Quick AC/THAC0 Question

[Blackdrop]

Quick question for people with some 2e system mastery:

Is there anything about the AC/THAC0 system that prevents you from just...inverting the entire thing? I.E., making -10 the AC for an unarmored character and 10 the Maximum? Also, obviously, inverting the Modifiers on the Dexterity table and making magic armor add to your AC rather than subtract.

As far as I can tell inverting it shouldn't cause any catastrophic changes, but I just wanted to double check with people that know the system better than I do.

[meschlum]

If you're using 2e, you should be fine. Per page 53 of the DMG, natural 1s are automatic misses and natural 20s are automatic hits, so you can just compute the necessary roll and be done with it.

Hint: if you add Armor Class to the attack roll, you hit when your total is 20 or more (or on a natural 20, if your final modifier is negative). That said, if you want to switch the bonuses around, you can easily see why later editions adopted AC = 10 + bonuses as a target roll.

You might also want to check some monster ACs, as I believe some of the great wyrm dragons could get ACs below -10, but that's just math.


Had you been using 1e instead, you'd have to deal with pages 73-75, which have a roll of 20 repeated 5 times before increasing. So bonuses to hit are better than penalties to AC in some weird edge cases, because of course (and page 73 says you can treat bonuses to hit as penalties to AC, naturally). There is also some mention of natural 20s hitting, since it makes things more confusing if so.

[LibraryOgre]

Not really; you have to recalculate ACs on existing things, and it's a bit more popular to stick with 10 being the base AC, and climbing from there (so leather gives you a +2 to AC), but there's no reason you can't invert it if you want.

[Anonymouswizard]

It's basically what 3e did, going from 'THAC0-attack roll=AC' hit to 'attack bonus+roll=AC hit'. having AC start at -10 instead of 10 (or 9 in Basic)makes it a bit more difficult.

The big thing is you're not going to get rid of subtraction easily. in fact inverted AC still works better with descending THAC0 if you start it at 0, with you getting roll-THAC0=AC hit. Which is why most OSR games with ascending AC have unarmoured default to about 10 (lotFP uses 12, but it also has characters begin with a higher attack bonus).

[Zombimode]

Quick question for people with some 2e system mastery:

Is there anything about the AC/THAC0 system that prevents you from just...inverting the entire thing? I.E., making -10 the AC for an unarmored character and 10 the Maximum? Also, obviously, inverting the Modifiers on the Dexterity table and making magic armor add to your AC rather than subtract.

No, nothing prevents that.

Even though people like to cite THAC0 as "complicated" it is mathematically the same als 3.x d20+mods vs. DC

[Anonymouswizard]

No, nothing prevents that.

Even though people like to cite THAC0 as "complicated" it is mathematically the same als 3.x d20+mods vs. DC

People have a tendency to think maths is harder than it is, especially subtraction for some reason. Out of the four basic operations three are about as easy as each other and the fourth is division, but because the ones you're most likely to practice in everyday life are addition and multiplication people are much less confident with the other two.

Like, there's nothing stopping us from putting algebra or calculus in RPG mechanics, but even 0e D&D knew they were probably difficult enough not to be fun. THAC0 and descending AC is really just changing a few signs compared to an ascending AC system, and worst comes to worst can be subbed out for a to-hit table.

It's not like your attack roll result is roll=AC²-6AC+9.

[Blackdrop]

Alright, as I suspected everything should be cool to inverted. Thanks y'all.

People have a tendency to think maths is harder than it is, especially subtraction for some reason. Out of the four basic operations three are about as easy as each other and the fourth is division, but because the ones you're most likely to practice in everyday life are addition and multiplication people are much less confident with the other two.

Like, there's nothing stopping us from putting algebra or calculus in RPG mechanics, but even 0e D&D knew they were probably difficult enough not to be fun. THAC0 and descending AC is really just changing a few signs compared to an ascending AC system, and worst comes to worst can be subbed out for a to-hit table.

It's not like your attack roll result is roll=AC²-6AC+9.

Academically, I know that "Subtracting a negative = number go up." But whenever I've had to put it into practice my brain says "Subtracting a number makes it go down, you stupid mouth breather." And since I turned 30 last year and I'm still doing it, I've become somewhat concerned that I'm never going to stop doing it. So, if inverting the system does nothing but remove the thing that makes my brain skip like a scratched CD, then it's getting inverted.

[Anonymouswizard]

I mean, it doesn't help that IIRC the book doesn't suggest the best way to do it. Calculate adjusted THAC0, make roll, subtract roll from THAC0, that's the AC you hit, no need to deal with subtracting a negative number. Well, unless you suddenly have to use a weapon you're not familiar with.

Honestly this is part of the reason I like dice pools. People can generally do this stuff, but the feeling that it's harder tends to matter. Dice pools tend not to require anything more than counting, adding/subtracting physical dice tends to help people, and some systems even just use a 'highest rolled number' system. Normal people are fine with such systems, although mathematicians sometimes struggle

[Khedrac]

Like, there's nothing stopping us from putting algebra or calculus in RPG mechanics, but even 0e D&D knew they were probably difficult enough not to be fun.

