Sunday, July 27, 2014

De Profundis

Out of the depths I have cried unto Thee, O Lord, Lord, hear my voice.
Let Thine ears be attentive: to the voice of my supplication.
If Thou, O Lord, shalt mark our iniquities: O lord, who can abide it?
For with Thee there is mercy: and by reason of Thy law I have waited on Thee, O Lord.
My soul hath waited on His word : my soul hath hoped in the Lord.
From the morning watch even unto night: let Israel hope in the Lord.
For with the Lord there is mercy: and with Him is plenteous redemption.
And He shall redeem Israel: from all his iniquities.
Eternal rest give to them, O Lord.
And let perpetual light shine upon them.
May they rest in peace.
Amen.

Tuesday, July 22, 2014

Save or Die! Reviews Seven Voyages of Zylarthen


The current Save or Die Podcast, Episode 94, has a detailed hour-long review of Seven Voyages of Zylarthen. Save or Die was one of my primary sources of inspiration in writing the game, and so, to quote DM Jim in another context, I couldn't help feeling "warm and fuzzy" listening to my favorite podcast people--Mike, Liz and Jim (Glen was not on the show this week)--thoughtfully discuss Campion & Clitherow's "re-imagining" of the three little brown books. As usual, the members of the Save or Die cast were fun and funny as well as highly informed and intelligent...in the true NPC definition of the term!

Almost as cool were the references to Zylarthen's "Petersonesque" quality. My wife--she who was kind even to kobolds--let out a laugh of unmitigated joy and delight upon hearing that mention. She can tell you I carried Playing at the World around like a bible for a few weeks. I too would love to hear what Jon Peterson thinks. Though, just as I did before that Save or Die episode, I would probably fortify myself with a few drinks first. 


For those who may not have not yet encountered Save or Die (shame on you and/or where have you been?), it is I believe the only "straight" podcast dedicated exclusively to original and classic D&D and related games and materials (by "straight" I mean, devoted to discussion and not, say, to actual play reports). I think it's by far the most entertaining and informative OSR podcast out there (and yes, I thought that long before Episode 94). I'll be talking a bit more about the show in general in a later post. But I'll say here that if you haven't yet encountered any of the episodes--now stretching back almost four years--you're in for a treat.


You can listen or download this (or any?) episode from their website here. And it is also available, free of charge on iTunes and RSS.


Any considered and thoughtful reaction to an author's work, positive, neutral or negative is of course valid. On the other hand, there is nothing more gratifying for an author than to believe that a reader (or in this case three of them) just, well, "gets it" about what he or she was trying to do. It's also neat when a critic takes a "smaller" or less obvious idea, and just runs with it, prompting the author to re-evaluate what he or she might have (somehow) channelled from the creative font of all things. So it was with the False Gnomes. My wife gave another laugh of delight at their final appearance in the closing credits. Cheers, guys! I really appreciate it.


BTW: No damn idea how to "correctly" pronounce the name. I've gone back and forth myself. (I can't believe Spalding just admitted that!)  Xylarthen (spelled with an "x") was the first sample character in Men & Magic. Jeff Rients riffed on him in his excellent convention module Under Xylarthen's Tower. So perhaps Jeff or Jon might have an idea.

Monday, July 21, 2014

Link to Me, Baby!


I just spent a few hours updating my OSR blog link list (results at right). It was fun and I made a number of great discoveries. But undoubtedly I left off many worthwhile entries out of ignorance. Please email me or comment, below, if you would like your OSR gaming-related blog to be included.

In return, if you think my blog is worthy, add me to your blog roll. Or, rather...


LINK TO ME, BABY!!!


(I could use the hits)


The fun illustration, above, Monsters Holding Hands, is by Jonathan Frazin, an artist and illustrator working in the Chicago area. He started the piece at our mutual place of business with a fifty-nine cent mechanical writing implement. Then, as he said later in private correspondence, "I was able to do much closer detail once I had my proper pencil." I think that's like a magic wand or something. For more of Mr. Frazin's wonderful work, visit his website, here.

