Fixing ThAC0 once and for all

edited April 2013 in Make Stuff!
For people who are into D&D and retroclones, there's always the discussion about how to deal with "to-hit" rolls. ThAC0? Descending AC or Ascending AC? To-hit cross-referencing charts, or attack bonus by class? And so on. How do we calculate the hit chance, compare it to an armor class, and get a result? How much math is involved? How intuitive is it, do we need to reference a chart, do we need to subtract numbers?

By using some math, many different formulae are possible. For instance, "Delta's D&D Hotspot" uses the following calculation:
Attacks: d20+HD+AC ≥ 20
Uses (old-school) descending AC.

This means you roll and add numbers (except for negative AC, I suppose), and then always compare the result to 20.

I don't know how I feel about this method, but it's an interesting one in that it's mathematically identical to the original D&D rules but is very different to use!

Browsing that blog, I came across a few other interesting ideas. Here are two ideas that jumped out at me, rewritten a little bit:

Option One
A way to cut out math pretty much altogether, for everyone involved. Just compare two numbers.

This one is pretty cool, with only two drawbacks I can see:

1. Those high d20 rolls are no longer necessarily good. (Could be a problem if you're seriously nostalgic. But it wouldn't be too hard to add in a "natural 20" critical hit rule if you just can't live without.)
2. If you want to extend your attack bonuses or armor classes past a 0-10 range, you may need to involve some funky math for very advanced characters.

Here's how it works:

Each character has a "to hit" number, the higher the better. Let's say the "to hit" number starts at 11 and you add applicable modifiers (e.g. +2 for Strength, +3 Fighter's attack bonus, or whatever). Any time you roll higher than this number, it's a miss. If you roll lower, tell your target what you rolled; they'll tell you if you hit.

Each character has an Armor Class, the higher the better (probably in the 1 to 10 range). Your opponent's roll has to beat your Armor Class to hit you.

That's it! Pretty elegant.

I roll a d20. If it's lower than my "to-hit" number, that's my attack roll.

The target compares my attack roll to their Armor Class. If it beats the AC, it's a hit! Ouch. But pretty slick.

The only potential problem is that if you want your "to hit" bonuses to cover a range of more than 10 or so, you'll need to add some rule for what happens if your "to hit" number exceeds 20. I can see two easy options:

1. When your "to hit" number exceeds 20, subtract some number (would have to do the math to figure out what number) and add other dice to your roll. Maybe you subtract 5 points to roll a d10 along with your d20, and keep the better result, or something like that. Or you just get to roll two d20s and keep the best one (or just plain old make two attacks per round!). Something like that.

2. The scale "wraps around". This emulates the way D&D's "to hit" bonuses normally work much better. To do this:

When your "to hit" number exceeds 20, subtract 20 from it and write it down with some kind of special symbol. So, 25 becomes 5!!!.

From now on, any roll is compared to the target's Armor Class (there's no such thing as an automatic miss). But if you roll less than your new "to hit" number, add 20 to the result. (So, if you roll a 3, treat it as 23.)

Personally, I would just cap the number at 20, I think, but this second method is mathematically identical to the way D&D normally works, so that may help if you're using some kind of conversion from a certain system.

As I mentioned before, you can keep the "natural 20" effect if it's important to you. Just increase all the numbers by one, and have all natural 20s be automatic hits.
Option Two
Use a narrowing range of numbers, which are recorded by the target. This is not at all identical to how D&D works! It's a totally different way to use the d20 roll. I'm including it simply because it's so different.

First, you have some kind of basic miss chance. Maybe it's based on your Dexterity or natural AC or dodge ability or whatever. Maybe for a normal human, it's 1-7. So you write that down.

Second, any armour you wear reduces damage by a certain amount (and it can be a pretty good amount, no need to be stingy here). How extensive is the armour? Write down how many body parts are covered:

[this list is from the blog comments]
one arm or partial both arms
+other arm or rest of the arms*
one leg or partial both legs
+other leg or rest of the legs*
Upper left body*
Upper right body*
Lower left body*
Lower right body*

*-the armor can optionally only cover part of a section of the body. You could just protect one arm, or wear gauntlets on both arms.

For each body part covered, add 1 to your "armour range" (there are 10 body parts in this list, so this is a 0-10 value; you could design it some other way, of course). This range either begins where your "dodge/miss" range left off, or it starts at 10. (Depending on how quickly you want to be able to calculate it on the fly.)

When someone rolls to hit you, they just say what they rolled. (And optionally add some kind of hit bonus to their roll.)

