Monday, March 14, 2016

Monte-Carlo Measures of Monster Levels, Pt. 7

Finally, some squirmy-wormy creatures at the end of our list who may have evidence of being possibly broken in our Arena monster combat simulator:

Monsters vs. Spells: The Arena OD&D simulator is purely a 1-on-1 man-vs-monster combat (as of this writing); monster of high Hit Dice value need to be cut down one d8+1 sword blow at a time. Of course, an associate wizard with proper spell selection could radically simplify the process, but this depends on the monster involved. For low-level mobs, then area-effect spells could clear the room, as with sleep, fireball, or cloudkill. But for single high-powered monsters, then a targeted save-or-submit spell like charm or hold monster or disintegrate could end the fight immediately. While I'm happy to use the fighting EHD as a baseline for lesser monsters, at the upper end things get a lot more hazy about whether spell options should really be the major consideration.

Hydras: Hydras with 6-8 heads are listed in OD&D monster table Level 5; and Hydras with 9-12 heads are on the Level 6 table. As usual, in each case I picked one representative type for my Arena input. The 6-headed Hydra is reasonably given EHD 11, about double the HD 6. But the 10-headed Hydra came out at EHD 44, unprecedentedly more than 4 times the HD of 10, and at least twice the EHD of the next-lower monster on the list.

So: Hydras are dangerous, really dangerous. The fact that it can make so many attacks, possibly up to 10 dice of damage per turn, and those attacks are at a high hit-level of 10 HD or more (even after losing some heads), really makes it a whirlwind of death to a lone fighter. A high-level fighter with higher abilities, with magic plate, shield, and sword of multiple bonuses, will have a much better time against it (both in avoiding more of the bite attacks, and getting average damage above 6 points means you can probably reduce the head count by at least one each round). The AD&D Monster Manual made a major rule adjustment: no more than 4 heads can attack any one creature; but that limitation does not appear in OD&D. Perhaps that restriction is both reasonably balanced and also intuitively realistic (in that some limitation should prevent innumerable heads from all getting tangled up in one space, just like any other monster is limited in number of attacking bodies they can throw against a PC).

If we think about including spell-casters in our game, then subjectively this could be altered further downward, but the exact level depends keenly on adjudications regarding Hydras, not explicated in the rules text for any edition. For example: I've seen many D&D games get quagmired when the DM drags out a Hydra, a PC hits it with a spell, and then no one has any idea how rule on it. For example: Say a fireball is rolled for 20 points of damage; does this apply one time to the whole Hydra (killing at most 3 heads), or area-effecting all the heads separately (killing them all)? Assume that a charm monster spell is cast at a Hydra: Does it affect a single head (causing it to attack other heads), or does the entire Hydra become subdued with a single saving throw? What about disintegration? Would a cloudkill or death spell consider each head as separate 1-HD creature (if "yes", then the hydra is defeated; if "no", then the hydra is immune).

Now, personally I would rule that in the spirit of the thing, heads are never treated as separate creatures for the purpose of spell effects, and I hope that most of us would agree (so: average fireball gets maybe 3 heads; sleep, cloudkill, and death spell have no effect; but charm, hold, and disintegrate stop the whole monster). On the other hand, I have seen some DM's go the other way with that; and more worrisome, it's a little unpredictable because it seems that many of us haven't thought it through in advance. The exact risk level, and hence XP value, of Hydras depends a lot on this off-book decision-making. But clearly they are dangerous top-of-the-food-chain monsters.

Purple Worms: I set my simulator to do a binary search of fighters between levels 0 and 50 to find the best match for any given monster (with 10,000 fights between random monsters and fighters at each level). Initially it had a maximum level of 20, but I found a number of monsters bumping up against that ceiling. We can find one monster that will bump up against any ceiling we specify, that is, it has undefinable (effectively infinite) EHD in this model; the Purple Worm (HD 15).

