Revisting an old problem: THAC0 WTF?

[Otogi]

What exactly is the difference between To Hit Armor Class 0 and AC? Is there a way to simplify it? To get rid of it all together?

[Flickerdart]

What exactly is the difference between To Hit Armor Class 0 and AC? Is there a way to simplify it? To get rid of it all together?

In earlier editions of D&D, AC was reversed: the smaller, the better, with AC -10 being the smallest, I believe. THAC0 is "to hit AC of 0", how much you have to roll to hit a 0 AC monster. It's the archaic equivalent of attack bonus, not AC.

[Tsotha-lanti]

It's incredibly simple.

THAC0 is "to hit armor class 0." It's the minimum number you need to roll, on a d20, to hit AC 0. To hit a specific AC, you subtract the AC from the THAC0.

So if your THAC0 is 20, and the AC is 8, you need to roll 20-8=12.

If your THAC0 is 13, and the AC is -4, you need to roll 13-(-4)=17.

Thus, high (positive) numbers are bad, low (negative) numbers are good, for AC. A high number is bad for THAC0, and a low number is good.

3.X got rid of it, and made the system even more simple (and more intuitive): rolls are now d20 + bonus against a target number; your result must equal or exceed that target number.

Edit: To be more specific to your question, the difference is that AC is a defensive capability, and THAC0 is an offensive capability.

[Kish]

Someone came up with a fix to this, indeed.

I think the fix was called Third Edition.

[Cubey]

The problem with THAC0 was not that it was mathematically complicated. While less intuitive than 3rd ed AC, it's still just simple deduction/substraction. The problem is that because it, along with other stats, decreased as you got better, bonuses were extremely muddled. Is a magical item that gives you -1 THAC0 a beneficial or a detrimental one? What about +1 to each save? It could be interpreted in both ways, and that's not a good thing.

[Kurald Galain]

And, likewise, I predict that when Fifth Edition comes out, people will mock 4E for having such "difficult" concepts as that a "burst 3" isn't the same size as a "blast 3".

[Tsotha-lanti]

I suppose you could streamline it as such...

AC becomes a target number. Since an unmodified base THAC0 is 20, AC 0 will become 20 (since you are now trying to roll equal to the AC). This means that he unarmored base AC is 10. Armor adds bonuses to AC, equal to 10 minus the armor's old AC value; so chain mail, with AC 5, adds a +5 bonus, and plate, with AC 3, adds a +3 bonus. Shields add a +1 bonus.

Instead of a THAC0 that goes lower, classes get a class-based attack bonus. You get this bonus for each level by taking the THAC0 table and subtracting each value from 20. A 2nd-level fighter would have THAC0 19, and therefore has an attack bonus of +1.

The odds of hitting remain the exact same, but the roll is now in a more intuitive "d20 + bonus equal to or over target number" roll.

It's also the system used in D&D 3.X, with less streamlining (i.e. starting everyone at +0 and progressing in a weird way, etc.).

So, yes. 3.X took the backwards unintuitive calculations and made them more intuitive.

[John Campbell]

THAC0 is exactly like BAB, except that instead of adding your roll to your attack bonus to determine what AC you hit, you subtract your roll from your THAC0 to determine what AC you hit.

WHY IS THIS SO HARD TO UNDERSTAND?

[OzymandiasVolt]

Because lower being better is unintuitive, especially when it goes into the negatives?

[SimperingToad]

It's not that difficult, really. Wonky, sure, but not difficult. It's quite understandable if you can't grasp calculus (heh... that one almost cost me a H.S. diploma), but sheesh, folks, we all learned basic math in grade school.

It just did not appear out of thin air to confuse mere mortals. The concept was actually present in the appendices of 1E (which no one to my knowledge used), but it really was a method to allow the DM (who was the only person at the table who needed to know how to use THAC0) to calculate a 'to hit' without looking on a chart. The 1E chart, in turn, was a holdover from the original game, which had it's roots in miniatures wargames where lower numbers were better. So, descending ACs were better in OD&D/AD&D.

So much for the history lesson.

Really, the two concepts are not that far apart (1E/2E v.3E) except one uses descending numbers, the other ascending. Both are based on determining a number to beat, only AD&D 2E required a simple calculation to find the base number. Then in both cases, the attacker adds his modifiers to a die roll.

Over on Dragonsfoot, someone worked out a system to convert 1E attack tables to a 3E equivalent BAB and ascending AC. With a little tweaking, 2E can be done as well using this as a basis.

