Showing posts with label combat. Show all posts
Showing posts with label combat. Show all posts

Monday, 21 May 2018

Surprised and Confused

In Conclusion

This turned into a long look at how surprise has worked through the early editions in order to try to fix the mess that later AD&D surprise became, so I decided to put the conclusion first so it’s easy to refer back to.

So what’s the fix? Quite simply, to go back to the original idea of the surprise die indicating both surprise and range, with “complete surprise” being the case where melee can start without any closing of range. Literally “in your face” in the case of the catoblepas and some other monsters.

I don’t want to simply go back to OD&D, however. Many players feel that multiple surprise segments is a core feature of AD&D and so I want to retain that. But I do want to get away from the idea that anything can cause an adventuring PC to be unable to react for half a minute or more.

The proposal is:

  1. Each party rolls for surprise (usually on 1d6).
    1. If surprise exists, individuals modify this rolled “surprise number”:
      1. Unencumbered figures may apply any reaction bonus.
      2. All figures apply any reaction penalties.
      3. Figures with heavy gear get +1 to their surprise number.
      4. Figures who are encumbered get +2 to their surprise number.
    2. A modified score of 0 or less is un-surprised.
    3. A modified score of 1 is surprise.
    4. A modified score of 2 or more is complete surprise.
    5. If no one is surprised after these modifications, then it is a standard encounter at normal ranges.
  2. Surprised creatures are “frozen” for one segment.
  3. Completely surprised creatures are “frozen” for two segments. If one is holding a crossbow of speed, it fires in the second segment.
  4. The less surprised (un- Vs surprised or completely; surprised Vs completely) figures have automatic initiative on the first immediately following combat round. If both sides are equally surprised then there is no initiative advantage.
  5. If all the members of a party have the same score then that modified score is used to determine the party level of surprise and encounter range. Otherwise, range is determined based on the party die roll (and maximum available space, of course):

    Party A Party B Effect Range
    Unsurprised Unsurprised None, proceed to 1st round. Normal
    Unsurprised Surprised B immobile for 1seg; A gains initiative 3”
    Unsurprised Completely B immobile for 2seg A gains initiative 1-3”, at A’s choice
    Surprised Surprised 1seg wasted 2”
    Surprised Completely A: 1seg wasted; B: 2segs 1”
    Completely Completely 2seg wasted 1”

If any opposing figures are not surprised then any “frozen” segments are part of any combat round which is engaged in by those unsurprised figures.

Notice that this already allows for the possibility that a surprised party will receive three sets of attacks before being able to answer back, so I don’t think there’s any need for a “3 segment cap”.

Note roundup

These notes are in priority order where there is a clash - so #3 can not override #1, for example.

  1. Monks above second level can never be completely surprised by anything.
  2. Piercers only ever surprise, they never completely surprise no matter what penalties the target has. This is more to do with their need for a ranged attack than the level of shock they create.
  3. Aerial Servants which are not detected always gain complete surprise without a roll; otherwise normal rolling is done based on a chance of 1-4 on d6.
  4. Quiet things grant +1 to the chance of surprising others. Quiet things include undead, bugbears, hobbits or elves in non-metalic armour, rangers, golems, cats of any kind. Some of these are already noted in the books, some are not.
    • A party only gains these bonuses if all the members qualify. There’s no use a ranger and a hobbit sneaking about if they have a donkey tapdancing on the stone floor.
  5. Modifiers to the chance to surprise others are cumulative only insofar that they reflect different advantages. Being silent is one advantage; being hidden is another. Hiding in shadows while invisible is a single advantage. As a specific example, an elven thief hiding in the shadows of a forest surprises on 1-4, not 1-5. In effect the hiding in shadows is assumed as part of the elven ability to blend into woods. Monsters appear to have slightly different rules, but PCs generally can only get +2 to their chance to surprise.
  6. A party with any members with a reduction in chance to be surprised gains the best such reduction.
  7. Surprise reduced from 1 in 6 goes to 1 in 8, then 1 in 10, 1 in 12, 1 in 20. In the opposite direction, 5 in 6 goes to 7 in 8, to 9 in 10 etc.
  8. When encountering settlements, and fortresses use the standard rules on DMG p182-183.
  9. Wilderness encounters with surprise are as per general encounters (1-3”).
  10. Wilderness encounters without surprise are as per DMG p49.
  11. Ruins are spotted at 1d10 half miles if no surprise; and 1-3” if the party is surprised. This score is shared by any monsters within.