The save-or-die poison tail sting is bad enough, but as Vol-2 rightly asserts, "its mouth is the more fearsome weapon". With a roll of more than 4 points over the to-hit number, the purple worm swallows its prey into its gullet, where it dies automatically 6 rounds later (and is irrecoverably disintegrated 6 rounds after that). Note that for our baseline fighter in chain & shield, AC 4, the worm effectively always hits (20 − 15 − 4 = 1 to hit!), and thus swallows on any roll of 6 or more -- 75% chance on any attack to instantly take the fighter out of the fight, of any level (for a total probability of 99.99% to win such a fight). Or let's compare to the case of a fighter fully equipped with magic +5 plate, +5 shield, and +5 sword (assume average Dexterity), AC −8; so the worm still hits almost half the time (20 − 15 − (−8) = 13), and still swallows on an 18+ roll -- 15% chance to end the fight on any attack, regardless of opponent level (overall, the worm is favored at 57% to win a fight against any fighter of any arbitrarily high level in this model).

As an aside, we see that the Vol-2 rule clause of "or 100% [natural 20] in any case" is effectively redundant, as any character of any possible AC value is swallowed on some roll of less than 20 anyway.

In OD&D, there is simply no mechanism mentioned such that a swallowed character can escape on their own (excluding friends presumably killing the beast and cutting them out in time), so we know that the solo fighters in the Arena will definitely be destroyed as soon as a Purple Worm swallows them. The later AD&D Monster Manual added a remedy to this situation, by stating, "Note, however, that a creature swallowed can try to cut its way out of the purple worm's stomach. The inner armor class of the 'worm is 9, but each round the creature is in the worm it subtracts 1 from the damage each of its  attacks does." Now, at first glance this rule might seem reasonable to us (a nod to Jonah), but personally it always gives me indigestion. Notice that the character swallowed is under no threat of attack or damage while inside, and the inner AC of 9 is the easiest possible target in the game (a high-level fighter should automatically hit it, much like the Purple Worm automatically hit him in the first place). So in practice it turns out that, under this rule, the safest place to fight a Purple Worm is inside it. I've seen fights degenerate into a comical sequence of: fighter gets swallowed; fighter cuts way out; fighter gets swallowed again; rinse and repeat, etc. With this rule, the Swallow attack is not so much a feared ability, it's actually the best defense against the Purple Worm itself. For this reason, I am very much opposed to the AD&D rule, and keep the special ability as a Doom-That-Came-To-Swallow kind of menace. Bring lots of friends to cast missiles and cut you out, or don't face off against a Purple Worm in the first place.

The Arena simulator reflects this pure-OD&D adjudication, and so the Purple Worms are favored to eat up any single fighter regardless of level; and thus the EHD is effectively undefined for this type. Perhaps we should use other monsters as a guidepost and say that it likely tops out at about triple HD/XP?

Conclusions: Taken as printed in our Arena output chart, we could take the listed EHD's as the exact number to use in place of HD when we look up awards in the XP table; or more simply using Vol-1 rules, compute EHD × 100 in each case. But granted that even this is a rough model, and that some subjectivity exists for consideration of multiple party members and spell-casting, perhaps the simplest and most honest thing to say that at best we may have the right magnitude of multiplier by which to adjust XP. That is: either double or triple XP, as shown under the "Multiplier" column in the table, and not pretend to more precision than that.

Even this has some interesting discoveries, I think, like: Wights, wraiths, mummies, lycanthropes, and even giant constrictor snakes probably don't deserve any XP bonuses. Basilisks and Medusae are probably reversed in the tables in terms of danger level. Most monsters likely don't deserve more than a single doubling of XP, with only the rarest of exceptions (even Vampires with their half-dozen abilities may only deserve one doubling, according to this).

Now, while OD&D Vol-1 didn't make any mention or awareness of the need to adjust monster XP for special abilities (actually, the Troll example explicitly avoids making any such adjustment), the need must have been rather quickly noticed, because a D&D FAQ article in Strategic Review #2 (Summer 1975) did bring up the topic:
Experience: ... For purposes of experience determination the level of the monster is equivalent to its hit dice, and additional abilities add to the level in this case. A gorgon is certainly worth about 10 level factors, a balrog not less than 12, the largest red dragon not less than 16 or 17, and so on. The referee's judgement must be used to determine such matters, but with the foregoing examples it should prove to be no difficulty.

In broad strokes, this is the same method we recommend here (add some integer number to the Hit Dice to adjust for special abilities, before computing XP, without any extra table or more complicated calculations being made). How much do we agree with those suggestions? The Strategic Review article probably undervalues those top-level monsters by quite a bit. For Gorgons it suggests "about 10 level factors", but here we think 15 is better. For a Balrog it says "no less than 12", and strictly speaking we agree with the inequality statement, a value of 22 being reasonable. For the largest Red Dragon it says "not less than 16 or 17", and the Arena simulator would suggest that a value of even 45 would not be out of the question for eldest type.