On your sheet, you write down your ranges. Let's say the basic miss range is 1-7, and you're wearing heavy armour on your torso (4 areas), a helmet (1 area), and your left arm (like a gladiator -- one more area), for a total of 6 armoured areas. So, on your sheet, you write down:

1-7 Dodge
8-13 Hit to armoured area
14+ Hit to exposed area

So, when your opponent tells you what they rolled, you look at the chart and you know whether you a) avoided the hit altogether ("Dodge"), took a hit to an armoured area (in which you subtract the armour's defensive value from the damage), or got hit somewhere which really hurts.

It's neat in that it requires very little math in actual play: I roll a number and add something and then tell you what it is, and you tell me what happened. Knowing whether the hit was to an exposed area or not could also be important for, say, skin contact attacks or something like that.

But now we're pretty far afield from how D&D works!

What clever methods have you seen? Why do you prefer those over others?

Can you come up with any other d20-to-hit variations with interesting side-effects or cool math?

My favourite attack-roll-type rules are those which combine the quality of the attack with the damage dealt. So you don't get the "lousy hit, high damage roll" or "amazing blow, lousy damage roll" kind of disappointment effect. Do you know of any D&D variations which do this elegantly?


  • edited April 2013
    I got a variant of option 1, but it's more BRPish (Fading Suns style) than d20.

    - Add 10 to your Str/Dex ability score and that's your to-hit.
    - Roll equal or under your to-hit, but higher than your opponent's AC (which is [Dex/Int]+AC or the armor's AC), to damage your opponent.

    If your to-hit is increased beyond 20, it's turned into ≤X instead. So five higher than 20 is written ≤5. This means that you will succeed as long as you roll over the opponent's AC or equal or below your own value (five in this case). You will crit if you roll the same number as your to-hit value.

    EXAMPLE 1: You got a to-hit of 18 and the opponent an AC of 5. You will succeed if you roll between 6 and 18 and a crit occurs on 18.

    EXAMPLE 2: You got a to-hit of ≤3 and the opponent an AC of 14. You will succeed if your roll is between 1-3 or 15-20. You will crit if you roll a 3.

    The downside is the tricky way of handling crits. I also don't really see the point with my suggestion, because 1d20+value vs AC is still a simpler way of handling it (OK, my variant got no addition) AND it follows the general d20 idea of high is always good. I guess the same goes with your suggestion as well.
  • The number to hit is: 19 - AC (except 20 always hits, 1 always misses)
    Monsters have a to-hit bonus of + HD (-1 if < 1HD)
    Characters have a to-hit bonus of: +Str bonus in melee, +Dex in missile,
    and if their level >= 4 +2

    This is exactly the same as Moldvay, except for monsters of >10HD


  • I like that, Rickard.

    robb, I'm not sure I follow. What does "if their level >= 4 +2" mean? Otherwise, that just looks like the basic D&D rules to me!
  • edited April 2013
    Attacks: d20+[attack bonuses]+AC ≥ 20

    is by far the easiest, in my experience (Stars Without Number uses this method). If the AC is negative, you subtract it from the roll (adding a negative number means subtraction, as we learned in school :).
  • Right on. That's what "Delta" uses.
  • I think I've plumbed this well pretty deeply myself. I've ended up preferring the boring old 3rd edition calculation of d20 + bonus vs. DC. The reason is that it distributes responsibilities for the numbers "correctly" (player calculates his character's quality of performance, GM calculates the resistance), which then provides maximum flexibility with e.g. whether the player knows the target number or not. It's the overall simplest vehicle, enabling you to focus on elaborations.

    I use the attack roll mechanics universally for all checks (again, like 3rd edition), and there's no particular guarantee that the bonuses would stay within certain ranges. (My conceit of doing ability+d20 instead of transforming the ability score into a smaller bonus range means that even 1st-level characters can theoretically have up to 20 points of difference in their bonus stacks.) The various roll-under mechanics require fiddling to achieve big variations in the ranges, which is contrary to my own convictions about what D&D does - to be specific, I think that D&D's mathematical sweet spots happen when the various bonuses derived from the fiction end up causing pretty large swings in the numbers involved. It's not that exceptional at my table to have two bonus stacks differ by e.g. 10 points, and 20 is also routine.

    (Many feel that big swings in bonus stacks are a huge problem in D&D, as most specific mechanical applications have a huge bonus mean that it does not matter what you roll on the d20 - you drop "out of the RNG". This is not the case in my implementation, as I rely heavily on degrees of success, which in turn have supralinear impact on the outcome - the roll will matter plenty even if you're down or up 20 points. For example, a fighter who is in such a superior position that they are guaranteed to hit is no longer rolling about the hit - they're rolling about whether they'll one-shot their foe, skipping the hit point damage step altogether.)

