Armor class

In Dungeons and Dragons, your armor class, or AC, represents your defense against attacks from monsters. NetHack borrows this concept; as in older editions of D&D, a lower AC is better than a higher one.  A character with no armor or protection has AC 10. It is best to reduce your AC below 0. An ascension kit usually includes an AC below -20, -30, and sometimes -40.   Note that having a good AC is not enough to protect from some attacks; you also need to obtain resistance. In particular, reflection is a good idea.

Because you always know your AC, you can identify the enchantment of armor by wearing it. For example, +1 armor lowers your AC by one more than normal.

How it works

Your AC is used to calculWhen a monster attack you, 1d20 is rolled.  Rolling a target number or lower results in a hit.  In simple situations at low levels, this target number is equal to:

10 + your AC + the monster's level (ie number of hit dice they have).

So, say your AC is 6, and you are fighting a level 1 Orc.  The target number for the orc to successfully attack you is 10 + 6 + 1 = 17.  This is bad news; the orc is going to hit you 80% of the time.

At higher levels and in funny circumstances, things become more complex.  The precise detailsDungeons and Dragons are:

• If your AC is negative, the formula for the target number is 10 + (a random number from -1 to your AC) + the monster's level.
• Circumstantial modifiers may be applied.  For instance, if the monster can't see you or is trapped, subtract 2 for each.
• If the final target number is so good that it would be less than or equal to zero, set it to 1.  In this way the monster always has a small chance of hitting you by rolling that perfect 1 on the d20.
• If the monster gets multiple attacks, each attack beyond the first is made as if the die rolled had an extra side.  So a monster with three attacks would roll 1d20, then 1d21, then 1d22.  In this way each extra attack is less and less likely to hit you.NetHack

Examples of these more complex cases:

1. Your AC is -5. Since it is a negative number, a number between -5 and -1 is chosen at random. In this case, it is -3. 10 is added to that, giving 7. The monster has a level of 4, and it has two attacks. Added together, that gives us 11. On the first attack, the random number chosen is 10. The monster hits. On the second attack, the random number chosen is 12 (out of a possible 21). The monster misses.
2. Your AC is -20. A number between -20 and -1 is chosen at random. In this case, -17 is chosen. 10 is added to that, giving -7. The monster has a level of 1. Added together, that gives -6. Since -6 is less than 0, it is set to 1. On the first attack, the random number chosen is 1.  The monster gets very lucky and hits.
3. Your AC is -20. A number between -20 and -1 is chosen at random. In this case, -4 is chosen. 10 is added to that, giving 6. The monster has a level of 1. Added together, that gives 7. On the first attack, the random number chosen is 5. 7 is greater than 5, so the monster hits.

Damage reduction

Any AC of negative value (-1 or lower) also decreases the damage you take. Armor

Let's take a look at example 3 and see how a lower AC would reduce damage. The monster does 5 points of damage when it hits.

First, it determines if your AC is less than 0; in this case it is. The damage is then reduced by a random number between 1 and the negative value of your AC (a negative of a negative is a positive), which in this case would be 1 to 20. For any value lower than 1, it is set to 1 (the monster will always do at least 1 point of damage when it hits). (This is applied before half physical damage, if you have that as well.)

This is another good reason to reduce your AC as low as you can get it.

Order of Armor class

The order of body armor in AC from highest to lowest is dragon scale mail, plate mail, crystal plate mail, bronze plate mail, splint mail, banded mail, dwarvish mithril-coat, elven mithril-coat, chain mail, orcish chain mail, scale mail, studded leather armor, ring mail, orcish ring mail, leather armor, leather jacket, and no armorProtection.

How much is enough?

The data for the following table comes from 500,000 simulated minotaur attacks (claw 3d10, claw 3d10, butt 2d8). Minotaurs appear often, hit hard, and ignore Elbereth, making them the biggest physical damage threat in the late game and a natural choice of benchmark.

The percentage entries indicate how likely you are to take less than a certain amount of damage. For example, if your armor class is -15, 50% of the time a minotaur's three attacks will do less than 16 damage total. And if your armor class is -25, you will take no damage 25% of the time.

Armor class	Mean damage per round	25% less than	50% less than	95% less than	99% less than
-10	23.1	17	24	40	47
-15	16	9	16	35	42
-20	11	3	11	30	37
-25	7.5	1	5	26	34
-30	5.4	1	3	23	31

In the notes for the MIT Nethack course, Raxvulpine recommends AC -20 as the baseline for an ascension kit. This is a reasonable guideline; with smart play, 11 damage per enemy turn is manageable.

Two things should be noted. First, the value of an additional point of AC starts diminishing rapidly around AC -25. Second, due to the nature of the attack and damage calculations, no amount of armor class can protect you with 100% certainty. Even if your armor class is -30, one time in a hundred a minotaur will hit you for at least 31 damage in one round.

References

Ascension kit