The Problem

On the surface of it, surprise is a very straight-forward mechanism in AD&D: when any encounter happens each side rolls a d6; on a 1 or 2 they (not the opponent) are surprised and spend that many segments in a state of basic helplessness as they fumble or drop weapons or what have you.

Characters with low dexterity are not surprised more often, but instead take longer to recover if they are; high dexterity is the same, not reducing the incidence but improving recovery time. There is a slight asymmetry in that high dexterity can eliminate recovery time, so in a practical sense the high dex character is actually surprised less often.

This basic system is then absolutely screwed up even at this early stage by the sort of over-explanation that melee weapons Vs spells suffers from. Because, the above is all you really need to know and it is a simple and obvious consequence of these rules that if a PC walks around a corner and meets an orc and both roll 2 for surprise then the net effect is that both are helpless for 12 seconds but unable to exploit their opponent’s state, while being surprised for 1 segment against an opponent spending 2 segments fumbling gives you one segment to act.

Sadly, it was decided to spell this out in gruesome detail which (aside from a misprint in early printings, which didn’t help) gave the impression that the DM was supposed to subtract actual time spans from each other, leaving a muddle about what happens when two parties are surprised but one or more extreme-dexterity individuals do not share the result of their companions.

So: the first rule of surprise club is that surprise is measured in segments and you never, ever subtract one side or individual’s surprise from another. If I wait for ten minutes and you wait for 15, that doesn’t somehow mean that you only have to wait for five minutes.

But, sadly, things did not rest even there. That 1-2 on d6 has some exceptions even in the days of MM/PHB/DMG AD&D. For one, elves surprise on 1-4 on d6 when in natural surroundings. For another, rangers are only surprised on a 1 on d6.

Now, the elves are a problem. Because each segment of surprise allows an unsurprised opponent a full rounds’ worth of attacks. And four rounds of attacks is deadly. Those elves could be 7th level fighters, so they get 6 attacks in that time. Given that this is all down to basically pure luck, that’s a very big advantage, and if you have a dexterity penalty then leaving the house is basically suicide.

You're surprised for...4 days!

It gets worse. Later monsters introduced different dice, and eventually we have the example of the greenhag from MMII who can attack from invisibility, gaining surprise on 1-19 on d20. Strictly speaking, that’s a potential 19 rounds’ worth of attacks from a 9HD monster with 2 attacks per round - against AC -5 she’ll do an average of 71¼ damage!

Additional complications include what to do about a ranger’s implied -1 to surprise when faced by such a monster. Do we say that the greenhag surprises a ranger on 1-18? Big deal! Note that the DMG specifically rules out the alternative suggestion made by some that we treat the ranger’s bonus as a 50% modifier, which would reduce the greenhag to surprising on 1-10 (and only doing an average of 136hp damage to an unarmoured opponent).

There are various monsters which surprise on x on d8 and d10 floating around too.

What a mess.

How it was in the old days

So, how did we get here? That’s a multi-stage process.

LBB

The very first published version of D&D included surprise. In book three (The Underworld & Wilderness Adventures) surprise is introduced as a roll of 1 or 2 on a d6 and it states that the existence of surprise indicates that encounter distance is between 10 and 30 feet.

The primary effect of surprise is to grant “a free move segment, whether to flee, cast a spell, or engage in combat” (my bold).

In addition, the surprise roll is referred to as the “surprise distance determination die” with a roll of 2 indicating a distance of 10 feet.

At this point I’m going to get controversial. The normal belief is that melee range in D&D is 3”, because that’s what it was in Chainmail. However, Book III of D&D contradicts this once in plain language and once more by implication, in both cases when dealing with surprise. The first is when describing surprise distance in the wilderness: the statement is made that a range of 10 yards (1”) will enable a monster to attack. Under the 3” rule, this would be a redundant statement since the surprise range is between 10 and 30 feet - all of which would be in Chainmail’s melee range. The second case is in the primary discussion of surprise in the underworld where surprise is described as being an opportunity to close distance and also the encounter example which continues from determining a range of 10’ (1”) to the wyvern attacking as if there were a connection. I believe that these passages were written with a 1” melee range, the same as AD&D, in mind. This becomes more important later.

In addition to granting one “free move” having surprise also grants initiative on the first round of combat (a rule that is referenced in DMG without any real explanation).

