THAC0 is a rule used in Advanced Dungeons & Dragons 2nd Edition, to form a baseline by which a character's attack roll is calculated.
The term THAC0 is an acronym for "To Hit Armor Class 0," and represents the lowest unmodified attack roll a character may make on a 20-sided icosahedral die and still hit a target with an Armor Class of 0.
In gameplay, a character's THAC0 forms the baseline for all attack rolls, and that number is then modified by a number of permanent or situational variables, such as the character's Strength and Dexterity Ability Scores, the plus bonus of any magic weapons used, and a target's Armor Class.
Regardless of a character's THAC0 and all modifiers, in Second Edition Dungeons & Dragons a roll of 20 is always a critical hit, and a 1 is always a critical miss.
In game, if attack rolls are shown (enable in game-play settings), the game will show attacker Attack Roll + (defender Armor Class Modifiers - attacker THAC0 ) = result. Where, result + defender AC (not shown) = zero or greater will be a hit. (Recall that minus a negative number results in a positive number.) Thus, the lower (more negative) the AC the tougher it is to be hit. Likewise lower THAC0 makes it easier to achieve hits. Critical hits [due to Attack Rolls of 20 (and possibly 19)] will also be hits regardless of other values.
AD&D 2nd Edition has four different THAC0 progressions, based on rate of decrease and by level.
- Warrior classes (Barbarian, Fighter, Paladin, Ranger, and Monk) have the best THAC0 progression, with a THAC0 that decreases at a rate of 1:1 (to a max of base 0 at level 21).
- Priest classes (Cleric, Druid), have the second best THAC0 progression in the game at a rate of 2:3 (to a max of base 6 at level 22).
- Rogue classes (Thief, Bard) have a THAC0 progression of 1:2 (to a max of base 10 at level 21), giving them the mathematical oddity of having a better THAC0 than a priest at level 3. Rogues remain roughly on-par with priests (albeit slightly in the Priest's favor) until level 9, and are thereafter surpassed by priest classes at an increasing pace.
- Wizard classes (Mage, Sorcerer) have the worst THAC0 progression, at a rate of 1:3 (to a max of 13 at level 22).
In Dungeons & Dragons 3rd Edition and later, Armor Class and attack were reworked to always trend upward by using attack roll + attack bonus -enemy AC= 0 or greater to determine hits. This has the advantage that better scores don't go into the negative numbers but rather continue growing in the positive integers.
Example Cases Edit
In the Baldur's Gate series, lower THAC0 scores are favorable versus higher scores since the score determines the minimum die roll required to hit an enemy when rolling a 20-sided die.
For example, a character's THAC0 of 18 means to hit a target with an AC of 0 the die roll must be at least 18 (a 3/20 or 15% chance of success). A much lower THAC0 of 4 means that to hit the same target, the die roll must be at least a 4 (a 17/20 or 85% chance of success).
It is possible to calculate minimum rolls for different AC values other than 0. To do this, subtract the AC of the target from the THAC0 score. The equation is:
Minimum roll required to hit = (THAC0 of attacker)-(AC of target +Armor Class Modifier) [Same as equation above but this way of thinking about it might make more sense to some readers]
For example, you have a THAC0 of 18, and the target has an AC of 8. The minimum roll required to hit the target is 18-8=10.
Die rolls of 1 and 20 are the exceptions, where a 1 is treated as a critical miss, and 20 a critical hit. These exceptions are guaranteed to always occur. In BG:EE if a 19 is a critical hit due to weapon style proficiency points, it too is an automatic hit.
For example, your THAC0 is 16 and the target has an AC of -5. In this case, the negative AC would be subtracted from the THAC0 of 16. 16-(-5)= 16+5= 21. So in layman's terms, a roll of at least 21 from a 20-sided die is required to successfully hit the target, which appears to be impossible. However, rolling a 20 guarantees a critical hit, ensuring a 5% chance of damaging the target against all odds.
Another example: your THAC0 is 5 and the target has an AC of 5. AC is subtracted from THAC0 so: 5-5= 0. So in layman's terms, a roll of at least 0 from a 20-sided die is required to successfully hit the target, which appears to be guaranteed since every value on the die is greater than 0. However, rolling a 1 guarantees a critical miss, ensuring a 5% chance to miss even when the odds appear stacked in your favor.
THAC0 Bonus Versus THAC0 Modifier Edit
When an item describes a THAC0 Bonus, it actually means that the THAC0 score decreases while wielding the item. For example, elves have a +1 THAC0 bonus while wielding short bows, long swords, and short swords. The +1 THAC0 bonus actually describes a -1 reduction to THAC0 score when one of these weapon types are equipped. A +1 THAC0 bonus can be described as a -1 THAC0 modifier.
To Hit Modifiers as it Relates to THAC0 Edit
A positive to hit modifier is an equivalent reduction to THAC0.
For example, an Assassin has a bonus +1 to hit, which is equivalent to a -1 THAC0 modifier.