    One thing I've noticed is that many people in the Internet seem to find avoiding addition and subtraction a compelling argument for the mechanical aesthetics of this type of roll. I have to honestly say that this has not been a factor in my gaming experience: players do not complain, and even newbies without a mathematical background (teenage girls, say) seem to buckle up and rise to the challenge of summing 17 + 11 when they're asked to. I would certainly not be surprised if this was some sort of cultural difference between schooling environments, attitude towards mathematics, etc.

    Also, one thing to consider here is whether you wish to build your combat application to utilize armor class or armor bonus. The difference is subtle, it's about dynamic vs. static target numbers: armor class thinking is that the game setting includes several relatively routine combat situations that each have their own static difficulties to perform. Armor bonus, on the other hand, thinks dynamically: the difficulty of combating a given foe successfully depends on their bonus stack, which consists of all sorts of variables that are summed together.

    The armor class thinking, as I describe it above, was dominant in early editions of D&D: hitting a man in leather armor was a different type of task than hitting a man in plate mail, and they each had their own degree of difficulty technically independent of the other. The concrete mechanical solution happened to resemble "having an armor bonus" a bit, as you could derive to-hit target numbers by adding and subtracting numbers, but the underlying thinking was different. This can be seen in e.g. the weapon vs. armor tables. Abilities did not originally affect your armor class, either - how could they, when your "armor class" meant what type of armor you wore in the fiction.

    I personally like static target numbers in D&D. There are various good reasons for this (stopping bonus inflation being perhaps the most prominent), but my most idiosyncratic one is simply that it's interesting to play with static target numbers when all the modern post-Forge game design generally relies on Heroquest-style relative contests. Due to this preference of mine, my D&D implementation has a very static armor class implementation: even an extremely high-level player character will generally have DC 20 to hit them unarmored, DC 30 when in full plate. (Routine ability to dodge attacks and whatever is represented by hit points, while very high-level characters use various special maneuvers to supplement their static armor class.)
  • My personal favored solution was just to switch to a roll-under system. You can even use positive AC if you make AC into the lower bound of your roll-under.

    In other words: if your Attack is 14, and you're fighting a creature with AC 3, you hit on a result of 4-14. An AC 2 would let you hit on a result of 3-14. Nice, painless, works pretty well in my thinking.
  • Eero,

    I'd love to hear more about how you handle armor class and damage in your game, and how it's affected by special maneouvres and range of success (I think you mentioned at some point that you use 5-point ranges, and count levels of success beyond the basic difficulty).
  • @CarpeGuitarrem:

    That's "option 1", above! I like it too.
  • I should also say that I like "option 1", it's elegant. I don't feel that it's very D&D (it's a game of epic scope, you're gonna hit that 10-point cap unless you limit the game to levels 1-3), but mechanically it's a beautiful idea. Also, as we've seen in this thread, you can go all Heroquest on the cap and start counting masteries in various ways, so it's not an insurmountable issue in any way.

    Regarding armor class and damage in my homebrew D&D, here's the short story of how attack and damage works:

    Combat consists of discrete actions that are arranged by the initiative system (a separate topic, really). "Attacking" is a basic sort of action you can declare in combat. In the D&D tradition we have a default attack move that is used where nothing else applies; the system doesn't really care about the fictional particulars of how such an attack is performed, it's just a a choice of weapon, declaration, check of validity (are you range and capable of launching the attack with the weapon in question) and then a general "to-hit" roll of the dice. In my campaign this attack is made as d20 + [ability score] + [attack bonus] + [conditional modifiers] roll, which is then compared to a difficulty number. A result of 20 might be considered average, all told, but the system is pretty swingy in several ways, so your average 1st level fighter might be expected to hit 25 pretty consistently. Getting bonuses and penalties ranging from -5 to +5 isn't that difficult, either, as many kinds of fictional detail provide those.