Tuesday, July 15, 2014

The Monsters of Seven Voyages of Zylarthen, Part II


Author’s note: I’m writing a series of posts on Zylarthen not so much to plug it, nor merely because I like talking about my work. Rather, I think of Zylarthen as sort of a love letter to early OD&D. Thus, I hope that the design issues I grappled with and the eventual choices I made might be of interest to those who enjoy “thinking about Original Dungeons & Dragons”, whether or not they have read, played, or have any intention of reading or playing my attempted “re-imagining” of it.

In this post I break down the precise sources for the various Zylarthen monsters.

In a previous post I wrote that I decided to include all and only those monsters appearing (in whatever form) in “official” D&D sources through the fall of 1975—those three sources being the original 1974 edition of the game (henceforth the three little brown books or 3 LBB’s), the first supplement—Greyhawk—and the first four issues of The Strategic Review. Interestingly, this cut-off point yielded roughly two hundred distinct creatures, even excluding most of the various “man-types”—leveled non-player characters, hirelings, soldiers and the rest—almost triple the initial number of monsters described and “statted” in the first part of Monsters & Treasure. The place to begin, though, is with those monsters:

Note: in the following lists, re-imagined creatures, my own extrapolations and extrapolations based on later sources will generally be denoted by italics.

THE MONSTERS from Monsters & Treasure, pp. 3-20
Bandits, Basilisks, Berserkers, Black Pudding, Buccaneers, Cavemen, Centaurs, Chimerae, Cockatrices, Dervishes, Djinn, Black Dragons, Blue Dragons, Golden Dragons, Green Dragons, Red Dragons, White Dragons, Dryads, Dwarves, Efreet, Air Elementals, Earth Elementals, Fire Elementals, Water Elementals, Elves, Gargoyles, Ghouls, Cloud Giants, Fire Giants, Frost Giants, Hill Giants, Stone Giants, Goblins, Gnoles, Gnomes, Gorgons, Gray Ooze, Green Slime, Griffins, Hippogriffs, Horses, Mules, Camels, Hydras, Fire Breathing Hydras, Kobolds, Werebears, Wereboars, Weretigers, Werewolves, Manticoras, Medusae, Mermen, Minotaurs, Mummies, Nixies, Nomads, Ochre Jelly, Ogres, Orcs, Pegasi, Pixies, Purple Worms, Rocs, Sea Monsters, Skeletons, Spectres, Treants, Trolls, Unicorns, Vampires, Lesser Vampires, Wights, Wraiths, Wyverns, Yellow Mold, Zombies

Number of Monsters: 77.

Notes: These should obviously make up the core of any OD&D monster list. As it happens, none of them are non-SRD. A few are extrapolations. So, for example, I felt that Camels should be added to Horses and Mules, and that Lesser Vampires (the victims of the Stokeresque Vampires) should be added to Vampires. I fiddled with Gnomes to make them genuinely strange (as opposed to being merely more whimsical Dwarves). And I preserved the spelling of “Gnole” from the original Dunsany story as well as ignoring both the initial description of these monsters—“A cross between Gnomes and Trolls…otherwise they are similar to Hobgoblins”—and the description that would come a few years later in the Monster Manual—“There is a great resemblance between Gnolls and Hyenas”—in favor of leaving them explicitly undescribed, as they are in the story.

OTHER MONSTERS from Monsters & Treasure, pp. 20-22
Androids, Cyclopes, Gelatinous Cubes, Flesh Golems, Iron Golems, Stone Golems, Juggernauts, Living Statues, Robots, Salamanders, Titans

Number of Monsters: 11.

Notes: Some of these—Gelatinous Cubes, Golems, Salamanders and Titans—would later be more fully described in Greyhawk. For the fun of it I named all twelve of the Titans.

