Mechanic Series: THAC0 & Armor Class

One flips through gaming books and sees all of these numbers and hears complex terms like COMBAT MATRIX, descending armor class, combat modifiers. The deal is that it is harder to talk about math than it is to just solve the problem. None of the math problems that we’ll have to solve during play will involve any tool more advanced than a basic calculator, and everybody can use a calculator! Once you get going with the system it forms an algorithm and players can quickly do the math in their head, as it isn’t anything that you don’t do every day anyway.

THAC0 simple means, “To Hit Armor Class 0” When the second edition included this as core, it revolutionized the game, sort of. It was always kind of there, but what it allowed was for us to write down just one number on our character sheets and this would help us figure out what we needed to roll to hit a target regardless of how challenging the target was to hit.

Inventing a system this easy to use took a lot of testing and tinkering, prior to Dungeons and Dragons, the game’s inventers played wargames, and one always had to come up with a system which randomized if a hit was successful or not in a fast and concise manner. Dice proved a great universal method. Once we figure out a system, then we have to figure out how to describe the system so that others can use it as well, which since math is never changing, math is the best way to figure all of this stuff out.

Prior to the THAC0 system, the game designers created Combat Matrixes, tables that when rolled against, told you if you hit or not, some of these were more complex than others, but they all strove to achieve the same goal, the more universal the better.

We get the term Armor Class from Wargames as well, specifically Naval Combat where different ships had different amounts of armor to protect them, players found that a descending armor class was more functional in the game than ascending Armor Class systems, but in Naval Combat, the ships AC never changed, the same goes for all mass combat systems, so when Gygax wrote the Chainmail Rules, he used a universal Armor Class system shared by all of the troops in a battalion.

When it came to D&D, the terminology was kept, and we have the AC system, but instead of a fixed number, the number for an individual target isn’t constant. A ships ability to hit another ship always stayed the same, but with individuals we wanted to simulate improvement, this required some additional thinking, and more complex combat matrixes.

In the first edition of AD&D, players wanted lots of ways to fight and modify things to make an opponent either easier or harder to hit depending upon choices that each player made. The AD&D system kept this matrix hidden from player view by putting it in the DMG, you rolled the dice and the DM told you if you hit or not. This provided a mystery because you didn’t know how the DM achieved this target number, as the DM wanted to keep all of the stats secret. It didn’t work, players caught on to the formula, either from sneaking a peek at the DMG or just playing enough to realize the DM’s system. This also required even more work on the DMs part, and users were coming up with their own methods of changing it up to make it easier for them to come up with a universal system that could still be modified quickly.

It was a bunch of computer scientists at UCLA who were playing the game regularly that figured out that you didn’t need the entire combat matrix for the game to function, that if you just told them how to hit AC 0, and add all of the modifiers separately, you just needed to know one single number. Gone were the pages and pages of overly complex combat matrixes. For whatever reason, Gygax didn’t like it, it is briefly mentioned in the DMG, but dismissed as too simple. Dave Cook however saw it as the ever elusive universal system so it was officially added to the 2e mechanics, and it made play a lot faster.

Detractors instantly rejected this method, saying that it dumbed down the game, and others claiming that it made combat too difficult to figure out. 2e was still learned, not by yourself and on your own, but by playing the game with others who had been taught by somebody else who already knew how to play the game. If one looks at the THAC0 system by itself, it can be confusing, but all it takes is the player sitting next to you to help you figure out if you hit or not for a couple of sessions before it is permanently implanted in your brain in a way that will never go away . . . ever.

In third edition, they changed descending AC to ascending AC which really threw 2ers for a loop. You play with this system enough it becomes ingrained in you and even something as simple as making AC 1 as bad is enough to throw you off, so I know that going back to a descending AC is the same way for others, just know that us holdouts didn’t refuse to move on to 3e because of ascending AC, when it comes down to it, 3e is too ridged of a system when you get used to the freedom that earlier editions allow.

So what is the formula? Well, it is easy. Look at the THAC0 grid, and find the number you need for your level. This number never changes, it doesn’t float around, and it is always the same. When you have a modifier you don’t apply it to your THAC0, you apply it to your opponents Armor Class. Thus, a sword+3 doesn’t change your THAC0, it changes your opponent’s AC from 4 to 7. Penalties also change your opponents AC, if you have a -2 to your roll, you take it from his AC, which turns an AC of 4 to an AC of 2.
Simple yet elegant, isn’t it! Suddenly all of the complaints that it requires to much math are dismissed. The problem wasn’t the system; the problem was that people kept trying to modify their THAC0 numbers.

Once you get it figured out, and can start playing with more advanced rules, the THAC0 system still functions. Now you can have missile combat and melee combat taking place in a forest at the same time using the same ruleset without having to change anything. The floating AC rule allows combat to flow smoothly and naturally so that both sides can focus on play without having to get all technical.


