA articles also suggest adding dice to your pool instead of piling on static modifiers, keeping the highest 2 results for your total. This results in skilled characters tending to get results at the high end of the distribution and getting fewer low results (the bell curve shifts to the right), but without increasing their maximum results. In other words, skilled characters succeed more reliably than unskilled characters, but don't hit DCs that are unreachable for unskilled characters. One possible way to integrate this into the 13th Age background system while still allowing some flexibility when designing backgrounds would be to assign each character 4 background dice. While this results in less granularity than 8 background points distributed as you see fit, most PCs typically have between 4 and 2 unique backgrounds, with 3 being quite common. Having 4 background dice allows you to have 4 single-die backgrounds, 2 backgrounds that would add 2d10 to your pool (again, keeping only the highest 2 results to total), or 1 background with 2 dice and 2 backgrounds with 1 die. This roughly parallels having four 2 point backgrounds, two 4 point backgrounds, or three backgrounds with two at 3 points and one at 2 points (odd that a 3 background character will have 1 good background with the dice pool system vs 2 good backgrounds with the point system, but it's not a deal breaker). Further Backgrounding would give you 1 background die (as would any talent or other ability that grants you 2 background points), while the higher-valued background talents like the Ranger's "Tracker" would give you a 2d10 background.
Obviously once you start rolling more than 2d10 it becomes a lot tougher to model the natural d20 result triggers, but such triggers don't come up on skill checks. If for some reason you were to add one or more dice to an attack roll that has triggers, you'd simply need to complicate things a little more. You'd need 3 or 4 unique, individually identifiable d10s and you'd need to rank them. Then whichever two dice came up with the highest result, you'd use the higher-ranked die as the primary and the lower one as the secondary. For example, I have a light blue percentile set and a dark blue percentile set, so the dark 10s die could be ranked highest, and then in descending order would be the dark 1s die, the light 10s die, and light 1s die. For "roll twice" effects like Barbarian Rage I'd simply keep the two light dice together as equivalent to one d20 roll, and the two dark dice as the second roll.