Hopefully this gives some additional perspective and confidence when assigning XP under the Original D&D (Vol-1) system. Perhaps equally important, it was a great motivation to crawl into the guts of the OD&D monster special abilities, and be forced to think about the specifics of adjudicating each, given the level of complete discipline and specificity that our computer programming framework forces upon us.


Eaten any thoughts? Devoured any intellects?


42 comments:

  1. One thing I've begun to wonder is if we should take monster weaknesses into account. For example, every dragon has a chance of being asleep when encountered, all save gold dragons have at least one elemental weakness that can be exploited, and a few magic items exist that specifically affect dragons. Vampires can be turned or staked. Mummies, purple worms, and basilisks are all very slow (6" move) and are therefore highly vulnerable to hit-and-run tactics with ranged weapons. Stuff like that.

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  2. quote
    For a Balrog it says "no less than 12", and strictly speaking we agree with the inequality statement, a value of 22 being reasonable. For the largest Red Dragon it says "not less than 16 or 17", and the Arena simulator would suggest that a value of even 45 would not be out of the question for eldest type.
    unquote

    This made me laugh!
    So, in academic terms, you and SR#2 are in perfect agreement on the subject of balrogs and red dragons :)

    Anyhow, I agree with your suggestion on how to deal with spells vs. the hydra. That's how I would rule it as well.

    Regarding purple worms, I rule: 2 successful hits are required to slash your way out of the worm. The first at AC9 to cut through the stomach; the 2nd at AC6 to cut through its skin. The resulting -2 lasts until healing (so, most likely the whole combat).

    The, wizards and spells vs. monsters; it is hard to properly adjudicate the effect of magic, as wizards are so strongly resource-limited. May a wizard fully unload within the Arena simulator or not? Does it have access to the appropriate spells? I really appreciate your clean approach of EDH based on single fighter statistics.

    And although I have no problems with EDH's of 45, an EDH of infinity is a bit problematic, especially if you would like to base XP on the EDH.

    For these cases you might want to consider another metric: the amount of fighters you need to subdue a monster in at least 50% of the fights.

    Not sure if you should take 1st level fighters only, n fighters of nth level, or n fighters of mth level. And if the metric should be the amount of fighters, or the combined level. And what does 'defeat in at least 50% of the cases' mean? A single surviving fighter out of 50, does that count as a victory?

    But still, I think it may help to get a grip on the (EDH) of (high) level monsters.

    Ah, and then there is of course the programming ...

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    1. It's a pretty good point that infinity XP awards would be problematic. :-D And your intuition on multiple fighters at the end is excellent, basically you're going to get your wish starting with the new version next week.

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    2. Ooohhh! More simulations! Looking forward to that!

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  3. Dan,

    Not to be picayune, but Jonah (not Noah) was the biblical figure swallowed by the big fish.

    Have you considered the effects of certain gear on your EHD evaluations? For instance, how would a nth-level fighter equipped with +3 plate compare to a "standard" fighter of the same level equipped with chain and a shield? Just a possible point of future investigation.

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    1. Oh, good grief -- thanks for the fix!

      Initially I was trying to make an assumption like everyone got a +1 bonus to items every 4th level or something, but the gradient of the discrete jump was too radical. So then I was doing a 5% chance per level, but I was concerned that might not match well to enough people's campaign milieus. In the end I thought it best to have the fixed baseline as a gauge, representing "raw hit dice", and then people could modify for how high/low magic their world is.

      As you can see above, I did go in and jimmy up a fighter with +5 everything to fight the purple worm (still loses most of the time), so it's possible in theory if we want that.

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  4. Forgot to mention how much I've enjoyed your analysis of D&D monsters! Love this stuff.

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  5. Thank you for all of this!

    "Eaten any thoughts? Devoured any intellects?"