There are no rules given for both sides being surprised but it’s not hard to imagine that the expectation was that the DM would count this as a cancelling out. Since there was only one segment of action possible, there was no real need to go into any detail.

Greyhawk

Greyhawk introduced nothing new except for the bugbear, who surprises parties 16⅔% more often (in one sense, in another 50% more often). In other words, they surprise on a 1-3.

Notice that this has no real problematic aspects in the rules as stated so far. There’s still only two questions being answered by the surprise roll:

  1. Does either side get a surprise bonus move?
  2. If so, are they in melee range to attack?

As before, if both sides are surprised then there’s just a general fumbling about and then combat proceeds as usual. Some surprise is still all surprise and we can probably assume that a roll of 3 from the bugbear means that it’s in melee range, just as a 2 did for the wyvern. The binary nature of both surprise and melee range means there are no questions about being very surprised compared to only slightly surprised.

Although thieves are introduced in Greyhawk, the only mechanical application of their ability to move silently is to allow them to make a backstab attack.

The guy at the bottom is still not
completely surprised

Blackmoor

Blackmoor does very little about surprise except for one paragraph in the introductory material dealing with monks, which are a new class based on the Destroyer books of Warren Murphy and Richard Sapir.

  • Third-level monks, it says, are surprised only on a 1 on d6.
  • Fifth-level monks are surprised on a 1 in 8.
  • Seventh and higher level monks are surprised on a 1 in 10.

It seems from this that a 3rd or higher level monk can not find themselves in a surprise situation where their opponent is in melee range unless they have the advantage (i.e., that is indicated by the opponent’s die). This situation is still not a complication, however because both parties are still surprised equally, in terms of time.

The paragraph (still dealing specifically with monks) goes on to note that “extremely silent creatures will double surprise possibilities, i.e., halflings, thieves, bugbears, and undead”.

In the context of a monk who has a 1 in x chance of being surprised, doubling the chance is the same as saying that the monster increases the chance by +1 - so 1-2 on d6 or 1-2 on d8 etc. Which fits what we were told in Greyhawk about bugbears but is innovative here, as far as I can see, in extending this to thieves and so forth.

Nothing in the text implies that this +1 to surprise is extended to situations not involving monks, but I think that’s logical in the same way that I assume that the thieves in question must have rolled a successful move silently check.

Eldritch Wizardry

EW took a look at the whole question of initiative which had been studiously ignored in D&D up to this point, with DMs assumed to have cobbled together something based on Chainmail’s Man-to-Man Combat section. As well as being incredibly opaque it introduced many key concepts such as segments and (implied) spell casting time and the surprise die as a number of rounds of free attacks. It may also hold the seed of a mistake.

EW tried to create a individual clockwork initiative system whereby the round was divided into segments and each combatant would be assigned an attack rhythm within that round which would essentially repeat from one round the next, at least as long as they fought the same opponent with the same means.

On the initial round of combat, surprise was used to modify this system and the notes on the tables involved included the statement that “complete surprise is basically a die of 2 when checking” (EW p6).

So you're saying...what exactly?

To throw another spanner into the works there is also a note that says that “surprise is basically a die 1 when checking, or a die 2 in those cases where the creature in question is difficult to surprise and has only a 1 in 6 chance of being surprised” (my ephasis).

The implication of this last statement is that in the EW system the chance of being surprised is 2 in 6 for everyone and the effect of being hard to surprise is just that you don’t suffer the penalties for complete surprise. It’s pretty weird if it’s not a typo.

Anyway, we are also told that “If surprised lose the 1st segment on a die roll of 1 and the 1st and 2nd on a die roll of 2”. This seems to mean that you lose your first one or two attacks, in the context. And another way of looking at that is that the opponent gets one or two rounds of attacks free of reply. Sound familiar?

And note the phrasing: the text does not say that a character that rolled 2 missed 2 attacks because he was completely surprised. This creates a dangerous link between the number on the die and the length of time a character is unable to fight back. EW never considers the possibility that a surprise die might be 3 or more - much more.

My suspicion is that Tim Kask (who wrote the EW initiative system) was simply carrying on the previous tradition of surprise starting either outside of melee or within melee, and that was the distinction between plain surprise and complete surprise with no further consideration given to higher values.

But by not saying “If surprised lose the 1st segment and the 1st and 2nd if completely surprised” he unwittingly left the door open to 19 attacks from greenhags etc.

AD&D

  • The Monster Manual

    No further tweaks were made in official supplements to normal combat before the Monster Manual came out. So, what initiative system was assumed to be in play for MM?