1E combat in 3E style

[Behold_the_Void]

It's not hard to understand once explained, it's just unintuitive, as people have said.

[Matthew]

THAC0 is just basically one step ahead of BAB calculations. When rolling 1D20 to hit do you want your target number to be higher or lower? (the answer is lower, assuming you want to hit). That's all THAC0 is, the target number you need to hit armour class 0. As Cubey mentioned, the real problem was with imprecise bonus/penalty nomenclature, which sometimes had to be guessed from context (Hmm, Berserk Rage = +2 to hit and +1 armour class...?)

Roll 1d20, add the armour class of the target, if it's equal or higher than the attacker's THAC0, it is a hit. Very simple stuff.

[pirateshow]

Thac0, in addition to being a weirdly counterintuitive approach to figuring out what roll is required to hit in melee, is also the name of my cat. Much amusement was had when I picked him up after recent surgery and asked how he was, and my vet's receptionist told me that he had "passed his Fortitude save".

[Tsotha-lanti]

Because lower being better is unintuitive, especially when it goes into the negatives?

Well, it's also because instead of comparing a sum of two numbers to a target number (all of which are positive), you compare one number to the difference of two numbers (both of which may be negative or positive).

People deal way better with the first kind of task.

[Premier]

It's really simple.

THAC0=Attack Bonus
AC=DC

Look, in 3E, you want to roll a number that's equal to or higher than the difference between the enemy's DC and your Attack Bonus, right? If your AB is +5 and the target's DC is 16, then you'll want to roll (16-5=)11 or higher.

Same thing in 2E, only you get the difference by extracting the target's Armour Class from your "Attack Bonus", not the other way around. So, your THAC0 is 16, your target's AC is 4. (16-4=)12 or higher is what you want to roll.


Also, regarding the ubiquitous "It's unintuitive!" complaint: No it isn't. You're misusing the word. "Unintuitive" would mean that humans are inherently built to equate "higher number" with "better quality". However, this is plain simply not true. 1 is a lower number than 2, and yet, nobody ever says that "1st class train tickets being better than 2nd class ones is unintuitive!" Nobody ever whines "Why do they call excellent actors (or any other professionals) "1st rate" and bad ones "3rd rate"? Higher numbers should mean better! It doesn't make sense!" A Petty Officer 4th Class and a Petty Officer 2nd Class on a Navy ship never get confused about who's superiour to whom. Heck, even spaceships are launched on a countdown, not on a countup from zero to ten, and nobody ever criticizes the technique on grounds of descending numbers being unintuitive.

Why? Because "higher number is better" is NOT, I repeat, NOT some inherent, biologically or mentally determined principle, and therefore it's not something you can properly call "intuitive".
I mean no disrespect to anyone in specific, but over time I've become convinced that whenever someone complains of THAC0 being unintuitive, they in fact mean one of two things. The first is "I find subtracting a small number from another small number, let alone a single-digit negative number, to be too hard, or at least significantly harder than an addition of numbers, because my primary school math education sucked. However, I'm too narcisstic to admit to sucking at math, and too lazy to fix it with practice; so I'll just criticize the game instead."
And the other is "I want to belong to the cool kids, and the cool kids are all hissing and spitting and booing at descending AC, so I'll just mimic them without thinking about whether they're actually right or not."

Again, no offense to anyone; but I've read way more threads and arguments about the matter than I care to or could count, and after a while you start seeing the same patterns of arguments and "criticism tactics" emerge everywhere, and at one point you just can't help but connect the dots and draw your conclusions.


Oh, and an afternote:

Well, it's also because instead of comparing a sum of two numbers to a target number (all of which are positive), you compare one number to the difference of two numbers (both of which may be negative or positive).

Not true, or at least doesn't need to be. You could just as well say that you add up your die roll and the target's AC, and compare that to your THAC0. If the side with your roll is higher, you hit.
You see, now it's a sum of two numbers, just like in 3E, and not a difference; so you can't say that it's inherently less intuitive. Mathematically, it's the same difficulty; it's just that critics tend to deliberately and maliciously pick the more "complicated" (subtracting) version instead of the simpler additive one, because without that they wouldn't have an argument.

[monty]

THAC0 is a goblin monk, obviously.

