The Attack Roll (PHB)

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At the heart of the combat system is the attack roll. This is the die roll that determines whether an attack succeeds or fails. The number a player needs in order to make a successful attack roll is also called the "to-hit" number.
Attack rolls are used for attacks with swords, bows, rocks, and other weapons, as well as blows from fists, tackling, and other hand-to-hand attacks. Attack rolls are also used to resolve a variety of potentially injury-causing actions that require accuracy (for example, throwing a rock at a small target or tossing a sword to a party member in the middle of a fight).
==Figuring the To-Hit Number==
The first step in making an attack roll is to find the number needed to hit the target. Subtract the Armor Class of the target from the attacker's THAC0. (Remember that if the Armor Class is a negative number, you add it to the attacker's THAC0.) The character has to roll the resulting number, or higher, on 1d20 to hit the target.
:Rath has reached 7th level as a fighter. His THAC0 is 14 (found on Table 53), meaning he needs to roll a 14 or better to hit a character or creature of Armor Class 0. In combat, Rath, attacking an orc wearing chainmail armor (AC 6), needs to roll an 8 (14-6=8) to hit the orc. An 8 or higher on 1d20 will hit the orc. If Rath hits, he rolls the appropriate dice (see Table 44) to determine how much damage he inflicts.
The example above is quite simple—in a typical AD&D game combat situation, THAC0 is modified by weapon bonuses, Strength bonuses, and the like (the next section "Modifiers to the Attack Roll," lists the specifics of these modifiers). Figure Strength and weapon modifiers, subtract the total from the base THAC0, and record this modified THAC0 with each weapon on the character sheet. Subtract the target's Armor Class from this modified THAC0 when determining the to-hit number.
:Rath is still a 7th-level fighter. He has a Strength of 18/80 (which gives him a +2 bonus to his attack roll). He fights with a long sword +1. His THAC0 is 14, modified to 12 by his Strength and to 11 by his weapon. If attacking the orc from the earlier example, Rath would have to roll a 5 or higher on 1d20 in order to hit (11-6=5). Again, table 44 would tell him how much damage he inflicts with his weapon (this information should also be written on his character sheet).
The DM may also throw in situational modifiers, (for example, a bonus if the target is struck from behind, or a penalty if the target is crouching behind a boulder). If the final, modified die roll on 1d20 is equal to or greater than the number needed to hit the target, the attack succeeds. If the roll is lower than that needed, the attack fails.
==Modifiers to the Attack Roll==
In combat, many factors can modify the number a character needs for a successful hit. These variables are reflected in modifiers to the to-hit number or to the attack roll.
Strength Modifiers: A character's Strength can modify the die roll, altering both the chance to hit and the damage caused. This modifier is always applied to melees and attacks with hurled missile weapons (a spear or an axe).
A positive Strength modifier can be applied to bows if the character has a special bow made for him, designed to take advantage of his high Strength. Characters with Strength penalties always suffer them when using a bow weapon. They simply are not able to draw back the bowstring far enough. Characters never have Strength modifiers when using crossbows—the power of the shot is imparted by a machine, not the player character.
Magical items: The magical properties of a weapon can also modify combat. Items that impart a bonus to the attack roll or Armor Class are identified by a plus sign. For example, a sword +1 improves a character's chance to hit by one. A suit of chain mail +1 improves the Armor Class of the character by one (which means you subtract one from the character's AC, changing an AC of 5 to an AC of 4, for example). Cursed items have a negative modifier (a penalty), resulting in a subtraction from the attack roll or an addition to Armor Class.
There is no limit to the number of modifiers that can be applied to a single die roll. Nor is there a limit to the positive or negative number (the total of all modifiers) that can be applied to a die roll.
Table 51 lists some standard combat modifiers. Positive numbers are bonuses for the attacker; negative numbers are penalties.
 Table 51 Combat Modifiers
Situation 	Attack RollModifier
Attacker on higher ground 	+1
Defender invisible 	-4
Defender off-balance 	+2
Defender sleeping or held 	Automatic*
Defender stunned or prone 	+4
Defender surprised 	+1
Missile fire, long range 	-5
Missile fire, medium range	-2
Rear attack 	+2
:* If the defender is attacked during the course of a normal melee, the attack automatically hits and causes normal damage. If no other fighting is going on (i.e., all others have been slain or driven off), the defender can be slain automatically.
==Impossible To-Hit Numbers==
Sometimes the attacker's to-hit number seems impossible to roll. An attack may be so difficult it requires a roll greater than 20 (on a 20-sided die!), or so ridiculously easy it can be made on a roll less than 1. In both cases, an attack roll is still required!
The reason is simple: With positive die roll modifiers (for magic, Strength, situation, or whatever), a number greater than 20 can be rolled. Likewise, die roll penalties can push the attack roll below 0.
No matter what number a character needs to hit, a roll of 20 is always considered a hit and a roll of 1 is always a miss, unless the DM rules otherwise. Under most circumstances, a natural 20 hits and a natural 1 misses, regardless of any modifiers applied to the die roll.
Thus, even if a character's chance to hit a monster is 23 and the character has a -3 penalty applied to the die roll, he might be able to score a hit—but only if the die roll is a 20 before any modifiers are applied. Likewise, a character able to hit a monster on a 3 or better, waving a sword +4, could still miss if a 1 is rolled on the die.
There are no sure things, good or bad, in the unpredictable chaos of combat situations.