## Tuesday, April 2, 2013

### Two Dice, Roll Under

Occasionally, I've talked about a quick, easy substitution for the standard D&D combat system: instead of rolling d20 + mods over some target number, just roll 2d6 under (descending) AC. The good part is that the D&D AC system and the 2d6 approach seem made for each other*: the lowest 2d6 roll possible is the lowest AC number possible, and the AC for "no armor" is well within the range.

* Yes, I realize the Chainmail table that uses the eight D&D ACs is a 2d6 table, so in a sense they were literally made for each other... but the Chainmail table is roll high and none of the listed weapons quite duplicates the way a straight 2d6 roll under works.

The problem, as I've mentioned, is that, if you want the probabilities to hit to be about the same as under the d20 system, it won't work. A 1 HD creature or normal man has a 55% chance of hitting AC 9 using the alternative combat system or Target 20, but the chance of rolling 9 or less on 2d6 is 83%. The d20 chance of hitting AC 2 is 20%, but the chance of rolling 2 on 2d6 is 3%. Light and no armor thus become easier to hit with 2d6, while metal armor becomes much more difficult. There's also the related fact that a +1 or -1 modifier to the roll does not equate to a fixed 5% or 10% change in probability.

That might not bother some people. Maybe you want metal armor to be better, and don't care if the steps aren't even. I'm kind of tempted, myself.

But you can improve things a little bit with a couple changes:
1. Switch to d8+d4, which I've discussed before. A 1-point difference between numbers in the 5 to 9 range is a +/- 12.5% difference in probability. 4 and 10 aren't too far off.
2. Exclude shields from AC. Instead, if an attack hits an opponent who has a shield, the opponent rolls a d6 and only takes damage if the damage roll is equal or higher,
3. Change the AC numbers so that they are in 1-point steps instead of 2-point steps.
• No Armor = 7
• Light/Leather = 6
• Medium/Mail = 5
• Heavy = 4
Note that chainmail has the same AC under the new system as it did under the old system, so that makes it easy to remember.
The probabilities still don't match the d20 approach, but it's a serviceable system.