Broken, no; subjective, very. If you up and decide to use a different method of deciding how combat is resolved, then you aren’t playing AD&D. Taking it out makes all of the other rules in the AD&D system not work anymore, period. The game encourages you to tinker with the AC system, applying modifiers as you see fit to factor in advantages and disadvantages depending on where exactly each battle is taking place. Can you get carried away with modifiers? You bet! And the AD&D system will let you do this, but the DM can always decide exactly how many or how few of the optional rules and modifiers work best for their particular game.

We had to go here, I hope that I was able to clear up some confusion about how the THAC0 system is supposed to work, because it isn’t this mechanic that weakens the game, but what LOTS of people do with it that does, which we can now explore.


Chris Mata said...

Great post!

Ripper X said...

Thanks Chris! But do make sure that you remember that if one of those preppy popular kids ask you if you are playing one of those complex math games, then it is your DUTY to always say, "Yes!", and if he still wants to play then you must string him along as long as possible.

GreyKnight said...

"Gygax [...] dismissed [it] as too simple."

If there's one thing Gary didn't like, it was simplicity. :-)

Ripper X said...

That may be an inaccurate statement that I made, I can't tell you too much. I know that he touches upon it in the 1e DMG, but by the time Gygax got to sit down and write the DMG the MM had already been in print for a couple of years. Talking about THAC0 could had just been a nod to a mechanic that was too late to implement.

This stuff was before my time, I was just a little kid. What I'd like to know is how in the hell did anybody play AD&D without the Combat Matrix? The MM was published one year, than the PHB the next, the DMG was last to be written, and it contains most of the info that makes the game playable. My only guess is that there must had been a combat matrix in the first printing of the MM.

Brooser Bear said...

Hey, Rip! You further defined me as a FIRST Edition AD&D DM! I don't confuse my players with game mechanics, they need to have uncluttered minds to make decisions and interact with the hell that I put them into!

I am not a fan of Gygax or a hater of Simplicity, however, if you want your game to reflect realism, and be reflect the real world tactics that is line how medieval weapons were developed and used, your game will get nuanced and more complex! Personally, I don't want to be figuring out the 'rithmetic, while DMing. What I do instead is have a set of To Hit and To Be Hit numbers written on my copy of the player character's sheet, already prefigured with all of the modifiers. One line for each melee weapon, 1H and 2H use line for the bastard sword, and three lines for each missile weapons - at different ranges. This way, I see the number I need based on what the player tells me, I roll and call it without having to do any math. I use a lot of modifiers - Weapon vs armor table, I added a few tweaks to make combat more tactically relevant in a direction different from the Combat and Tactics.

Ripper X said...

Realism and D&D are two very different things, especially when it comes to combat, but I get what you are saying. Either you are a fan of the THAC0 system, or you aren't. Me personally, I can't use a combat matrix, I don't like them and I never have. I can work with the THAC0 system much faster, I already know my THACO, just give me the modified AC and I can tell you if I hit or not.

I personally have developed a deep love for math, but calculating THAC0 isn't complex enough to even be called math. But I get it! I do. It is a preference thing, but the cool thing about it is that you and I can play the same game with two different tables and come out with relatively the same results regardless of the method that we are using, so you are correct, using the 1e matrix system instead of THAC0 doesn't break the game down, it is still functional.

Brooser Bear said...

Oh no, Ripper, I bring the Combat in all its mortal glory to my D&D players. Consider this: Combat is non-linear, meaning that any injury can be fatal. I see fear in my players' eyes every time they go into battle. I have am elegant mechanic for determining, if a critically injured character remains on his feet; and if he remains conscious after an arrow pierces his chest, before bleeding out. I use a hit location table, but not for damage, rather to see of the armor will avert a critical hit. Armor is very expensive and warriors have to spend money and seek out master armorer and accumulate good armor piece meal. If you got a solid metal piece protecting the area, then nothing under sixth level can deal a death blow with natural weapons through a solid metal armor. Players can develop their unique fighting style by trial and error, that matches historical experience.

I don't use THAC0, because there are a set of static modifiers to hit, and then there are tactical modifiers that apply to the to hit roll based on characters' actions in battle, and, if they use the weapon in accordance with the purpose, for which is was developed, they get a tactical advantage - Unseating riders, trapping and pulling shields from melee opponents, etc. If I want to learn the players something, I have their opponents use the tactic on players.

I also make my D&D game realistic in terms of consequences of their decisions, that players face in the game.

The chief benefit of all this house-ruling is that players are forced to think, and that power games are rendered impotent. They have to get into the game to be able to perform. This style of DMing evolved, when I got a group of outsiders to gaming, wbo all wanted to play fighters (they had a pretty sound logic - simplest character type that they can understand, and therefore, control). I decided to make playing fighters in my game as interesting, as it is to play thieves and magic-users.

1e Matrix suits me better, but I see the advantages of using THAC0.

Post a Comment


Contact me at

Search This Blog

Blog Archive