    It’s very hard to tell. I believe that Gygax never even considered using the EW system - he simply wasn’t that mad - and that it died a quick death just like the hit location system of Blackmoor (which, to be fair to Kask, was actually worse).

    Orcus is listed as having a tail which strikes as if 18 Dex, but this could either look back to the “adjusted dexterity” system in EW, or it could look ahead to the AD&D system where high dexterity grants bonuses to both surprise and ranged attacks (which the long tail might be seen as).

    There are several references to “complete surprise” in the MM and also in PHB and DMG. That’s an interesting clue as it suggests that even when Gygax had definitively abandoned EW’s system (which he had by PHB where he had gone back to a foundation in Chainmail with its weapon factors and first strike rules, even though he had not yet formulated the final system), he had decided to retain that division.

    In the Monster Manual and PHB we encounter monsters and characters gaining surprise on 1-4 on d6.

    Piercers have a 95% chance of surprise.

  • DMG

    With DMG we finally got the official word that surprise was the number on the die, even if it was a 4, and no explanation of what “complete surprise” actually was, despite the fact that whatever it was it gave you a bonus in various situations (or a penalty, if on the receiving end).

    As far as I can see, Gygax’s next step was to forget all about this and go back to pre-EW days, at least as far as initiative and surprise was concerned.

    There was never a single official explanation or expansion of the initiative and surprise rules in Gygax-period Dragon magazine. Nothing. The world of AD&D DMs and players was baffled by the presentation of the rules yet this was never addressed in over 100 issues of the in-house organ.

    The simple reason was that Gary was as ignorant of the DMG initiative rules as he was of the falling damage rules. He continued to play to the rules in his head, leaving the formal rules for people who wanted to play in tournaments. It’s entirely possible that Gary didn’t even write the DMG rules, just as “Gygax & Blume” had not written the system in EW. No one else has admitted responsibility, however.

    The DMG combat rules were certainly not well proof-read in any case, with dead-end cross-references and a table explaining surprise which had a hideous error in it (to say nothing of the screeds of combat examples in PHB and DMG which simply didn’t match up to the rules given).

    As Gary went on creating monsters, he retained the distinction between surprise and complete surprise in his head but nothing much else. So, even in the MMII we find several new monsters still referring to complete surprise alongside monsters that cause crazy numbers.

    Like Kask before him, Gary simply didn’t think about the consequences of making that link between the number on the die and the number of segments of free attacks and largely acted as if it didn’t exist. Because, I suggest, that link did not exist for him.

    So, what to do about all this? Go back to the top of this document to see.

Sunday, 23 April 2017

Magic Items: The Wolf Banes

The Wolf Banes

The Wolf Banes are a set of enchanted weapons and armour specifically for combating wolves: a spear, a shield, a scimitar, and a shortbow make up the full set:

Skinner

A scimitar +1, +2 Vs wolves. Does double damage (i.e., (1d8 x2)+2) against all wolf types and in addition, if wielded by a fighting class, allows one attack per level as if the wolves were <1HD.
xp: 800
gp: 5000

Pricker

A 7' spear +1, +2 Vs wolves; includes a cross-bar like a boar-spear. Does double damage against all wolf types and in addition, if maximum damage is rolled against a wolf, the creature must make a save Vs death or expire instantly. May be set against a charge, possibly resulting in an additional doubling of damage so that against a warg or winter-wolf it would do (1d8 x4)+2 damage.
xp: 750
gp: 4000

Comet

A shortbow +1, +2 Vs wolves. Does double damage against all wolf types and in addition, if wielded by a fighter, each arrow acts (if wished) as a flame arrow doing an additional +1 damage on striking. Unless the struck wolf makes a save at 16+ (cloth Vs magical fire), it will catch fire for 1d4 rounds, doing 1d4 damage each round (1d4+1 for winter-wolves). The wolf struck must make a morale check at -50%, and all wolves within 1" must make normal checks.
xp: 750
gp: 4500

Door

A medium shield +1, +3 Vs wolves. Causes attempts by wolves to overbear the user to fail automatically. Additionally, winter-wolf breath attack damage is halved or totally negated if the save is made, unless the user is surprised.
xp: 800
gp: 3500

Notes

The Wolf Banes set will attract a sale bonus of +10% per item over the first, so a complete set will have a sale value of 22100. However, the items are unique and derive from an ancient tribal hero who fought wolves. That tribe may still exist and may track down the current owner of any of these items. What happens then is up to the DM.