MONSTER LEVEL TABLES and WILDERNESS WANDERING MONSTERS from The Underworld & Wilderness Adventures, pp. 10-11 and 18-19
Apes, Boars, Lions, Snakes, Spiders, Giant Ants, Giant Beetles, Fire Beetles, Centipedes, Giant Hogs, Giant Lizards, Giant Rats, Giant Scorpions, Giant Poisonous Snakes, Giant Spitting Snakes, Huge Spiders, Large Spiders, Water Spiders, Giant Toads, Giant Weasels, Cave Bears, Dire Wolves, Mammoths, Mastodons, Saber-Toothed Cats, Spotted Lions, Titanotheres, Wooly Rhinoceroses, Brontosaurus, Pterodactyls, Stegosaurs, Triceratopses, Tyrannosaurus Rex, Cyborgs, Doppelgangers, Invisible Stalkers, Shadows, Thoblins, Apts, Banths, Calots, Darseen, Black Martians, Green Martians, Red Martians, Ancients, Therns, Holy Therns, Lotharians, Yellow Martians, Orluks, Sith, Tharks, Thoats, White Apes

Number of Monsters: 55.

Notes: So, counting the Zylarthen extrapolations, the number of these “missing monsters” almost equals the fully described monsters in Monsters & Treasure. The attentive reader will notice the cases where I consulted Blackmoor or even the Monster Manual. But some monsters such as Giant Ants were intentionally re-imagined. (For the Ants, think those creepy bugs from that great Outer Limits episode, “The Zanti Misfits”.) Of course the four varieties of White Martians are extrapolations based on the actual Burroughs stories. For all Martians, I learned much from David Bruce Bozarth’s A Barsoom Glossary as well as from the original Warriors of Mars and the OD&D version by “Doc”.

NAVAL COMBAT in The Underworld & Wilderness Adventures, pp. 28-35
Giant Crabs, Crocodiles, Giant Crocodiles, Dragon Turtles, Giant Fish, Giant Leeches, Giant Octopi, Giant Sea Snakes, Giant Squids

Number of Monsters: 9.

Notes: Some of these appeared in the earlier encounter tables, and all them (I think) reappeared in the aquatic-fixated Blackmoor.

Other Monsters from “The Three Little Brown Books”
Amazons, Assassins, Barbarians, Bats, Huge Bats, Bears, Elephants, Halflings, Prisoners, Rats, Tigers, Vikings, Witches, Wolves

Number of Monsters: 14.

Notes: This is perhaps the most interesting group. There are illustrations of Amazons, Barbarians and Witches in Men & Magic, yet these beings were never described in that source or in any other early source (1974-75) nor have they been included in any of the retro-clones, as far as I am aware. Witches would seem to be almost paradigmatic in terms of being staples of fantasy stories as well as being featured in the classic explanation of the charisma ability score in Men & Magic. Vikings (or “Viking” things) are actually mentioned four times in The Underworld & Wilderness Adventures but they fell out in later editions I assume because they were too “historical”. Ditto for Amazons. For Amazons I jettisoned the sexist (though intriguing!) interpretation that they fought without clothing (I kept that for Barbarians, and there is historical justification for that) but kept the fun (for me at least) assumptions concerning body modification and the rumor that Amazons would temporarily take captured males as lovers. I took some of the inspiration for Barbarians from the description of them in that great Avalon Hill wargame Caesar at Alesia, though inexplicably I forgot to cite it in my otherwise relatively long Sources section. There’s a fair amount of reference to “prisoners” in the Treasure Tables of Monsters & Treasure so I decided to expand on that.
Gods and Goddesses
Apollo, Artemis, Athena, Balder the Beautiful, Girra the Fire God, Ishtar, Isis, Kali, Lakshmi, Manannan the Sea God, Math the Great Wizard, Odin the One-Eyed, Pan, Set Lord of Shadows, Silvanus, The Spider God, Thor, Thoth the Terrible, Tsathoggus, Untamo God of Sleep and Dreams

Number of Monsters: 20.