    The target number that the attack roll is compared to is derived as follows:
    • The normal target number, and the general minimum, is the target's armor class, or "passive defense", representing the inherent difficulty for the attacker to succeed in their task resolution. An unarmored human has armor class 20, and it goes up from there pretty according to the usual D&D numbers. A blind human is at 15, immobile (or surprised) human is at 10, for comparison - 5 points of your armor class are considered to be caused by dynamic reacting to environment, and another 5 points by human capability for movement, so that's what we shave off when these basic defensive capabilities are compromised. (See the next step, this immobilization stuff is just an application of that.)
    • Armor class is generally modified by very few special considerations. This is because almost all environmental or inherent conditions of the fictional situation are wrapped into bonuses or penalties on the attack roll, and supposed personal ability at e.g. dodging is handled by other mechanisms (see below). Magical armor may give armor class modifiers, but that's just about everything.
    • If the attacker declared a special attack or "called shot" of some sort, then the target number determined by the armor class might be modified or substituted. For example, an attack to trip an opponent generally ignores armor, so the DC is determined by the referee without regard for the armor class (usually it's 20 - equal to attacking an unarmored target). The methodology for making rulings on these alternative DCs for attacks is somewhat intricate, but practically usable in the end, once the referee masters the probability math of the bonus+d20 random distribution - basically the referee looks at comparison benchmarks ("Is this more or less difficult a feat than this other thing for which the DC is already known?"), realistic balance ("What factor am I ignoring, for my proposed DC to come out so difficult that this realistic action could never happen, or so easy that this seems unrealistically preferable a choice?") and system elegance ("Does setting this number achieve some elegant comparison to a similar situation, is it easy to remember in the oral tradition, is it neither too detailed or too vague a ruling in comparison to our rendering of the fiction?") to make their call. Usually the answers are really easy, I don't seem to get into the sort of decision stress paralysis that some GMs get.
    • An "active defense" is when a character specifically acts to dodge or block an attack. Doing this costs 2 points of initiative (yes, it's individual persistent initiative, 3rd ed. style) and barring special feats requires either a shield (a shield doesn't give AC in this system, it just enables this action) or a prepared action to dodge. The active defense is produced essentially like an attack roll, with the defender rolling for it. If the result is weaker than the character's armor class, they use the better defense, so you can't worsen your defense by actively defending.
    Note that this isn't a prescriptive procedure, but rather merely descriptive: these are the considerations that tend to occur routinely. If we pinpoint other defensive factors in the fiction, then those are folded in in various ways. There could be e.g. defensive spells cast, which usually don't manipulate armor class directly in D&D (Mage Armor is an exception, really).

    The keen observer will at this point note a few remarkable qualities of my system: the active defense conceit is generally more useful for higher-level characters, and as armor and skilled defense do not stack, a higher-level character therefore has somewhat less interest in wearing armor at all. Also, as attack bonuses (of fighters, mainly) rise relatively unchecked at higher levels, while armor class remains in a pretty static bracket, the game inherently requires characters to solve the issue of defense in some way not inherent in the armor class system. This is all very intentional: my theory on what D&D experience levels represent is dramatic exceptionality, so it works for me quite well that armor is a life-saver for low-level characters, while being more of a stylistic choice at higher levels.
  • The significance of producing an attack result and defense result is that D&D has a "you need to be this high to ride" combat system: a character who cannot reliably overcome the AC of the opponent has a drastically lessened impact on anything at all. Conventionally this is called a "miss", even if it's not all that clear-cut in the fiction. (I go with one-minute combat rounds, and specifically deny that an "attack" action in combat has any particular relationship to a sword being swung in the fiction.)

    Anyway, characters who miss in combat achieve nothing, generally speaking. The opponent might have some special feat that activates on a bad enough miss (a "counter-strike", for example), but the basic outcome is zilch. This is an intentional preference, as that's just how D&D combat is - removing it messes with timing of combats, as individual combat rounds are guaranteed to achieve some outcome.

    Assuming that a character does pass the defensive barrier of the defender, though, this has a few immediate procedural effects:
    • A degree of success is calculated: passing the DC is °1, and every full five points increment after that is another degree. A natural '1' on the roll gives one "degree of failure" that may either be deducted from the successes, or utilized laterally for a sort of "partial success" effect - you hit your enemy, but also trip and fall, for example. A natural '20' either explodes or gives an extra degree of success, depending on taste - both are fine mechanics, it just depends on how much variance you want in the dicing outcomes. (A degree of failure is calculated the same way but to the opposite direction, incidentally, although it's not used as much in practice.)
    • After the degree of success is calculated, and usually before the damage is rolled, the player may declare "stunts" to allocate any extra degrees of success in the attack to various effects. This basically represents how the character found performing their combat action to be so easy that they managed to do that as well as get a little bit extra. For attack actions normal stunts are disarming, tripping, blinding (for one round with e.g. sand to the eyes) an opponent, swinging on chandeliers, hitting in a particularly destructive way, hitting two enemies with the single attack - whatever small, discrete action the player can describe in the fiction. A °5 success (a full 20 points over the DC) is an extreme example: it can be used to bypass hit point damage altogether, causing an immediate critical hit against the foe, which is usually pretty much a save or die effect.
    • One degree of success is ordinarily mandatorily taken up by the basic effect of the attack, so a player can't declare one action and then stunt it into another after the roll. That °1 buys you the default effect of your declared attack, which usually would be some hit point damage depending on the weapon (although you can declare a more specific attack as well when choosing your actions in combat - if you specified that you attack to trip, for example, then that's what your first success would buy).
    The above is pretty much all there is to it by default. Various special skills and feats and whatnot will obviously modify things in all imaginable ways - that's their purpose, to be an exciting and varied mechanical layer over a simple basic structure. I don't go for 3rd ed. style character builds, though, so usually pretty much everything that makes sense in the fiction can be tried mechanically as well by all characters, and you cannot actually become mechanically more competent in doing things that cannot reasonably be trained or specialized in in the fiction; you don't need to get a "Tripping" feat to try to trip an opponent, and so on. The stunting rule carries a lot of weight, as do the principles of dynamic DC rulings: a player can declare e.g. that they'll attempt a trick shot to the eye, and the system enables us to make a ruling and determine what happens, all without ever causing artificially favoured tactics to arise - and that's what I count a success in a D&D combat system. (I refer here to the tendency of homebrew rules ideas and rulings to deconstruct the rules system destructively. For example, called shots have been instituted in the game uncounted times by homebrew efforts, and the usual outcome seems to be either a rule that nobody wants to use, or a rule that starts dominating the game as players rely on it over all proportion.)