    I see what you did there... only if I rolled a 1in6... ;)

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  6. I honestly like the "the best way to win is from inside" idea. It's got a certain amount of genre precedent, and it feels like one of those elements that reward players for paying attention and using their heads. If the optimal strategy is to repeatedly get swallowed and cut your way out again, that's kind of silly... so I'd want to find a way to put anyone swallowed into a one-shot kill-or-die scenario. This may offend people who prefer simplicity and universal mechanics in their game structures, but I wouldn't mind seeing some kind of mini-game for a swallowed fighter to see if they can do enough damage to various organs to kill the worm, and then hack or claw their way out, before the hostile environment inside (stomach acids, muscular contractions, little to no air, etc.) kills them.

    Let me also say that it's been an interesting read, and I'm looking forward to the mass-combat version to see what new insights come out of your project here. Thanks for putting all that work into it! 8^)

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    1. You had me at "some kind of mini-game". :-) I'm picturing something a bit like Tom Wham's Snit's Revenge? Thanks for the kind words!

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  7. Excellent series. Great content, as usual.

    Question: I love the target 20 system, but does this possibly indicate that the monster HD attack bonus should be capped?

    In btb OD&D, the worm would hit the AC 4 arena fighter not on a 1 but a 5. Maybe not a huge difference, but it does (if my quick pre-coffee math this morning is correct) mean that the Vol 2 statement is not redundant because the tricked-out –8 AC fighter would be hit on a 17.

    But mostly, I guess, I’m curious what you think about the potential of capping the Monster attack bonus. (Sorry if you’ve addressed this in an older post that I missed.)

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    1. That's a really good point, and I'm unhappy that I overlooked that above. The only save I can make is that in the LBBs the maximum armor/shield bonus is +3 (best AC -4), so the worm would still hit on 13 and swallow on 18. But as soon as you use Sup-I with armor up to +5, that rule does become relevant. That's for pointing that out.

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    2. Yeah, when I was driving into work it dawned on me that btb OD&D (pre Sups) you'd not have that tricked out fighter anyway. Thanks for being gracious in pointing that out!

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    3. I think in true LBB armour and shield / other magic things don't stack, so the best is equivalent to AC -1, although it's written as AC 2 with 3 subtracted from the attack die, of course and I don't remember playing it that way, but I didn't really start until 1977.

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    4. You're basically right that it gets complicated like that. Vol-2 p. 31 says: "Armor proper subtracts its bonus from the hit dice of the opponents of its wearer. If the shield's bonus is greater than that of the armor there is a one-third chance that the blow will be caught by the shield, thus giving the additional subtraction."

      So with a magic shield there's at least a chance each attack that the shield's bonus stacks to penalize the attacker. (Unless by "additional" he meant "higher".) Super glad to have that rule scrubbed out.

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    5. I always read that "additional" as "higher," personally. So if your shield is +3 and your armor is +2, you have a one-third chance of the "additional" +1 taken into account. It was a weirdly-phrased mess from start to finish - like the usage of "hit dice" to refer to the attack roll. Cleaning that up was one of the best things Supp-I did. Of course, with the advent of variable weapon damage, Gary kind of needed to buff shields in order to make them a viable alternative to two-handed weapons.

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    6. Agree that was a critically necessary fix-up in Sup-I.

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  8. Sorry, I don't think I was understood. I'm saying keep your baseline of fighters in chain, shield, and +1 sword, and put them up against better (or worse) equipped fighters (instead of monsters) to see how much difference alternate equipment makes in EHD.

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    1. Oh yeah, that's a good idea. I'll see if I can find time for that in the future.

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  9. Have you read the "Monstermark" series of articles by Don Turnbull from the early UK White Dwarf magazines (1977)? They were pencil and paper calculations almost exactly like these. He found the number of first level AC2 FM needed to kill each monster in the game if queued in a line and fighting one by one. Many found it a little too mathematical, but I loved it and based my early exp. system on it. The table he produced was also an excellent monster quick reference sheet. Really got me into D&D. This was LBB plus Greyhawk, which was what most of us did around the time of Holmes.

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  10. ...or it might have been the number of hit points expected to be handed out by each monster to such an infinite line of fighters before it went down. It was a long time ago now, I'll try and dig it out to check. I remember he had problems with level drain and pulled a bonus out of thin air for that.

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    1. That sounds great, I'd love to see it! I don't think I've ever had my hands on a single copy of White Dwarf ever in my life (but it always sounded great). I must admit I feel super lucky to live in the era of copious computing power that makes these exercises a lot easier.

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    2. I'll see what I can type in. I do have original issues 1-20 or so, but I'm nervous about posting a scan because of copyright issues, so I'll think about some fair use quotes.