For these items, Yeth Hounds are not wolves, however werewolves are, even in human form.

Tuesday, 5 April 2016

Dagger, Dancing

Copyright 2013 Javier Perez (http://javierperez.es/)
Not quite what I meant
Appears to be a normal dagger (so it sheds no light) but radiates alteration magic. If used in the off-hand the user will feel it tugging at their grip and if let go of it will perform its actions on its own, leaving the owner to fight with a single weapon or draw a second off-hand weapon. In the latter case, the user will be able to employ a three-stage attack routine (dagger/off-hand/main). The owner could also drop their main weapon and take up a two-handed one.*

The dagger can be commanded to defend, in which case the user's AC against the first melee attack against them in the round will be raised to 0 and against all others to 7; if the user's AC is already better than this the dagger gives no extra protection. The dagger may only defend or attack in the course of any single round and can only change mode on the owner's initiative (specifically sub-step D).

The general enchantment of the dagger means that it strikes as a magical weapon but has no plus, and so will not affect any target that requires +2 or more to hit. It does however strike as if wielded by its owner, so if he or she has strength bonuses the dagger will too.

Once combat has ended (no combat within 12"), the dagger will fall to the ground inert.

These daggers may occasionally exhibit special characteristic; roll on the unusual swords table on DMG p166 with -10 to the dice.

* Clarification: the dagger must be used for at least one round in the off-hand before it will dance; it can not be simply commanded to dance from the outset of combat.

Xp value: 350. Gp value: 4000

Monday, 15 June 2015

Macho Women with Hit Locations

Here's a hit location system a friend and I designed years and years ago (about 1988).
The idea is that instead of having specific hit location tables for each monster, the DM imagines a square area in front of each figure representing the possible areas they could strike. When a hit is rolled, the location is determined by rolling for the type of weapon (1-handed, missile etc.) and the using that on the appropriate hit location display. The DM then makes a subjective call as to what specific part of the target has been hit. With higher skills, characters had the option of adjusting the hit location die. Initially we had a RuneQuesty system for assigning hit points to locations but after seeing the system in Macho Women With Guns, where hit location adjusted the damage dice (e.g., from d6 to d8 or d3), we switched to that.
Hit Location Tables (d20)
Area1-handed
or 1-edge
2-handed
or 2-edge
ThrustMissile
1111-21-2
22233-4
33345-6
4445-107-10
555-711-1211-12
66-98-1113-1413-14
710-1112-131515-16
812-1614-151617-18
917-2016-2017-2019-20

Hit Location Displays
Left Handed
897
645
213
Right Handed
897
645
213

Monday, 17 November 2014

Mass Combat 1

Mass combat in D&D can be handled quite nicely by rolling a d20 and applying a bit of binomial theory. I'm not going to bore anyone with the theory but the results are a bunch of to-hit tables which vary based on the number of attackers.

Using the tables is pretty easy. Combat is from an attacking side consisting of identical figures from one or more units and a defending side consisting of figures from a single unit.

First, you decide how many figures on one side can attack the defending unit. If a row of goblins are attacking a unit of humans, perhaps the front 10 goblins can attack. If a mass of archers are firing at a single dragon, maybe hundreds can take a shot while it's in the air while a dozen knights on horseback might be able to charge it on the ground.

Next, find the attackers' to-hit needed using the normal methods. E.g., a gang of berserkers attacking a row of men in mail and shield decide to take a single attack at +2 with their bastard swords rather than once each with that and their hand-axes; they need a 15 to-hit. If using two-handed swords and armour Vs weapon rules, they would need 13. As another example, a 10th level fighter attacking the same men with a longsword would require a 7 (probably a lot less if strength and magic are applicable), and would roll using the "10 attacks" table.

A d20 is rolled for the attackers. This is found on the left-hand side and cross-indexed with the to-hit score to find the number of attackers who hit. E.g., 8 of the berserkers mentioned with the bastard swords are attacking the men-at-arms and roll a 13. The to-hit score was 15, so 3 of them hit.

Damage is then found based on the number of hits.

In the case of the berserkers, damage is easily handled by rolling 3d8 and applying it to the defending unit, moving the defenders down when damage accumulates equal to half the total hit points of the members.

But with larger units this can become unwieldy and it may be easier to become more abstract if you have a calculator to hand. The first option is to simply multiply up the average damage rather than rolling it, so our berserkers do 14 damage (13½ rounded up) and applied as before.