    I probably explain all this in an unnecessarily complicated way in an attempt to be analytically exact, but in practice this is a really easy system - we run it all completely without written notes, as an oral tradition. The only thing remotely difficult is that the numbers that are totaled or subtracted are often considerably higher than in out-of-the-box D&D: you might have an Ability at 14, +4 attack bonus, various condition modifiers, and then you roll an exploding result for 32. The numbers don't usually go above 50, but I do definitely admit that anybody who dislikes numbers would find making this system flow exhausting, simply because you need to be able to produce and calculate solid numbers at the drop of the hat. Especially calculating degrees of success - if you can't subtract to find the difference between two 2-digit numbers and then divide by five in real-time, then you'll need a differently adapted rules mechanism. My experience is that players don't find this too difficult, though, so I wouldn't change a thing. (Or rather, I'd change things only to achieve a different aesthetic.)
  • Thanks, Eero!

    Very interesting, and sounds like a fun way to play the game. I agree that the large numbers are a bit of a problem, though. (Mainly because I feel like there would be a more elegant way to get the same results without having to deal with those huge numbers all the time.)
  • Very interesting, and sounds like a fun way to play the game. I agree that the large numbers are a bit of a problem, though. (Mainly because I feel like there would be a more elegant way to get the same results without having to deal with those huge numbers all the time.)
    There are, certainly. Not just with the same exact aesthetic parameters. For example, if I'm allowed to drop the traditional d20 roll and ability scores (doesn't look much like D&D mechanically at that point, anymore), then it's easy to get similar granularity and range of outcomes with more robust random distributions with less math by using e.g. dice pools.
  • Yes, exactly.
  • I like AD&D 1e's solution of just writing down your part of the attack chart on a character sheet personally. Sure, it's a pain the times you have to write it down, but is actually faster to resolve than any other method I've seen in actual play.
  • I like AD&D 1e's solution of just writing down your part of the attack chart on a character sheet personally. Sure, it's a pain the times you have to write it down, but is actually faster to resolve than any other method I've seen in actual play.
    I thought I was the only one who felt that way!
    (although I used it more with B/X)

  • How did that chart work?
  • It's just a number of armor classes from the teens to the negatives. Under each you wrote your to-hit number. That way you just say 'It's armor class six, so I need a fourteen..." and roll and beat fourteen.
  • …or, if you don't know the AC number, you roll and declare "I hit AC 6 or better!".
    Which is actually a clunkier version of playing with ascending AC, you know.
  • …or, if you don't know the AC number, you roll and declare "I hit AC 6 or better!".
    Which is actually a clunkier version of playing with ascending AC, you know.
    My impression was that it was more an issue with multiple mods (and two digit) mods that made ascending AC a clunky system out of an otherwise sensible and straight forward system.

  • It still sounds pretty complex compared to some of the simpler options being discussed here, though.

    Compared to Option 1, for example, you've got to make a chart (and update it when necessary), find out what the Armor Class is, look up the result on the chart, and compare your roll to that. And that's before any modifiers get involved.
  • …or, if you don't know the AC number, you roll and declare "I hit AC 6 or better!".
    Which is actually a clunkier version of playing with ascending AC, you know.
    My impression was that it was more an issue with multiple mods (and two digit) mods that made ascending AC a clunky system out of an otherwise sensible and straight forward system.
    Yeah, that sounds like a sensible observation. Way too many positioning-related factors and other circumstantial modifiers (things you can't just write down under a "Total bonus to hit" heading on your character sheet), from D&D 3E onward, are recorded as to-hit bonuses instead of, I don't know, something else (damage bonuses, to-hit rerolls, damage rerolls, initiative bonuses, AC bonuses, etc.).
  • It still sounds pretty complex compared to some of the simpler options being discussed here, though.