[HidaTsuzua]

It's really simple.
Also, regarding the ubiquitous "It's unintuitive!" complaint: No it isn't. You're misusing the word. "Unintuitive" would mean that humans are inherently built to equate "higher number" with "better quality". However, this is plain simply not true. 1 is a lower number than 2, and yet, nobody ever says that "1st class train tickets being better than 2nd class ones is unintuitive!" Nobody ever whines "Why do they call excellent actors (or any other professionals) "1st rate" and bad ones "3rd rate"? Higher numbers should mean better! It doesn't make sense!" A Petty Officer 4th Class and a Petty Officer 2nd Class on a Navy ship never get confused about who's superiour to whom. Heck, even spaceships are launched on a countdown, not on a countup from zero to ten, and nobody ever criticizes the technique on grounds of descending numbers being unintuitive.

Why? Because "higher number is better" is NOT, I repeat, NOT some inherent, biologically or mentally determined principle, and therefore it's not something you can properly call "intuitive".
I mean no disrespect to anyone in specific, but over time I've become convinced that whenever someone complains of THAC0 being unintuitive, they in fact mean one of two things. The first is "I find subtracting a small number from another small number, let alone a single-digit negative number, to be too hard, or at least significantly harder than an addition of numbers, because my primary school math education sucked. However, I'm too narcisstic to admit to sucking at math, and too lazy to fix it with practice; so I'll just criticize the game instead."
And the other is "I want to belong to the cool kids, and the cool kids are all hissing and spitting and booing at descending AC, so I'll just mimic them without thinking about whether they're actually right or not."

The main "unintuitive" reason is what's better Plate Mail +1 or -1? Which lowers your AC and which increases it? Plate Mail +1 is what's better and lowers your AC. Would you guess that if you didn't know the rules? Maybe, but it's less likely that you guessing correctly 3.x's way.

Also your examples aren't good. Those are all rankings (which this isn't) or a countdown. You don't add or subtract rankings, "1st class - 3rd class = 2nd class" for example. I'll grant the countdowns, but you don't add to the countdown if the event countdown to is happening earlier (nor do you often move the event's time). You don't see "bonuses are minuses and penalties are pluses" in a system very often (The game show Debt was one such case). It's not some profound psychological truth that subtraction is harder than addition though.

3.X's system works better for a larger range of attacks and armor classes. A great wyrm red dragon has an AC of 41 and a BAB of 40. In THACO terms, this would be AC: -21 and THAC0: -20. So a dragon attacking another dragon with just BAB (mods cancel each other out or something) would use the following formula (Hit if Roll+AC>=THAC0) would be Roll+-21>=-20. It's the same as 3.X's (Hit if Roll+BAB >= AC) Roll+40>=41. The math works out the same, but you don't encounter negative numbers as often elsewhere.

THAC0 isn't a fundamentally bad system. It's just inelegant and doesn't add anything.

[Reinboom]

The comparisons given are quite different uses of numbers.
"What comes first" (1st rank), is a positional statement and not a variable or quantitative statement for number usage.

A countdown is variable, however, it doesn't have a constant adjustment greater than 1 (and if it did, you would get people calling out "unintuitive") and also, more precisely, its a physical measurement (of time) in this case.

Next, neither "1st" or a countdown will, in normal situations, continue below 0. A full to empty comparison for lack of not remembering a proper term. You will also notice countdowns start at 10. Both of these have the same origin and they are still considered intuitive for a rather simple reason. Most humans have something that can easily be set to a count, fingers. Fingers rarely go negative.



However, bleh to the unintuitive argument, that'll get nowhere.
Since AD&D 2e (don't have much knowledge of 1e) is a system at a whole with many things increasing (HP, thief skills, spell levels, level, attributes...) having a set of character defining terms work in two different directions has always made one or the other feel backwards, at least to me. Especially since some of them tie to each other. You increase your dexterity to lower your AC, for example.

Then there comes the larger issue of how bonuses are determined throughout the books.

As Cubey mentioned, the real problem was with imprecise bonus/penalty nomenclature, which sometimes had to be guessed from context (Hmm, Berserk Rage = +2 to hit and +1 armour class...?)

As matthew mentioned that Cubey mentioned.

And finally... why not positive/BAB? What does THAC0 have 'over it'?

[Aquillion]

Also, regarding the ubiquitous "It's unintuitive!" complaint: No it isn't. You're misusing the word. "Unintuitive" would mean that humans are inherently built to equate "higher number" with "better quality".

That's not it. The problem is that in 2e, the game would sometimes use higher numbers to indicate 'better', and sometimes use lower numbers, with no clear reason for the difference.

On top of this, the fact that nearly everything except armor used "plus = better" meant that designers and writers would write an armor as "+1 armor", which would mean that it had a lower AC. That is stupid, and there is no way you can seriously argue that that's not pointless complexity -- why not just set it up so +1 armor has one higher AC?