      I loved the early WDs, they were quirky and uneven but had a unique atmosphere. It lost it later when GW became a more professional business. I sold most of my collection (with all my OD&D stuff) for a pittance to a US serviceman when I went to university to raise cash. Not a great financial decision when I see what they go for now...

      Actually, I remember programming the MonsterMark formulae up on a HP calculator. Fun times.

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    3. Sounds like good material!

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    4. OK, I've found it. The Monstermark was published in White Dwarf 1--3 (Jun/Jul--Oct/Nov 1977), building on something earlier in 'Owl and Weasel' but much more complete.

      The basic idea is this.

      Defence (D) is the number of rounds a monster will expect to survive being attacked by a sword-weilding FM1 (this is all Greyhawk d8 HD and sword damage, but it doesn't matter for D).

      D = (HP * 40)/(9*(AC +2))

      Aggresiveness (A)is the amount of damage that a monster can expect to do in D rounds to AC2 targets (i.e how much it dishes out before it dies).

      A = D * Prob(hit AC2) * average damage

      For straightforwrad monsters, Monstermark (M) = A.

      Example, an ogre: D=12.1, A=M=29.9

      For 'special powers' there is a hand-tuned factor, e.g. if a paralysis attack, then M = 2A and so on. This is the weak spot in the system, especially with magic and level drain if the monster has otherwise low damage.

      He evaluates every D&D and EPT monster of the time from a kobold (M=1.1) to the Iron Golem (about 32,000 -- but not much is over M=2,000).

      Apart from checking the Greyhawk tables (he makes a new set of 12 levels), there's ideas for determining the number of wandering monsters and dungeon-stocking and what I remembered, a new exp system of exp=10*M/level (although '10 may be too high'). I only abandoned that later when I realised I was doing a lot of work for a relatively minor award compared to treasure.


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    5. A couple of observations: Don Turnbull uses a really nice, compact notation for monster attacks in one line of the form
      AC HD N : p1n1 : p2n2 ... : S
      where N is the number of attacks, p1 the probability of one causing damage n1 and S a letter code that keys to special powers. I like that, and had forgotten it. He didn't think Greyhawk made sense when some monsters attacked with both horn and bite (reflecting how long he saw a melee round as being, I suppose), so some are non-standard here.

      e.g. a vampire is written simply

      vampire 2 8 1:100% 5.5:LLMa (M=440)
      (two 'L's for two levels drained, Ma for other magical attack/defence!)

      or

      ent 2 8 2:100% 10.5:100% 10.5: - (M=420)

      And M really reveals the importance of AC rather than just HD in how tough a monster is.

      Finally, he makes the interesting observation in a couple of places that multiple monsters are much worse -- but it is impractical to calulate that. In particular, if experience refelects risk, then killing a group of 50 hobgoblins shouldn't just give you 50 times the experience of killing a lone hobgoblin -- the risk isn't linear. Over to your program!

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    6. That's really interesting! The M-metric idea seems like a good one.

      The one critique I'd have is I never have a good time parsing stat blocks with just numbers in a certain sequence; I always need labels to cue what I'm looking at. (AC 2, HD 8, etc.) In fact, I actually grade on that for graphs on my in-class tests. :-)

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    7. The reference for the M-metric is an FM1 and its value reflects how dangerous the monster is to a low-level fighter.

      High M indicates that the encounter is too much for a single FM1 PC and is better suited at high(er) level.

      However, since 'dangerousness' does not scale equally with level for all monsters, it might be that, say, a M=300 monster is actually more dangerous for a FM6 PC than a M=400 monster.

      So, the M-metric might not be a good basis to determine XP, after all.

      Or am I overlooking something?

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    8. ^ That's kind of what my intuition was, too.

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    9. Yes, but I think it is still OK for relative power until the monsters have 'special powers'. Then it becomes a matter of hand tuning/waving again.

      M is the damage that monster will hand out to any AC2 targets (which is common for PCs in OD&D) in the time taken for first level FM to kill it. Clearly that time gets less with higher level PCs, but a lower M will not be more dangerous than a higher M one, unless it has special attacks that throw it all off.