    Compared to Option 1, for example, you've got to make a chart (and update it when necessary), find out what the Armor Class is, look up the result on the chart, and compare your roll to that. And that's before any modifiers get involved.
    Have you ever used the system?
    It's pretty much untricky.

  • Oh, I have, and I agree.

    It still requires a few extra steps, though, like finding out what the Armor Class is, and it's hard to apply modifiers.
  • I disagree with Delta’s Target20 system and I would houserule it away when playing SWN or Other Dust (two fantastic games).

    The system, as I understand it, is the following sequence:

    • Player rolls
    • Player adds BAB
    • Player reports sum.
    • GM adds AC
    • GM compares to 20.
    • GM reports result.

    Compared to “Ascending AC with open info”:
    • Player rolls
    • Player adds BAB
    • Player compares to AC
    • Player reports result.

    Or “Ascending AC with secret info”

    • Player rolls
    • Player adds BAB
    • Player reports sum
    • GM compares to AC
    • GM reports result

    Still fewer.

    In any of the systems, you can juggle around the numbers to get things in an order that appeals to you. For example, I love rolling dice after the arithmetic rather than before.

    • Player adds BAB to AC (possibly notes it down or remembers it)
    • Player rolls
    • Player compares to sum
    • Player reports result.

    Future rolls vs the same AC will have the same sum.

    (Of course the BABs and AC need to have the right “polarity” of ascending or descending depending on the desired protocol.)

    I played in two Labyrinth Lord groups alternating weekly.
    In one, we did it the 3e way “Ascending AC with secret info”.
    In the other, we did it this way, which was supposedly older school. AC was descending.
    • Players rolled.
    • Players did a calculation to see what AC it hit (table lookup or subtraction
    • Players reported which AC they hit (which was hard to phrase)
    • The GM compared that theoretically-hit AC to the monster’s real AC
    • The GM reported the result.

  • One of the big issues is that AC doesn't stand alone in combat. Every part of combat is interconnected, so you can't just pick a THAC0/AC system without integrating all other parts first. You have to know what a combat round is (as someone else pointed out with the symbolic 1 minute old school rounds), decide on what hp & damage are, understand what armor does (separate from armor class), grok the basic probabilities of the system, consider number bloat, potentially think about weapon types vs specific armor types, and so on.

    A second big issue is that there are actually a lot of things at play here and we often blur what we're specifically talking about. Are we talking about the acronym itself, the system it's used in, the math of how it's determined, it's representative effectiveness, or what?

  • Generally, these different AC/to-hit systems are just math tricks. I don't see why you have to integrate other parts of the combat system or define a combat round or hit points to understand them.

    1. AD&D: d20 + bonus >? 20 - ac
    2. D&D 3e: d20 + bonus >? ac, where ac has been defined as the same as 1. AD&D's (20 - ac) to translate descending AC into descending AC
    3. Some other 3e system: d20 >? ac - bonus ... that's mathematically equivalent to 2.

    When you add reporting, denoted as "--> result", you get stuff like:

    1. AD&D with secret info: d20 + bonus - 20 --> result >? ac
    2. D&D 3e with secret info: d20 + bonus --> result >? ac

    Or a table lookup, denoted as "???" ...

    1. AD&D with secret info and table: d20 + bonus ??? --> result >? ac
    2. D&D 3e with secret info and table lookup: d20 + bonus ??? --> result >? ac

    It's obvious why AD&D has a table lookup and THAC0 as shortcuts, where 3e doesn't need them.

    In 3e's standard case, "d20 + bonus --> result >? ac", each operator is a point of contact, systemwise. The "d" is a die roll. The + is a mental addition and potential bonus lookup / sheet access. The --> result is communication, which requires the GM to be paying attention when the player is talking, so there's waiting and synchronizing (or noisome crosstalk). The >? is the GM comparing the player's result against the monster's AC, potentially requiring a lookup / notes access.

    And none of this included narration of events, which would make a fascinating (to me) IIEE discussion.

    Am I way off topic?
  • edited October 2014
    Since the OP was advocating for the Delta/SWN method, I don't think you were off topic at all, Adam.

    If I was designing a D&D game today, I'd do a descending "hitting number" and an ascending "don't hit me number". You'd add the two together -- attackers hitting number, defenders don't-hit-me number -- then try to roll that sum or higher. ACKS has something similar.
  • That's a good, simple way to do it. I like it!