It's not a huge thing, but when you reach the point of having a sword with a "+1 bonus to hit" alongside an armor with a "+1 bonus to AC", it's easy to see why people would argue that it's better to just flip AC around.

It's not a huge earth-shattering impossible-to-understand complex thingy. But if a suit of armor has AC 5, a +1 version of that armor ought to have AC 6, and the AC 6 should be better. It's hard to make a logical argument for 'intiuitive' vs 'unintuitive', but I don't think it needs much explaining to show why that is more intuitive than the reverse.

[Kurald Galain]

Also, regarding the ubiquitous "It's unintuitive!" complaint: [i]No it isn't.

What they actually mean is that it's inconsistent. In 2E, some mechanics are "roll 1d20 under target number", some are "roll base plus 1d20 over target number" and yet some others are "roll 1d6" or "roll d%".

What is unintuitive (to some people) is not any of these individual mechanics, but the fact that all of them are used throughout the game, without a clear reason why certain kinds of roll use different mechanics.

3E, whatever other flaws it may have, at least is consistent in that every single test uses "base + 1d20 >= target".

[Cubey]

And, likewise, I predict that when Fifth Edition comes out, people will mock 4E for having such "difficult" concepts as that a "burst 3" isn't the same size as a "blast 3".

It is not the same thing, however. Blast and burst are well-explained mechanics, their terms may mean the same for the layman but for someone who knows their DnD terminology it won't be a problem. It is not the case with some of stats in 2nd ed. Not because they're difficult to work with (they aren't), but because modifiers aren't perfectly clear on whether they upgrade or downgrade the attributes, due to the fact that attributes increase as they go lower, but some increases are written as +[attribute], while others as -[attribute].

Here's an example: Let's assume we have a fighter with 2 AC. He finds a magical ring that, as its fluff description says, makes him tough and hard to move like a stone. Crunch bonuses: 25% physical damage resistance and +1 AC. The first part is obvious. The other is not - does it make his AC 1 (because he's harder to hit due to his stone-like qualities) or 3 (stones are, obviously, slow)? As you can see, it could be interpreted both ways, and each of them would make sense.

[Kurald Galain]

It is not the same thing, however.

Nevertheless, wanna bet that it confuses people? And that people in the future will be glad that this so-called artificial distinction is gone?

Here's an example:

That's a bad example, because you're purposefully making up something that's confusing (as opposed to the actual rulebooks, which are generally quite explicit about whether something is a bonus or a penalty).

Here are some actual examples.

[Cubey]

Nevertheless, wanna bet that it confuses people? And that people in the future will be glad that this so-called artificial distinction is gone?

Yeah, but that's because some people are really bad at rules. As in, "can't count your +attack by adding BAB and bonuses" bad.

That's a bad example, because you're purposefully making up something that's confusing (as opposed to the actual rulebooks, which are generally quite explicit about whether something is a bonus or a penalty).

Here are some actual examples.

That's good to read, yet I recall there were situations where, while not as confusing as my deliberate example, sometimes modifiers WERE in fact unclear on whether they are a bonus or a penalty. It might've been just lousy translation though.

[ericgrau]

I've seen people who have enough trouble with addition as it is. It's a sorry state that math classes are in, but what can you do? Anyway I've heard of 2nd ed people converting THAC0 to AB while sticking to 2nd ed. You could always do that.

[Noneoyabizzness]

it is unintuiitive.

you roll high to hit a lower number which is a better ac.

this is why it is better the bab system 10=0. -10=20, thac0 converted. made to be intuitive.

kinda like 2e skill checks needed to roll lwer than your stat to make the check.

[Matthew]

it is unintuiitive.

you roll high to hit a lower number which is a better ac.

this is why it is better the bab system 10=0. -10=20, thac0 converted. made to be intuitive.

kinda like 2e skill checks needed to roll lwer than your stat to make the check.

It just depends on your own experience. For a long while I considered it "unintuitive" or "unnatural", so I was surprised to discover that my girlfriend found THAC0 a much easier concept than AB. Similarly, I was surprised to find people who really found THAC0 a hard concept even after explaining it in the simplest possible terms I could think of. As with preferences towards games, not everybody is the same, what is unintuitive for one, may be intuitive for another.

As I mentioned above, though, THAC0 is just one step ahead of AB, giving you the target number for armour class 0, rather than the number to add.