      I'm thinking poison: true, a lower level PC will have a harder time making a save than a higher level one will, but they also have 'less to lose' especially if a monster does damage with the attack as well that might kill them anyway. I could imagine that a spider, say, is deadlier to lower levels, but is still a risk to higher ones, whereas a ogre goes from fearsome to not much of a threat at higher levels. Not that I often got there alive...

      Magic just breaks the system. A high level MU wouldn't have a meaningful M really, it just goes back to intuition like Greyhawk itself.

      I'm not advocating M for experience, or anything else really, but this great series of posts reminded me of it (and provided a great excuse to dig out the articles that I have sent to Delta) and it might be fun to see how well it correlates. It's worth remembering that in 1977 a pocket calculator even was a luxury item, and most did not have access to any sort of computer, but a lot of the same thoughts were going through people's heads.

      On a side-track, I've never really been happy with experience for kills. It's pretty obvious form the pseudo-exponential level boundaries, and experience progression per HD (at lower numbers anyway) from Greyhawk, and scaling awards by monster level/character level in M&M, that the original designers had a real issue with players sticking around to bully goblins if they could get away with it!

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    10. I agree that the M-metric indeed tells something about relative power levels for vanilla creatures.

      Just to be sure, I really enjoyed your comments on the new metric and had not the intention to down play them.

      On XP for kills, I see your point, but flavourwise I think learning something from entering the fray is a valid design concept.

      Maybe it is also sub-optimal DM-ing? If petty humans get bullied by, say, ogres, adventurers are called for. I guess the goblins could do something similar when bugged by PCs, right?

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    11. Oh, I'm sure. I didn't think you were down playing anything and it's an interesting discussion how this does all work beyond vanilla combat (on both sides). If everything could be simply rated I suspect we wouldn't still be enjoying discussing a fifty-year-old game! Chess is a good example; we know a Rook is generally worth more than a Knight, but sometimes a Knight can be exactly what you need for a winning move and it's pretty hard to quantify their values despite the vast effort that has gone into it over many more games/datapoints and fewer pieces.

      Exp is such a key concept in D&D compared to many other games of its time. But I'm never entirely happy (a DM award seems too arbitrary, just as for treasure amounts, and for kills only encourages senseless murder and so on..). A lot of it is just 'feel': you must have some advancement sometimes, but not too easy.

      Certainly DMing of monsters is suboptimal. They are often played stupidly (or they would prepare and kill the characters most times). On the other hand, I've always taken a liking to extremely cunning kobolds who really offer much more threat than their hit dice/M or whatever suggests they should by working together. One of the good things about finding others on the net in the OSR is to find I'm not alone in my love of the little guys.

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    12. I totally agree with everything you just said, including your opinion wrt. kobolds.

      My avatar is, in fact, the kobold from 'Het oog des Meesters' (translated into English under the name 'Dark eye'); it was my first RPG back in the 80s. In that RPG kobolds were indeed physically weak, but very mean and cunning!

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  11. Yes, it's a bit unclear. Like the rest of 1974 combat really. It's just a pain to implement and I've always stacked anyway. Few enough PCs ever got good enough armour and shield, so good luck to those who did. And helping basic FM was often an effect I wanted as they seemed to be outclassed by everyone else in the end.

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    1. Sorry, this was meant to go intot the discussion of stacking shield bonuses. Don't know what happened -- iPad late at night, I think.

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    2. I've figured it out: even though I hit Reply directly below the comment that I want to reply to, it goes to the bottom if I then have to authenticate via Google. Once I have signed it, it goes where I expected it to... sorry for messing up the continuity here, I've moved one comment back up, but the earlier one isn't worth moving now, it has lost its place in the thread.

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    3. Right, it's something I have to deal with as well, so I'm accustomed to replies sometimes landing a bit further down.

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  12. Fair point. In practice, the stats are in table form, so there are headers. I've mailed you scans. My main compliant is the damage average, I'm fine turning 1-8 or d8 into 4.5, but I guess it isn't natural to everyone, and only giving the average is ambiguous as a quick reference.

    I work for a notoriously fussy institution that would slaughter a lot of the notation that is used, so I know what you mean about grading ;-)

    By the way, I meant to say I've really enjoyed your blog; I'm not often tempted to comment, so take that as a compliment of sorts :-)

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    1. Thanks so much for the comments!
      I've had at least one close friend recently say he was very impressed by the high-quality of comments we get posted here. So feel free to make me look smart any time you like. :-)

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