    (Although it may not be as suitable for people who like to "don't-hit-me" numbers secret.)
  • For secret AC it's hard to argue with 3e style.
  • The trouble with adding a small positive and a small negative is that it's not addition; it's subtraction, which has a higher handling time than addition, especially in cases like (+3 + -7), where you need to do a quick mental flip to get the sign right in your head.

    Comparison tends to be "free" in people's minds. Is 15 greater than 20? No, of course not, and you didn't have to think about it. Sure, it's really "is (12 +3) > (13 +7)?" but those are really quick additions.

    Combat only starts to bog down in these cases when people recompute their bonuses every freaking roll. A friend and I would get pretty snippy with players when they didn't just write down the number after the first calculation. You have a +2 Str, a +3 BAB, a +1 for the magical sword, and a +2 bonus for this power. Please just write down +8 next to that power. Please. <=) Do the same for your damage calculation (2d6 +2 +1 --> 2d6+3). Done. There is no need to recalculate this every time you swing your sword in the usual way. /rant
  • I'm suggesting that both the "hitting" and "protective" numbers are positive. Small, but, >0.
    For exampe on my Goblins card it says 6/5. This mean that they hit a 14 AC human on 4+6 = ten or higher. I note that ten at the start of fighting. The five is how much HP loss hitting causes.

    In the RAW, that 6 would instead read +4 (to be added to the roll).
    In "my ideal D&D", that 14 AC would instead read 4.
    My "compromise" allows me to use one system as DM (by just looking at the player AC last digit) while the players play as per the RAW. I'm not saying anyone else should do what I do here. I realize that my style is weird.

    But if we were fixing it once and for all, the numbers printed in the game and on sheets would be 6 and 4. You add them together and try to meet that on a d20.
  • If the hitting number is 4 and the protective number is 6, I am missing something. So as I get better at protecting myself, you have to roll higher to hit me. Makes sense. But when you get better at hitting stuff, why do you still have to roll higher to hit stuff?

    Wait. Does your hitting number go down as you get better?
  • edited October 2014
    Yes, it goes down.
    Nitpick: in my example, 6 was the hitting number and 4 was the protecting number, not the other way around, but that was just an example.
  • Think of it as your hitting obstacle, your hitting imperfection, the flaws in your technique that you iron out as you improve.
  • edited October 2014
    As for comparison being free: it's cheapest operation but it still doesn't cost zero.
    I think I rank them: division, reporting, multiplication, subtraction, addition, rolling, comparison. Others probably have a different mix, with reporting cheaper, but the point is to minimize both the total amount of operations and the total cost of operations. So in "my ideal D&D" (again, the ACKS guys were ahead on the curve on this), the first round there's only add, roll, compare, report and subsequent rounds there's only roll, compare, report.
    Compare this to 3e open AC which has roll, add, compare, report every single round, 3e secret AC which has roll, add, report, compare every round, or the way we played LL which was roll, subtract, compare, report, compare every round, or Delta's method which is roll, add, report, add, compare every round
    It's great to get away from the subtraction of LL, but there's too many operations.

    Finally, I also have a personal preference for all the adding being done before the roll. It's like before the die hit the table, while I'm picking it up, I can add calmly. Once the roll is made it's like "give me results now now now".
  • Your method, it seems to me, is particularly effective when there are repeated rolls - like large numbers of foes all at the same skill level, for example.

    I think a lot of people who play D&D effectively do what you're doing: write down (or mentally note) the "to hit" number for a certain situation, and then reference that directly from the die rolls for the rest of the fight. I would definitely do this, regardless of the actual system/calculation used: the first goblin's attack, we realize, hits on a 14 or higher, so that's all we really need to worry about from now on.

    Wait. Does your hitting number go down as you get better?
    The "hitting number"... is good old ThAC0, in fact. That's exactly what it is. ;)

    But it's combined with ascending AC, which makes it look a little unfamiliar.

    My "Option One" in the OP is a good example of a similarly simple system, but using descending AC and ascending "hitting numbers".

    Sandra's system works in the opposite direction: descending "hitting number" (ThAC0) and ascending AC.

  • Exactly. Again, credit goes to ACKS, who figured this out.
  • There is also a way to make it work with secret AC: just have the DM know the sum and just report your rolls.
    I think secret AC is what trips up ACKS. If I understand it correctly, it often becomes roll, subtract, report, compare due to secret AC. So ACKS in practice ends up more cumbersome than 3e due to secret AC. If I wanted secret AC I'd rather have the DM do the adding and just report the rolls without subtraction.

