The old thread got deleted accidentally, but here's the crucial element
This is a chart of the probability that the difference between two dice rolls will meet or exceed the listed number. Each dice roll is a 2d6*, or 2d6 upwardly-open pair.
How to use the chart: An example.
What is the probability that a light infantry (att=10) will hit a soulless (def=2, after applying the "fist" penalty)? The difference is (2-10) = -8, but hitting requires you to beat, not just meet, the enemy defense roll. So the roll difference must be at least (2-10)+1 = -7. Looking at the "-7+" row, you see that a light infantry has an 91.8% chance of hitting a soulless.
The reverse case:
Soulless has att=3 after applying the fist -1 att penalty, and a light infantry has def=12. So for a soulless to hit, it must score a differential roll of (12-3)+1 = 10. Looking at the "10+" row, a soulless has a 4.6% chance of striking a light infantry.
The chart can also be used for damage versus protection rolls, poison rolls, and probably morale and magic resist rolls. Almost all Dominions dice rolls seem to be of the form ((2d6* + attacker's modifier) - (2d6* + defender's modifier)), which this chart describes.
Testing (2d6*, labelled 0-5, offset=2) over 200000000 rolls.
Reverse-Cumulative Difference Statistics:
-30+: 99.994%
-29+: 99.992%
-28+: 99.988%
-27+: 99.984%
-26+: 99.978%
-25+: 99.969%
-24+: 99.957%
-23+: 99.941%
-22+: 99.918%
-21+: 99.887%
-20+: 99.844%
-19+: 99.785%
-18+: 99.705%
-17+: 99.596%
-16+: 99.447%
-15+: 99.244%
-14+: 98.969%
-13+: 98.601%
-12+: 98.106%
-11+: 97.442%
-10+: 96.554%
-9+: 95.373%
-8+: 93.822%
-7+: 91.805%
-6+: 89.194%
-5+: 85.852%
-4+: 81.605%
-3+: 76.281%
-2+: 69.830%
-1+: 62.391%
0+: 54.222%
1+: 45.773%
2+: 37.605%
3+: 30.165%
4+: 23.714%
5+: 18.388%
6+: 14.145%
7+: 10.802%
8+: 8.191%
9+: 6.174%
10+: 4.624%
11+: 3.444%
12+: 2.556%
13+: 1.894%
14+: 1.399%
15+: 1.031%
16+: 0.755%
17+: 0.553%
18+: 0.404%
19+: 0.295%
20+: 0.215%
21+: 0.156%
22+: 0.113%
23+: 0.082%
24+: 0.060%
25+: 0.043%
26+: 0.031%
27+: 0.023%
28+: 0.016%
29+: 0.012%
30+: 0.008%
-Cherry