But with bigger units, or units with lots of hit dice (the infernal legions of pit fields, for example) these numbers are still too tedious to work with and we can fall back on calculating damage based on hit-dice. For this, the paper record for each unit is simply a count of total dice, calculated as average hp divided by 4.5. So 20 goblins count as 16 dice, and ten pit fiends have 130 HD, and a dozen trolls is 88 HD.

For this method, each hit has to be related to hit dice - take the average damage and divide by 4.5 (note this with the unit). Each hit in battle does that number of hit dice damage. So, our berserkers' attack simply does 3 damage; if using hand axes they would do 7/9th x 3 = 21/9 = 2 damage; with two-handed swords, 11/9 x 3 = 33/9 = 4 damage. If the berserkers were attacking the trolls, these numbers would become 13/9 x 3 = 4, 5/9 x 3 = 2, and 7/3 x 3 = 7 damage because of the trolls' large size. Of course, the trolls are regenerating 9 damager per round ((3x12)/4), so that's not going to matter much. As I said, the damage per hit against large and small can be recorded with the unit's record and a calculator makes all this tolerably fast.

If the number of figures doesn't fit one of the tables given, make two rolls on those that you have, so 18 figures roll twice on the 9-attacks table, or 13 roll once on the 6-attacks and once on the 7-attacks table etc.

Once a unit has taken half its maximum damage, it's knocked down to a unit of half the original size, and therefore half the original attacking potential.

As an aside, let's assume the trolls can bring 6 of their members to bear on the berserkers for a reply. The berserkers have 8 HD and the trolls' attacks do 13/9, 13/9, and 14/9 each. Their to-hit against AC 7 is 6. Three rolls are made: 6, 2, and 5. This equates to 4, 3, and 4 hits, for a total of 16 HD damage. The berserkers are shredded, even with these relatively poor rolls.

Initiative and stuff

I generally count all units closing as if it were "precipitous" so the longer weapon gets first attack; defender in a tie. After being joined, faster weapon goes first unless it's more than 5 speed factors better than the opposing weapon (in which case, it's deemed to be too short to take advantage). On ties, or when I can't be bothered, just dice for it.

If a unit is partially damaged at the end of a combat, I assume that the percentage hit points or dice lost is reflected in the casualties, but this has to be mapped to individuals' fates. If a unit of 10 2nd level clerics has suffered 16 HD of damage, then a quick estimate is that only 2 have survived with 20% of their hp. A more detailed method is to roll the 16 dice damage (i.e., 16d8) and spread it evenly over the unit. If the end result is that more survived than were still fighting or that none survived then this can be explained as stragglers returning to the unit after combat or dying from wounds as applicable.

Leader figures with individual hit points take proportionately more damage if involved in the combat. For example, our 10 2nd level clerics are lead by their high priestess (9HD), so the unit has 29HD. 16 HD damage is rolled and comes up 82. That would be 7.45hp each, but the high priestess takes 9/2=4½ shares, so she takes 34hp damage, leaving 48 for the others, who suffer 5 damage each. This sort of detail is something that only really comes up when player characters are involved, of course.

I've glossed over things like constitution, magic and strength bonuses, but it should be obvious that they are simply converted to hit-dice equivalents.

Fireball!

Area effects such as fireballs and dragons can affect multiple units, but in each unit the damage done is limited to the hp of one figure and then multiplied by the number of figures struck. So a 5d6 (35/9HD) fireball which hits a unit of 50 orcs (50HD) and affects 20 of them does 20 HD damage to the unit. Against the 12 trolls it does a total 47HD damage as each individual troll has more HD than the spell does damage.

88hp from a dragon is equal to 20HD and would obliterate the trolls, as it should.

Notes

I've used variations of these "rules" many times, sometimes with figures or counters, but mostly without any physical representation at all. They're very loose and the DM can apply whichever rules from standard D&D that they like - morale, multiple attacks (which can be subsumed into one big attack), time and movement, flank and rear attack bonuses, shield use, and even surprise for units of hobbits and elves. It's very much an on-the-fly method but if you're not too much of a wargamer they're probably enough for most needs and the degree of abstraction can be slid up and down to fit the importance or interest of the battle, as can the size of units.

