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

The reason a lower armor class is better is thus:

1. The value of your AC is determined. For any positive value (0 to 10), that number is used. For any negative value, a number between your AC and -1 is chosen at random. 10 is then added to that number, whether it be positive or negative.
2. The monster's level is added to that number. If the monster can't see you, subtract 2. If the monster is trapped, subtract 2.
3. If that number is less than or equal to 0, it is set to 1.
4. A random number between 1 and 20 is chosen. If the monster has more than 1 attack, 1 is added to the upper bound for each additional attack. (i.e. If the monster has 2 attacks, the second attack is 1 - 21, 3 attacks, 1 - 22, etc.). If the first number is higher than the random number, it is a hit. This means that the monster is less likely to hit you on each additional attack.

Examples:

1. Your AC is 7 and 10 is added to that, giving 17. The monster has a level of 1. Added together, that gives 18. On the first attack, the random number chosen is a 12. The monster hits.
2. 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.
3. 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. 1 is not greater than 1, so the monster misses.
4. 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.

As you can see, no matter how low you get your AC, there is still a chance that the monster will hit you. This doesn't mean that you shouldn't try to get your AC as low as possible, since it still makes it harder for higher level monsters to hit you.

Damage reduction

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

Let's take a look at example 4 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 armor.

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.