Dominions Random Number (DRN)
Most skill checks use a Dominions Random Number, or a DRN. This includes virtually all Damage rolls, Attack rolls, Missile Hit rolls, and so on.
The DRN is two six-sided dice. A lower-case "drn" is one six-sided die. Any dice roll described as an "XdY" (i.e. 1d4) without saying it's open-ended is closed.
What makes this different from regular six-sided dice rolls? Well, Dominions Random Number dice explode; if you roll a 6, you make it a 5, and then you roll that die again. The extra roll is added to your total. You continue to roll until you stop rolling 6's. This is called an "open-ended" roll in-game, while regular rolls are known as "not open-ended" or "closed".
Understanding the DRN
Due to how the DRN works, there are few skill checks that are utter guarantees, and determining what the result of a roll will be is even more difficult.
drn Math (One Die)
You could zoom in on the odds of an open-ended six-sided die's results an infinite number of times, but let's just say you only expand twice at most:
Out of 216 Closed Rolls…
- 36 will be 1's (16.67%)
- 36 will be 2's (16.67%)
- 36 will be 3's (16.67%)
- 36 will be 4's (16.67%)
- 36 will be 5's (16.67%)
- 36 will be 6's (16.67%)
Average: 3.5
Out of 216 Open Rolls…
- 36 will be 1's (16.67%)
- 36 will be 2's (16.67%)
- 36 will be 3's (16.67%)
- 36 will be 4's (16.67%)
- 36 will be 5's (16.67%)
- 6 will be 6's (2.778%)
- 6 will be 7's (2.778%)
- 6 will be 8's (2.778%)
- 6 will be 9's (2.778%)
- 6 will be 10's (2.778%)
- 1 will be an 11 (0.463%)
- 1 will be a 12 (0.463%)
- 1 will be a 13 (0.463%)
- 1 will be a 14 (0.463%)
- 1 will be a 15 (0.463%)
- 1 will be at least 16 (0.463%)
Average: 3.930 (if the 16+ roll is ignored; ~4 otherwise)
DRN Math (Two Dice)
Out of 1296 Closed Rolls…
- 36 will be 2's (2.778%)
- 72 will be 3's (5.556%)
- 108 will be 4's (8.333%)
- 144 will be 5's (11.11%)
- 180 will be 6's (13.89%)
- 216 will be 7's (16.67%)
- 180 will be 8's (13.89%)
- 144 will be 9's (11.11%)
- 108 will be 10's (8.333%)
- 72 will be 11's (5.556%)
- 36 will be 12's (2.778%)
Average: 7
Out of 1296 Open Rolls…
- 36 will be 2's (2.778%)
- 72 will be 3's (5.556%)
- 108 will be 4's (8.333%)
- 144 will be 5's (11.11%)
- 180 will be 6's (13.89%)
- 156 will be 7's (12.04%)
- 132 will be 8's (10.19%)
- 108 will be 9's (8.333%)
- 84 will be 10's (6.481%)
- 60 will be 11's (4.63%)
- 51 will be 12's (3.935%)
- 42 will be 13's (3.241%)
- 33 will be 14's (2.546%)
- 24 will be 15's (1.852%)
- 15 will be 16's (1.157%)
- 12 will be 17's (0.926%)
- 8 will be 18's (0.617%)
- 7 will be 19's (0.54%)
- 3 will be 20's (0.231%)
- 4 will be 16's with another roll (0.309%)
- 4 will be 17's with another roll (0.309%)
- 4 will be 18's with another roll (0.309%)
- 4 will be 19's with another roll (0.309%)
- 4 will be 20's with another roll (0.309%)
- 1 will be a 20 with two more rolls (0.072%)
Average: ~8 (assuming the extra rolls add either drn average)
Dueling DRNs
Most DRN rolls are in opposition to another DRN roll. The Damage roll, for example, is opposed by a Protection DRN roll. The Attack roll is opposed by a Defence roll, the Penetration roll to make many magic spells work is opposed by a Magic Resistance roll, and so on. In these three cases, a base value (typically matching the name of the roll) is added on to whatever the result is, and what happens next is determined by the value.
- A hit is considered to hit if the Attack roll beats (doesn't tie with) the Defence roll, at least without any Parry bonus.
- A hit is considered to do damage if the Damage roll beats the Protection roll. The difference determines the damage done, but some attacks have "side effects" (such as the poison of an Asp bite) that only check if the hit did damage at all.
- A Penetration roll succeeds if it at least ties with the opposing Magic Resistance roll.