So, the previous post on converting ACKS' d20 X+ to a X:12 system as ASSH does got me thinking about pixelization and resolution of an image.
When you reduce an image, the math is done to convey as much of the previous information as possible in a smaller space. Converting those rolls from X+ on a d20 to X:12 on a d12 is somewhat similar - you're looking to convey the same general chance of success in a smaller space.
So let's take this all the way down.
Starting from 20, I go down the steps of the default dice, down to 2.
The last column, after the d2, is extra. It's the difference in percentage chance from the original d20 roll to d2. I had one of those for each number as I worked my way down. I wanted to get as close as possible to the d20's percentage for each choice, whether that be higher or lower - there's more than a few spots on this table where I could have used one or the other number, and the only difference was one was -1.666% and one was 1.666%, for example. I ought to have paid more attention to the delta, and will probably do that in the next iteration of this table.
If I'm looking for a 14+ proficiency throw in ACKS, then, I'll want that to be a 4:12 for a d12, 3 in 8 on a d8, 2 in 6 on a d6, 1 in 4 on a d4, and 1 in 2 on a d2.
Obviously, some things will convert better than others, but that's the nature of pixelization. An 18+ throw in ACKS at 15% goes up to 50% on a d2 - you've got to have *some* chance, and you've only got 2 numbers to convey it in.
I think next I'll start at d100 and work my way down through the DCC dice to d2.