*THAC0 is Easy

In the technical debate over using a d20 ascending system (D&D 3e to 5e) or a THAC0 descending system (AD&D 1e, 2e, BASIC RULES) -to calculate Armour Class and hit rolls- there is often found the argument that the former is more intuitive and easier to implement. Admittedly in later editions, where there are more off-the-cuff modifiers to combat, this may be true, but in practice there really is no problem using the THAC0 system when it comes to playing the earlier versions of the game.

The THAC0 system is stupidly easy to use. The main problem is that it's been smeared by 'rules technicians' and game developers that are always looking for 'improvements' or seeking something new.

Using the THAC0 system in gameplay, to determine what Armour Class was hit using 1e, 2e or the BASIC rules, is quick and easy.

The best method is for the players to roll the dice, work out what AC they hit, and then inform the DM who then says whether the roll hits or misses. The Players calculate for themselves what AC they hit and the DM does the same with the monsters. In game play the DM should literally be calling out to the players "What Armour Class did you hit?" Likewise, when monsters are rolling to attack the characters, the call from the DM will be "What Armour Class is your character?" 

The technical side to working out what Armour Class was hit is straightforward:

At the most basic level the THAC0 system is best understood through actual armour types worn where the lower the Armour Class number (AC 10 is unarmoured, AC 5 for Chainmail, AC 3 for Platemail) the harder it is to hit (which means you need to roll high numbers on the d20). It makes perfect sense from that point of view. Low AC numbers are hard to hit, and rolling high on a d20 (consistently) is difficult to do.

Remembering that THAC0 literally means the roll required To Hit Armour Class 0, we can immediately work out that rolling above that number will hit a better Armour Class than 0 - which in the original editions of the game was represented by a lower number, as already mentioned - and rolling under the THAC0 number meant you hit a worse Armour Class.

The following table shows how Armour Class improves in the 2nd Edition as it gets lower, including negative numbers. The table shows how Armour Class is closely associated with specific types of Armour:
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AC: 10          AC: 8                  AC: 5           AC: 3        AC: 1         AC: -1

No Armour   Leather Armour  Chainmail    Platemail   Full Plate   Full Plate + Dexterity of 16

A shield will improve (lower) the AC by one place. In the last example a character wearing Full Plate with a dexterity score of 16 (granting a +2 improvement to the AC) and carrying a shield (granting a +1 improvement) would make a total Armour Class of -2.
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Therefore, if your character's THAC0 was 15 and you rolled a 10 you obviously hit an Armour Class five places worse than AC 0. In this case the character hit AC 5. If you rolled an 18 you obviously hit an AC three places better than AC 0. In this case the character hit AC -3.

EXAMPLE:
In a situation where a character with a THAC0 of 15 is fighting Orcs with an Armour Class of 8 (Leather Armour) we would find the following:

DM: Roll to attack.
Player: [Rolls an 11]
DM: What Armour Class do you hit?
Player: [15-11= 4]  Sir Headstrong hits AC 4.
DM: You hit.

In another instance the character might roll differently:

DM: Roll to attack.
Player: [Rolls an 18]
DM: What Armour Class do you hit?
Player: [15-18= -3]  Sir Headstrong hits AC -3.
DM: You hit.

In yet another instance:

DM: Roll to attack.
Player: [Rolls a 5]
DM: What Armour Class do you hit?
Player: [15-5= 10]  Sir Headstrong hits AC 10.
DM: You missed.

If the same character happened to find and then use a magical weapon with a +1 enchantment the character's THACO would improve by one place making it easier to hit AC 0 (thereby hitting with a lower roll on a d20). In this case the character would only need to roll a 14 to hit AC 0. Write down the new THAC0 for that weapon as 14. In our example, we now find that any roll of 6 or above would hit the Orcs wearing Leather Armour, where previously a roll of 7 or greater was required.

Making situational adjustments to the roll in combat is not difficult either. If the spell Bless happened to be cast, which gives a +1 advantage to the hit roll, the earlier example might play out thusly:

DM: Roll to attack.
Player: [Rolls an 11]
DM: What Armour Class do you hit?
Player: [15-11= 4]  With a THAC0 of 15 Sir Headstrong hits AC 4.
DM: Don't forget you are Blessed which gives you a +1 bonus.
Player: Oh yeah, I hit AC 3 [which is a one place improvement].
DM: You easily hit.

No difficult calculations are necessary. All you have to do is work out how far off your die roll is from your THAC0 and you can easily find the Armour Class that was struck. If you have situational bonuses to the hit roll then the Armour Class struck will be lower. Don't fall for the all the mumbo jumbo when it comes to THAC0.

Video: AD&D 2e - THAC0 explained