3 Attacks

To-hit
1234567891011121314151617181920
132211111000000000000
232221111110000000000
333222111111000000000
433222211111100000000
533222221111110000000
633322222111111000000
733322222111111100000
833332222211111100000
933332222221111110000
1033333222221111110000
1133333222222111111000
1233333322222211111000
1333333322222221111100
1433333332222221111100
1533333333222222111110
1633333333322222211110
1733333333332222221110
1833333333333222222111
1933333333333332222211
2033333333333333333322

4 Attacks

To-hit
1234567891011121314151617181920
143222111110000000000
243322221111100000000
343332222111110000000
444333222211111000000
544333222221111100000
644333322221111100000
744433332222111110000
844433332222211110000
944433333222211111000
1044443333222221111000
1144443333322221111100
1244444333322222111100
1344444333332222111100
1444444433333222211110
1544444433333222221110
1644444443333322221110
1744444444333332222111
1844444444433333222211
1944444444444333332221
2044444444444444443332

5 Attacks

To-hit
1234567891011121314151617181920
154332221111000000000
254433222211110000000
354433322221111000000
454443332222111100000
555443333222111110000
655444333222211110000
755444333322221111000
855444433322221111000
955544433332222111100
1055544443332222111100
1155544443333222211100
1255554444333322211110
1355554444333322221110
1455555444433332221110
1555555444443332222110
1655555544443333222111
1755555554444333322211
1855555555444433332211
1955555555554444333221
2055555555555555444332

6 Attacks

To-hit
1234567891011121314151617181920
165443322211110000000
265444332221111000000
365544333222111100000
465544433322211110000
565554433322221110000
666554443332221111000
766555443333222111000
866555444333222111100
966555444333322211100
1066655544433322211100
1166655544433332221110
1266655554443332221110
1366665554443333221110
1466665555444333222110
1566666555444433322111
1666666555544433322211
1766666655554443332211
1866666665555444332221
1966666666555544433221
2066666666666655544332

7 Attacks

To-hit
1234567891011121314151617181920
176544332221111000000
276554433322111100000
376655443322211110000
476655444332221110000
576655544333222111000
676665544433222111000
777665544433322211100
877665554443322211100
977666554443332221100
1077666555443332221110
1177766555444333221110
1277766655544333222110
1377766655544433322110
1477776665554433322111
1577776665554443322211
1677777666555443332211
1777777666655544332211
1877777766665544433221
1977777776666555443321
2077777777777666554432

8 Attacks

To-hit
1234567891011121314151617181920
186654433322111000000
287655443332211100000
387665544333221110000
487765554433222111000
587766554433322111000
687766555443322211100
788776655443332211100
888776655444332221100
988776665544333221110
1088777665544433221110
1188777665554433222110
1288877666554443322110
1388877766555443322110
1488877766655443332211
1588887776655544332211
1688887776665544333211
1788888777665554433221
1888888877766555443321
1988888887776655544322
2088888888887766655433

9 Attacks

To-hit
1234567891011121314151617181920
197665543332211100000
298766554433221110000
398776554433322111000
498776655443322211000
598876655443332211100
698877665544332211100
798877665544333221100
899877766554433221110
999887766554433222110
1099887766554443322110
1199887776655443322110
1299888776655443322210
1399988776665544332211
1499988877665544332211
1599988877666554433211
1699998877766554433221
1799998887766655443221
1899999888776655443321
1999999988877666544332
2099999999988777655443

10 Attacks

To-hit
1234567891011121314151617181920
197665543332211100000
298766554433221110000
398776554433322111000
498776655443322211000
598876655443332211100
698877665544332211100
798877665544333221100
899877766554433221110
999887766554433222110
1099887766554443322110
1199887776655443322110
1299888776655443322210
1399988776665544332211
1499988877665544332211
1599988877666554433211
1699998877766554433221
1799998887766655443221
1899999888776655443321
1999999988877666544332
2099999999988777655443

15 Attacks

To-hit
1234567891011121314151617181920
1151311109876654432211000
21513121110986665443221100
315131211101098765543321100
415141312111098776544322100
515141312111099876554332110
6151413121110109876654432110
7151413121111109887654432210
8151413131211109987655433210
91514131312111010987665433210
101514141312111110987765443211
111515141312121110998765543221
1215151413121211101098766543221
1315151413131211111098776544321
1415151414131211111099876554321
15151514141312121110109876654321
16151515141313121111109887654321
171515151414131212111010987655432
181515151414131312111110988765432
1915151515141413131211111098876542
20151515151515141413121211109987653