Notes: As I wrote in the first post, it seemed a no-brainer to include gods and goddesses alongside the “regular” monsters. But I also thought the wide-open spirit of the original game dictated including beings from a diversity of sources—Classical, Egyptian, Norse, Middle-Eastern, Celtic, Finnish and of course Hyborian. Though most appeared in the 1976 Gods, Demi-Gods & Heroes or its later 1980 incarnation, Deities  & Demigods, the descriptive content was almost entirely taken from original sources. Unlike for the other monsters, I did not give statistics to these immortals, believing that that would be a waste of space as well as sending the wrong message. Any god or goddess could easily defeat a character of any level if he or she had a mind to, so what’s the point of saying so and so has 300 hit points? But for each god or goddess, I did try to provide meaningful and useful information on how to actually include him or her (or his or her followers) in a campaign or adventure, if and when the occasion arose.

Giant Flyers
Bumblebees, Butterflies, Dragonflies, Eagles, Flies, Hornets, Locusts, Moths

Number of Monsters: 8.

Notes: Giant Eagles are mentioned in Chainmail, but the others are extrapolations based on the mention of “Large Insects” or “Giant Insects” in the rules on Aerial Combat in The Underworld & Wilderness Adventures. It was another way to be “original” without completely departing from the sources. I thought these winged critters rounded out the list of standard giant creatures in a way that was both fun and added to the diversity of things.

Evil Men
Brawlers, Ruffians, Duellists, Black Knights, Rakehells, Villains, Bravos, Interfectors, Evil Lords, Malefics, Praecantors, Diabolists, Demonurgists, Black Magicians, Hecatontarchs, Haruspices, Evocators, Incantators, Necromants, Wizards, Lifters, Snatchers, Fingerers, Harpaces, Sicarians, Phansigars, Thugs, Evil Thieves, Evil Master Thieves, Evil High Priests or Priestesses, Evil Priests

Number of Monsters: 31.

Lawful Men
Fighters, Pavisers, Thanes, Knights, Guardians, Defenders, Protectors, Vindicators, Lords, Famuli, Chirosophists, Tregetours, Pellars, Theurges, Thaumaturges, Talismanists, Solonists, Mirabilists, Magi, Archimagi, Borrowers, Mousers, Gilters, Dodgers, Coursers, Rescuers, Targeteers, Swordmen, Thieves, Master Thieves, High Priests or Priestesses, Priests

Number of Monsters: 31.

Notes: I loved the evocative level titles of the early version of the original game—another thing that would gradually fall out over the editions. One thing that virtually everyone has noticed about Zylarthen is the (mostly) new level titles for both the Lawful and Evil members of the three main classes. This was done for legal reasons but also for the sheer fun of it. It’s true that Gygax chose some silly titles, but he also laid claim to some of the better and more obvious ones, so I can’t say the enterprise was quick or easy. A number of specialized dictionaries as well as the OED came in handy here. Zylarthen assumes that player-characters (even Thieves) are basically good-guys, so titles with sinister, dark or particularly violent connotations were reserved for the Evil list. Particular effort was taken to clearly distinguish practitioners of “white magic” from, say, the “Wizards” of the Old Testament and other historical sources. I think most people appreciated the new titles, but everyone (including me, secretly) has their choice for one or two they don’t like. Note that Priests and Evil Priests only have one level. Since in Zylarthen, priests and evil priests become non-player characters, I didn’t see a need fuss things up with a full list of levels. Evil High Priests and High Priests have many of the most powerful Cleric spells that were not collapsed into the list for Magic-Users (including Finger of Death for Evil High Priests) but Evil Priests and Priests simply have a sort of aura, or whatever, around them that helps their friends and harms their enemies.
Monsters from Greyhawk
Aerial Servants, Blink Dogs, Bugbears, Cave Creepers, Brass Dragons, Bronze Dragons, Copper Dragons, Silver Dragons, The Dragon Queen, The Dragon King, Druids, Storm Giants, False Gnomes, Half-Elves, Harpies, Hell Hounds, Hobgoblins, Homunculi, Lammasu, Liches, Lizard Men, Wererats, Ogre Magi, Owl Bears, Paladins, Phase Spiders, Phaetonians, Rust Monsters, Sea Horses, Shift Panthers, Giant Slugs, Stirges, Giant Ticks, Tritons, Will O’Wisps

Number of Monsters: 35.

