The frequent argument that is made against the system of THAC0 (or to-hit charts) in AD&D by people who either rarely played it or remember the math being onerous when they were 8 years old is that the math is somehow mystifying or even difficult. The fact that AC went DOWN was very hard for some people.
As hard as this is for me to say it, who fought actual real math anxiety in school, this view is a silly one, based not on reality, but on math anxiety, and I'm going to try to show you way, without numbers...or, more accurate, with only half the numbers.
To begin with, we're going to completely dismantle how Armor Class works. It's not going to go from -10 to 10, or from 1-30, or anything like that. It is going to be represented by letters.
A-type armor, the best armoring you can get, is so good only the best dragons, a few demons and angels have class-A armoring. It never gets any better than this.
B-Type armor is less good, but still awesome.
It continues on down to K, which is some fairly decent human quality armoring. K is like full plate and shield, maybe a protective item tossed in.
After K it gets worse to U, or Unarmored, which is the worst armoring can get. It's people like you and me, wearing lightweight clothes or nothing at all (well, I am wearing clothes, but this is the internet, and to each their own.)
You buy armor, and it tells you your armor grade. You add a shield, it goes up a grade, you add magical protection, it goes up a few more.
The player's handbook has a chart like this:
Your character sheet has a chart like this:
However, he's good at hitting with longbows, because he's an archer by trade, so his CHUB with a longbow is 8.This means he can hit an UNARMORED opponent on an 8 or higher.
So he fills out his chart for both dagger and longbows, because those are his only two weapons, like so:
When it's his turn to attack, his DM tells him his opponent has an Armor Grade of P, and he knows he needs to roll a 15 or higher to hit with his dagger, or a 13 or higher to hit with his longbow.
Can you tell what he'd need to roll to hit a L-grade opponent with his bow? An O-grade opponent with his dagger?
Congratulations, you just used AD&D style THAC0, and declining AC.
Here's the chart with the AC filled in:
OKAY, but why does this matter?
There are 21 spaces on the above chart. There are 20 numbers on a d20. For any d20 based system of combat, you are arbitrarily selecting where the number you're going to 'value' is going to be. For the chart above, we use the AC of 0 (Armor grade K!)
The BEST way of adding a permanent bonus (for example, having a +2 with all longbows, ever) is to adjust your THAC0 (or your CHUB, THAC4, whatever!) downward for every bit of bonus you have. On the character sheets my players use, there are 9 slots on the THAC0 chart, above, each with a space for the weapon and the numbers, and I've never had a player fill them all in (but I've had one use 8.) I give enough room for the person with the sword +2, +4 versus evil to use one line for "+2" and another for +4."
This allows you to only be adding to the roll on the actual die for temporary and status effects. Temporary and status effects (Bless, Blinded, Bard singing) tend to effect more than one person, so when "everyone has a +1" and you roll an 18, the DM understands when you say "I roll a 19." (My players, bless them, are more likely to say "I rolled an 18, with the bard that's a 19!")
Allowing you to add all the pluses you might have to your base die roll creates a ridiculous scenario where you are rolling a "23" on a 1d20. WORSE, it can create the scenario just full of cognitive junk in which a 20 doesn't, technically, hit. Well, see, a natural 20 hits, but a regular 20 (say 15 plus five points of permanent bonuses) does not hit. This kind of stuff insults me as a scientist. Numbers have meaning....either a 20 hits or it doesn't hit. If we're going to just arbitrarily pretend the die numbers themselves are valueless, lets have THEM be labeled A, B, C, D, etc.
The big problem with counting up, not counting down (a rant):
Most of my players through most of my life as a DM haven't fudged many rolls. I've seen a couple points here or there, and I've let it stand, and I've been a hard-ass and demanded to know how the hell something hit just to make sure that everyone at the table knew I was taking rolls for an encounter extra seriously. I created a combat calculator page with a table where a player could write down each of his pluses for a weapon (one side for to-hit, one for to-damage) and that made it easier to keep track of things. [For example, the "to-hit" side of the calculator (chart) asks if the player has a plus to hit from: "Weapon being magical or masterwork/ bonus from race or class/ + to hit from specialization/ + to hit from DEX/STR/, + to hit from Other./" then adds them up. Most characters are going to have maybe one or two of these. There is a paladin I have who literally has a plus in every box when using a particular longbow (which is an enchanted masterwork artifact which behaves differently for a paladin). It comes out to something like +12. (She's high level, so that's part of it.)]
Watching other gamers, I find players are more likely to cheat (and some of it is not intentional) when they are being told to add, and add, and add, to a die. If they have a permanent +3, and a floating +2, and a just right now +1, telling the DM you rolled a 20 when you rolled a 14 is correct. However, it's also easy to get confused and say you rolled a 20 when you rolled a 13... maybe you forgot to add your higher ground this time, or some such, maybe you added it twice. When the size of the numbers being added to the die are high enough, both the players and the DM can lose track of what's going on. That's why I like the THAC0 chart- because it only gets changed when you level or change weapons.
I honestly think, and this may sound dumb, that looking at a 15 on a die and telling the DM you "rolled a 20," makes a cognitive shift in your brain. It doesn't matter that you have a +5. I honestly believe that it tells your brain that the number on the die is unimportant, and you're more likely to lie, or even get confused. I think hard numbers, on the paper, saying you need to have a 6 to hit a specific AC , and saying you hit that AC or not, is better for the brain.
I also am giving my players information about their opponent. When they are hitting other people in armor, I'll usually give them an AC, and just ask if they hit it or not. If they have something they've never encountered, I'm more likely to ask them "what AC do you hit?" The party learns pretty quickly. When the party tank hits an AC of "-4" and is successful, they start looking for ways to hit that hard of an opponent. I don't see that in the adding up and up and up systems. I just don't.
Another thing I think encourages cheating, and I've said this time and time again, is high scores always being good. In uAD&D, skills and non-combat thinks usually take a low roll on a d20. If you have a die that always rolls high, you're screwed. I like the "higher better in combat, lower better other times." for that reason.
Then again, as many of you know, if I had my druthers, it'd almost always be percentiles.