20 Attacks

To-hit
1234567891011121314151617181920
1201716141211108766544321100
22018161514111010987654332100
320181715141312111098765432110
420181716151312111098765432210
5201817161514131211108766543210
6201917161514131211109876543210
7201918161514131211109876543210
8201918171615141311109876543221
92019181716151413121110987654321
102019181716151413121110987654321
112019181716151413121110987654321
1220191818171615141312111097654321
1320201918171615141312111098765421
1420201918171615141312111098765431
1520201918171615141413121098765432
16202019181817161514131211109875432
17202019191817161514131211109876532
182020201918171716151413121110986542
192020201919181716161514131211987643
2020202020201918171716151413121098754

25 Attacks

To-hit
1234567891011121314151617181920
125222017161413111097654432100
2252221191616151312119876543210
32523211918171514121110976543210
42523212018171614131210987643210
525232220191716151312111087654210
625232220191816151412111097654321
725232221191817151413121098754321
825242221201817161413121198764321
9252422212019171615131211108765321
10252423212019181615141211109765421
11252423222019181715141312109865431
12252423222119181716141312119875431
132524232221201817161513121110876432
142524232221201918161514131110976532
152525242321201918171514131210986532
162525242322211918171615131211987542
1725252423222120191816151413111087642
1825252423222120191817161413121098643
19252525242322212019181715141311108753
202525252524232221201918171615131210864

30 Attacks

To-hit
1234567891011121314151617181920
13026242119171614131110875433210
230272523211918161513101097653210
330272523222018171514121198654210
4302826242221191716141311108754320
5302826242321191816151312109764321
6302826252321201817151412119865321
7302826252322201917151412119875421
83028272524222019171614131110875421
93029272524222119181615131210976431
103029272624232120181715131210976431
113029272624232120181715141211986531
1230292826252322201917161413111086532
1330292826252322211918161513111087542
1430292827252422211918161513121097542
1530292827262423212018171514121197642
1630302827262523222019171614131198642
17303029282625242221191816151312108753
18303029282725242321201917151412119753
193030292827262524222119181615131210864
203030302928272625242321201817151412975

40 Attacks

To-hit
1234567891011121314151617181920
1403632292724222018161412108654310
24036343129262422201816141210875320
34037343229272523211917151311975421
440373432302826232119171513111086421
540373533302826242220181614121086431
640373533312927242220181614121097531
740383533312927252321191715131197531
840383634312927252321191715131197532
9403836343230282624222018161412108642
10403836343230282624222018161412108642
11403836343230282624222018161412108642
12403837353331292725232119171513119642
13403937353331292725232119171513119752
14403937353331302826242220181613119753
154039373634323028262422201816141210753
164039383634323029272523211917141210863
174039383635333129272523211917151311863
184040383735333230282624222018161411964
1940403937363433312927252321191715121074
2040404038373635333129272523211917141295

50 Attacks

To-hit
1234567891011121314151617181920
15044403734312926232118161311975320
250444239363431282623201816131195321
350464340373432292624211916141297531
4504643403835323027252220171512108531
5504744413835333028252320181513108631
6504744413936333128262321181613118642
7504744423936343129262421191614119642
8504745423937343229272422191714129742
95047454240373532302725222017151210752
105048454340383533302825222017151210752
115048454340383533302825232018151310853
125048464341383633312826232118161311853
135048464441393634312926242119161411863
145048464442393734322927242219171411963
155049474442403735323027252220171512963
1650494745424038353330282523201815121074
1750494745434138363431292624211816131074
1850494846444139373432302724221916141185
1950504846444240383533312825232017151295
20505049474644424038353330282522201714116

100 Attacks

To-hit
1234567891011121314151617181920
110090847872666055504540353026221713842
2100928680756964595449443934292420151162
3100938781767165605550454035302521161173
4100938882777166615651464136312621171273
5100948883777267625752474237322722171383
6100948983787368635752474237322823181384
7100948984797368635853484338332823181494
8100958984797469645954494439342924191494
9100959085807569645954494439342924191495
101009590858075706560555045403530252015105
111009591868176716661565146413631252015105
121009691868176716661565146413631262116115
131009691868277726762575247423732272116116
141009692878277726863585348433732272217116
151009792878378736863585348433833282317126
161009793888379746964595449443934292318127
171009793898479757065605550454035292419137
181009894898580767166615651464136302520148
191009895908681777267625752474237322621159
2010099969388847975706661565146403429231711