    But I advocate open AC. I wonder which came first, open AC or secret AC.
  • But I advocate open AC. I wonder which came first, open AC or secret AC.
    In practice they're concurrent developments among the early play culture (that is, both were taken up independently by different groups in response to the extreme ambiguity of the original game texts), but if I had to make a call as to what the texts advocate, I'd say that the balance of the subtext goes to open AC - the game seems to assume that AC is public information deriverable from stated detail of the fiction: if you say that the guy has a chainmail, then that's AC 5 according to the rules. (Specifically, the GM gets much of his authority in the original game from proper adherence to the sparse rules, there isn't any indication that you could just decide to give the guy in chain mail whatever AC you want.) It is also clear that in Chainmail combat statistics like that are necessarily public, so any group transferring from that to D&D organically would presumably have to make a conscious change from open to hidden combat statistics for the foemen at some point, if they would at all.

    The idea of secret AC can, in fact, seem a bit peculiar on the face of it, particularly after looking at the rules texts. It makes more sense when you construct the actual play context and realize that the game actually requires you to make a whole bunch of choices about tactical information, when and where it is provided from the GM to the players. Will the players know how many hit dice a monster has at a glance? How about a human enemy? Do they know what spells an enemy wizard has memorized? At what point are they aware of how many enemies there are? The pure public method would have the GM do no secret noteskeeping at all, so the moment e.g. a random encounter with orcs is generated, the players know, and the moment the GM rolls for how many orcs there are, the players know. I don't know if anybody plays that way (presumably you'd at least keep a dungeon plan secret and reveal it piecemeal, room by room), but at least open AC would be clearly consistent with the general publicity.

    Along those lines of thought, I myself tend to treat AC as just another detail of tactical information that can be given up or withheld depending on the information gathering techniques used by the PCs. The only difference between AC and the color of an enemy in a dark cave is that the former is a number abstracted out of a presumably complex set of combat behavior factors, while the latter is merely a detail that has to be perceived directly from the fiction. Nevertheless, both are something that the players should only know insofar as their characters are capable of perceiving the related fictional detail; can't observe the thickness of a creature's hide or the agility of their movements, no chance of estimating their AC. This philosophy leads me to play in a way where the players may have exact, vague or no knowledge at all of what the AC is. (And yes, the common "I'll let you know after the first combat round" procedure covers like 90% of the cases satisfactorily from this viewpoint - not only will the players get dicing data, their characters will also get a first-hand chance at engaging the foe, which should help them realize how formidable the opponent is.)
  • To me, the early editions with their lookup method really strain under secret AC.
  • You basically look up what AC you would hit, and tell that to the GM. So you roll 14, look in the table over what number you've written 14 (the AC on top row and to-hit numbers on the bottom seems like the usual arrangement), and then tell the GM "I hit AC 5". The GM compares that to the actual AC and informs you whether it was a hit or a miss (or not, I guess, if it's a really secret AC). It's all the same mathstuff, as has been established.

    Not that I myself get what the big convenience of that table lookup method is supposed to be, really. Seems to me like it'd be something I'd use after a stroke took away my ability to add small numbers :D
  • In which case there is: roll, lookup, report, compare.
    Small additions? Don't you mean subtractions
  • I guess, yeah. My preferred math for this is, as I probably already mentioned upthread at some point, the 3rd edition one: d20+bonuses vs. DC, except I also use the difference for a degree of success, so I need to perform a two-digit subtraction on top :D I've explained upthread why this construction suits me better than the alternatives; the biggest thing is that it's easier to hook degrees of success, evaluate DCs off the cuff and various post-roll manipulations of the results into it when you have a clear conceptual differentiation between the actor and resistance side of the inequation.

    In general I guess that my mechanical aesthetics tend to rank addition and subtraction all but identically, and I don't apparently make any difference for small (<10) vs. large (10+) numbers, either. Reporting rolls isn't a big deal either, as I largely construe the dicing as being something you do <i>together, so having others witness your results is essentially a zero-cost operation for me. Table look-ups are, as I've indicated, a big turn-off, on the other hand. These preferences naturally lead my D&D into what some have characterized as a mathematical hellhole :D
  • .

    Not that I myself get what the big convenience of that table lookup method is supposed to be, really. Seems to me like it'd be something I'd use after a stroke took away my ability to add small numbers :D
    Probably mostly an issue of gamer culture familiarity with Roll and Cross-reference style charts and mechanics from Avalon Hill and SPI boxed set wargames. Miniatures games sometimes used them, but were equally as likely to use a formula with a list of modifiers.

    Notably, D&D uses the cross-reference chart, while most other early TSR and most non-TSR RPGs used the second method.

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