The classic example of how not to do this is Marc Miller's Traveller (4th Ed). He tried to keep the physics as real-word as possible so one of the rulebooks is basically a book of all the physics equations (for things like rocket launch from ground to orbit, artillery range etc.). Having written a book that was basically 50% equatiosn and 50% telling when to use them, they then accepted so-called "printer's proofs" that used a different set of fonts to the actual printers, and thus produced a book where 75% of the formulae were wrong, the font used not actually supporting all the characters used in the equations (the main two that got substitutions were the square root symbol and the obelus division symbol)...

[subtledoctor]

I don't fully understand what OP intends to change here? You only mentioned inverting AC, so, you want change attack rolls to a roll-under system? Or, I guess just subtract AC instead of adding it?

Thac0 is not actually a score or attribute, it is just a roll target. The reason "lower is better" with thac0 (which people seems to drive people crazy) is that you want to roll higher than it.

Math:

attack roll >= thac0 = hit against AC 0.

Of course, some enemies have different AC. So the modified equation is:

attack roll + AC >= thac0 = hit

You could invert AC and subtract it instead of adding it; that would make AC like 3E+, but thac0 would remain a "lower is better" term so for some people it would not solve the "problem" with thac0. If you do this then thac0 becomes like an inverted BAB:

attack roll - thac0 >= AC = hit

Or to eliminate subtraction you could apply the attacker's thac0 as a bonus to the target's AC:

attack roll >= AC + thac0

As stated, all of this math is essentially identical, the only real difference is what you mark on a character sheet.

[Lo'Tek]

I've tried a variant that follows the principle of "add good effects and substract bad effects from the number you announce" (armor class one has, armor class one hits). I like it because when someone says "remember you have +1 from ..." I can just add 1. And it is mathematically equivalent to the 2nd edition to-hit and armor class system. (i've never played 3rd, but from rumors this may be close to how 3rd does it)

AD&D Thac0 weirdness, switching between adding and substracting and powerful creatures having an ac below 0, all comes from comparing the rolled value on a d20 to the maximum possible value on a D20. At level 1 the armor class one hits is the difference between the roll, and the maximum possible roll. Mathematically that is "AC^hit = 20 - d20". AD&D adds positive effects to the dice roll, and substracts negative effects from it: "AC^hit = 20 - (d20 + boni - mali)". But instead of adding a class based bonus that scales with level, this leveled bonus (LB) is substracted from the target number: "thac0 = 20 - LB" and thus "AC^hit = thac0 - (d20 + boni - mali)". (compare modified dice roll to thac0) One can move the leveled bonus (LB) and handle it the same way as any other bonus instead of making it something special: "AC^hit = 20 - (d20 + boni+LB - mali)" This result in the same AC^hit as before.
I went one step further by not taking the difference between 20 (or thac0) and the modified dice role, so that "AC^hit_new = d20 + boni - mali" Doing this however means changing the armor class of everything, AC_new = 20 - AC_old That sounds complicated, but actually creates a nice system, because positive effects now increase armor class, instead of decreasing it.

Defending

AC_new = 20 - AC_old

An unarmored human had ac 10 and now has 20-10 = 10
Wearing chainmal grants 5 points, so that is 5 -> 15

AC_old = 10 - boni + mali
AC_new = 10 + boni - mali

Adventurers typically start with 10, add positive effects and substract negative effects
A creature with AC_old of -8 in the monstrous manual has an AC_new of 20 - (-8) = 28

Changing everything mentioning AC in the books is the second largest hurdle after changing what i am used to.

Attacking

AC^hit_new = d20 + boni - mali

The "to hit improvement by class and level" is a positive effect: +1 per level above 1 for fighters, +1/2 for thieves, +2/3 for priests. level_bonus = 20-thac0.
The most annoying part with this is the "level -1" thing.
Other to hit boni may come from strength, magic weapons, spells like blessing and so on. These are already noted as +X in the books

Example:
A level 4 elven fighter has a level bonus to hit of +3. Attacking with a bow their high dexterity grants them +2, and being an elf another +1. However an enemy had cast blindness on them, which is -4
Roll a d20 + 3 +2 +1 -4. With a roll of 12 the elf hits armor class 14. A lizard man has an armor class of 16 (by the book 4). So that is a miss

By the book our elf compares the modified attack roll of (12+2+1-4) with a thac0 of (20-3), and announces hitting AC_old of 6.

"Don't forget you get +1 from blessing"
old: oh yeah. i hit 5, not 6
new: oh yeah i hit 15 not 14

[Zombimode]

You guys make a very simple problem sound very complicated

But yes, Lo Tek, your description of the process of converting AD&D style attack bonus and AC numbers to 3e+ style numbers is correct.

[kyoryu]

I think the biggest issue with ThAC0 isn't that the math is hard, but that it is unintuitive.

D&D 3.x AC is very intuitive. "AC is how hard they hit. More protection = higher AC, so more is more. Your attack bonus is how good you hit, more is also more. Roll a die, add how good you are, and see if it's good enough". It's just intuitive.