A) D20/3e = 1D20 + modified attack bonus = target armour class
B) AD&D/2e = 1d20 + target armour class = modified THAC0

A) Player: "Okay, I rolled a 15 for a total of 22." *Game Master checks armour class* "That's a hit, roll damage."
B) Player: "Okay, I rolled a 15 and have a THAC0 of 13" *Game Master checks armour class* "That's a hit, roll damage."

[Noneoyabizzness]

It just depends on your own experience. For a long while I considered it "unintuitive" or "unnatural", so I was surprised to discover that my girlfriend found THAC0 a much easier concept than AB. Similarly, I was surprised to find people who really found THAC0 a hard concept even after explaining it in the simplest possible terms I could think of. As with preferences towards games, not everybody is the same, what is unintuitive for one, may be intuitive for another.

As I mentioned above, though, THAC0 is just one step ahead of AB, giving you the target number for armour class 0, rather than the number to add.

A) D20/3e = 1D20 + modified attack bonus = target armour class
B) AD&D/2e = 1d20 + target armour class = modified THAC0

A) Player: "Okay, I rolled a 15 for a total of 22." *Game Master checks armour class* "That's a hit, roll damage."
B) Player: "Okay, I rolled a 15 and have a THAC0 of 13" *Game Master checks armour class* "That's a hit, roll damage."

b) yes nce you get it thac0 is easy. because 15 with thaco 13 is ac -2
a) rolled 15+7 to totql 22which equals ac 22.

they both equal the same result but 22=22 is a quicker more natural jump in logic than 13-15=-2

realized shoulda had 3e ac 10=10 -10=30. my err

[Matthew]

b) yes nce you get it thac0 is easy. because 15 with thaco 13 is ac -2
a) rolled 15+7 to totql 22which equals ac 22.

they both equal the same result but 22=22 is a quicker more natural jump in logic than 13-15=-2

realized shoulda had 3e ac 10=10 -10=30. my err

For some folks it is, for others it isn't. I find both equally simple, but I know folks who feel one way is better or worse. It's all preferential, rather than absolute.

However, what the game master actually does is add the armour class to the roll and compares it to the THAC0, not deduct the roll from the THAC0 [i.e. 15 − 2 = 13 = hit].

[Who_Da_Halfling]

To my mind, the 3e system is simpler. I never played with 2e, but i heard about concepts like THAC0, which sounded complicated (even though it isn't, really), which made the game more intimidating. It also means a little less work for the GM, since in my experience the 3e system's attacks are very easy to explain simply while, from what people have said here, a lot of people had trouble explaining THAC0 in the simplest way.

Of course, I always forget to write down FF and Touch ACs, so I end up having to do a lot of extra math anyway, so that ease is negated...

-JM

[Neek]

THAC0 and decreasing armor. I loved it so much. I'm not a defender of the system, I'm just a man who enjoys it.

A friend of mine once said that D&D originally was a group of differing systems working in conjunction with one another. AC and THAC0 worked well together, but they could replaced with another system, and not a whole lot needs to be changed. Same with saving throws. Same with skill systems (which is why there's two systems present in the PHB). It's better to understand "Saving throws" as one system, and attack rolls as another. Each component of the game is more or less modular in this respect--there are some lovely variable rules, however, such as turning attacks into opposed roles: Attack roll versus armor roll (d20 + AC modifiers), but twisting the game around to accept THAC0 is a bit more difficult, but the mechanics are already set. Try adding in a NEW combat system and see what you have to work with.

As for Armor Class bonuses, I never had a hard problem understanding it. Your gear's Armor Class is deducted from your base AC of 10. So a Chainmail +1 has an AC of 6. Deduct that from 10. You have your AC, 4. A ring of Protection +1 gives you an additional point of armor, 10 - (6+1) = 3. This has never been a hard concept for me to understand.

Your THAC0 is modified by their AC. You subtract their AC from your THAC0 and that tells you what you have to hit (so, To hit = THAC0 - AC). If your THAC0 is 20, and their AC is 10, you need a 10 or better to hit. In 3rd ed, with a +0 BAB and no other modifiers, you still need a 10 or better. I don't think the intent behind the mechanics have changed much. They just became less mathematically involved.

The math was an annoyance not because we weren't good at it, but because it detracted from the game. I don't think the time for combat has gone down, however, because we're doing less math, but because we're trying to remember all the variables (am I flanking this guy, did I remember to add my Bless bonuses?, et qqd.)

Still, I had fun with either. It doesn't matter to me much, but out of preference, I enjoy the d20 method more.