Notes: Even though these are relatively few in number, there are many canonical ones—so many that some don’t realize they didn’t exist in the original edition. This is why including Greyhawk was a must. A few of these as well some from the next two categories were non-SRD creations that I decided to modify into “science-fictional” or alien creatures. While I initially thought the issue annoying, I ended up with something I actually preferred, as the Androids, Cyborgs, Robots and Martians of the 3 LBB’s were now joined by entities hailing from Jupiter and the surface of the Sun.

Monsters from The Strategic Review
Clay Golems, Ghosts, Leprechauns, Lurkers Above, Guardian Nagas, Spirit Nagas, Water Nagas, Piercers, Rangers, Ropers, Shambling Mounds, Shriekers, Tentacle Men, Wind Walkers, Yeti

Number of Monsters: 14.

Notes: More canonical monsters. I liked what I did with Ghosts. Note that Zylarthen does include Rangers and Paladins (see Greyhawk, above), but only as non-player characters. I’m sure this was disappointing to many.

Monsters from Chainmail
Faeries, Solians, True Wraiths

Number of Monsters: 3.

Notes: Well, the last two fell out of the original for obvious copyright reasons (though the middle one would reappear in an inferior form). I decided to resurrect them.

Soldiers

From Men & Magic: Archers, Armored Foot, Barbarians, Crossbowmen, Heavy Foot, Heavy Horse, Horse Archers, Horsed Crossbowmen, Light Foot, Light Horse Bowmen, Light Horse Lancers, Mailed Bowmen (Medium Horse Bowmen), Mailed Crossbowmen (Heavy Crossbowmen), Medium Horse, Turcopoles

From Chainmail: Knights (Oddly, the term “Knight” appears nowhere in the 3 LBB’s), Javelineers

Extrapolations: Cataphracts, Cheirosiphoneers, Dwarf Guards, Elf Legionnaires, Halfling Slingers, Hoplites, Irregulars, Koursors, Peltasts, Pikemen, Mobs, Savages, Slingers, Varangians

Number of Monsters: 31.

Notes: I thought the original edition was simply begging for a clear and comprehensive list of soldier variations. And I thought it would be fun to include a table for the place of origin (native or foreign) and disposition of the soldiers upon encountering them. You probably don’t want to run into “friendlies” directly after they just got trounced in battle.

The AD&D Monster Manual
Troglodytes

Number of Monsters: 1.

Notes: My one concession to post-1975 modernity. Can you fault me?

So that’s the full list, 340 “monsters” if you count them broadly. Virtually all of them also appear in both the “Monster Encounter Tables” and “Wilderness Encounter Tables” of Zylarthen’s fourth and final volume—The Campaign. As with the encounter tables of the first version of the original game, a large proportion—one-third—are “man-types” of one form or another.

All in all, I’d like to think there’s enough “new” material to peak even the most veteran OD&D player’s interest.

Notes on Illustrations:

  1. This drawing doesn't appear in the Book of Monsters but rather in the Book of Magic, p. 21.  What is it? Perhaps a Homunculus small enough to conceal itself in its master's mouth. I suppose you need an additional spell for that. Cropped from an illustration from “The Vision Of Macconglinney,” in Jacobs, Joseph, More Celtic Fairy Tales, illustrated by John Dickson Batten, New York: G.P. Putnam’s Sons, 1895, orig. 1894, p. 73.
  2. A Pixie from Book of Monsters, p. 47. From “My Own Self,” in Jacobs, More English Fairy Tales, illustrated by John Dickson Batten, New York: G. P. Putnam’s Sons, 1894, orig. 1893, p. 18.
  3. A Witch from Book of Monsters, p. 62. From ”Morraha,” in More Celtic Fairy Tales, p. 87.
  4. An Evil Man from Book of Monsters, p. 22. Cropped from The Magic Purse, from “The Three Soldiers,” in Jacobs, Europa’s Fairy Book, illustrated by John Dickson Batten, New York: Knickerbocker Press, 1916, p. 73.
  5. A Ghost, one of the nastiest monsters in any category, from Book of Monsters, p. 25. Taken from the chapter illustration for “The Golden Arm,” in Jacobs, English Fairy Tales, illustrated by John Dickson Batten, New York: G.P. Putnam’s Sons, 1892, orig. 1890, p. 143.

Saturday, July 12, 2014

Of Orcs and Probability


In the last post, I addressed what in the comments section I called a "category error"—wrongly imputing the existence in the fantasy world of a unit of measurement in the game mechanic that existed only in our world. There are no hit points in the fantasy world, nor are there abilities such as Strength or Constitution, nor +1 modifiers to magic swords, nor players, GM's or potato chips. But there are genes (probably), creatures that are strong or have a sturdy constitution, magic swords of varying utility (some of which talk back to you), player-characters (as opposed to players), gods (sort of like GM's but easier to sweet talk) and almost certainly potatoes. Mixing categories, or mixing up worlds leads to all sorts of errors. Constructing a theory of evolution in the fantasy world based on hit points is a bit like basing it on potato chips.

But I want to leave that point for now. For the fun of it, let's assume that hit points do have a real existence in the fantasy world, like genes perhaps. And thus we can now go along with constructing a kind of evolutionary theory that might show how a community of, say, Orcs has its low hit point members gradually (or not so gradually) weeded out through fighting. There's no question that they would be weeded out eventually, of course, but it might be fun and interesting to track how the process would occur.

The initial set-up was specified in this blog post. You start with 100 one hit die Orcs with an average spread of 1-8 hit points—12.5 would have 1 hit point, 12.5 would have 2 hit points, and so on. They fight three rounds against a similar group of Orcs. Each Orc has an Armor Class of 6 and carries a spear that does 1-6 points of damage. At the end of this, how many Orcs would survive? Perhaps more interestingly, what proportion of each hit point group of Orcs would survive? And how would this change the overall spread of the different hit point groups?
The claim was made that:

From the final count, if we presume that any of these humanoids we're meeting have been in only 3 rounds of combat, only 1 in 100 humanoids should have 1 hit point.  Only 13% should have 3 or less. Nearly half, 45%, should have either 7 or 8 hit points.  More than three quarters, 77%, should have 5 or more.

This is because:

Trying to get my math right here.  The numbers are based on the chances of being hit once plus the chance of being hit twice and the chance of being hit three times, multiplied by the chance of any of those hits killing the humanoid.  The humanoid's attacks are not considered - only the chance of a humanoid with an armor class of 6 surviving three spear attacks during a given combat.

Actually, he didn’t get his math right.

That’s okay, we all make mistakes, and I owe a debt to that blogger for giving me an interesting puzzle in probability to occupy myself for an hour or so after the kids had gone to sleep.

The easiest way of seeing part of it is to focus on the weakest group—the 1 hit point Orcs. All they need is one successful hit against them and they go down. You don’t need to figure out the chances of, say, one hit versus two hits occurring, or how much expected damage might or might not be done with each strike. Rather, it’s quite simple: One hit and you’re dead.

What are the odds that you’ll be hit? Well, flip it—what are the odd’s you won’t be hit? Every round there’s a 60% chance you won’t be hit (1-12 is a miss, 13-20 is a hit). Thus, the odds for surviving three rounds are 60% x 60% x 60%, or roughly 22%. That roughly tracks this blog post’s leading graphic, above. 4 Orcs would reduced to 1.  12.5 Orcs would be reduced to 2.7. However, asking how many 1 hit point Orcs would remain out of 100 survivors has to take into account that many of the other stronger Orcs would also have fallen. As we shall see later, it comes to about 50%. So out of 100 surviving Orcs (imagine you started with 200), there would be 2.7 x 2, or roughly five 1 hit point guys still standing. So the proportion of the wimpiest would have been reduced from 12.5% to 5%. It’s a tough world. But not quite as tough or tough so quickly on the 1 hit point Orcs as was originally claimed. The answer after three rounds is not 1 in 100 but more like 5 in 100.

Quick digression: the original blogger pegged the to hit chances at 35% not 40%. Every early edition of D&D that I’ve seen, from the original 1974 version to the 1e Players Handbook, to Moldvay/Cook has one hit die monsters hitting AC 6 opponents on a 13. So why 35%? Most likely, the blogger made the same mistake that I sometimes make in my head: 13 to hit means a probability to hit of (20-13)/20, right? Wrong. Don’t forget to count the 13. The correct formula is 20 minus the highest roll to miss (12) not the lowest roll to hit (13). Or if you prefer, you can also just add 1 to the numerator. But pegging the chances at 40% rather than 35% actually kills the weaker Orcs quicker. If the chances to hit had only been 35%, then 27% or 3.4 (as opposed to 2.7) would have survived.

Moving on to computing the survival odds for all Orcs, I’m not going to explicitly go through the whole thing, but here’s a sketch:


1. The first thing to do is break down the odds for any Orc in a three round battle being hit 0 times vs. 1 time vs. 2 times vs. 3 times. You can represent it like this:

Permutation
1st round
2nd round
3rd round
# of hits
Probability






1
miss (60%)
miss (60%)
miss (60%)
0
21.6%
2
miss (60%)
miss (60%)
hit (40%)
1
14.4%
3
miss (60%)
hit (40%)
miss (60%)
1
14.4%
4
miss (60%)
hit (40%)
hit (40%)
2
9.6%
5
hit (40%)
miss (60%)
miss (60%)
1
14.4%
6
hit (40%)
miss (60%)
hit (40%)
2
9.6%
7
hit (40%)
hit (40%)
miss (60%)
2
9.6%
8
hit (40%)
hit (40%)
hit (40%)
3
6.4%

This gives totals of:

Chance of 0 hits
21.6%
Chance of 1 hit
43.2%
Chance of 2 hits
28.8%
Chance of 3 hits
6.4%

So, now, without doing any more calculations, we can also see why 7 and 8 hit point Orcs make out so well in the original blogger’s example. Since the maximum damage is 6 hits, an Orc with 7 or 8 hit points must be hit at least two times to be killed (and even then there’s a good chance he won’t be killed). But there’s only about a one-third chance this will happen. Why, in the original example, all the Orcs are fighting with spears as opposed to doing standard damage of 1-8, or using some of the better weapons assigned to Orcs in, say, the Monster Manual is a good question. But it shows up an interesting and almost paradoxical pattern. The less effective the weapons the worse the wimpier Orcs will fare relative to their 7 or 8 hit point comrades. The evolutionary process would happen quicker if Orc armies wielded daggers. Conversely, if the Orcs were all wielding two-handed swords or halberds, the proportions of surviving wimpy Orcs versus surviving strong Orcs would be less pronounced. Even doing the calculations with weapons that did 1-8 points of damage (as opposed to those spears doing only 1-6) would smooth things out on the survival curve (as opposed to the discontinuous break in the original example that separates the 7 hit point and 8 hit point Orcs out from the rest).

2. Now compute the expected damage chances for 1 hit, 2 hits and 3 hits. Here, we’re actually in familiar territory as we’re simply calculating the odds for achieving various totals using 1d6, 2d6 and 3d6. Many OD&D players almost carry those odds around in their heads.

3. Next multiply the two together in all the possible cases. I used an Excel spreadsheet, and again I won’t go though the details, but the final expected survival numbers after 3 rounds of battle are given on this table.

1 hp
2 hp
3 hp
4 hp
5 hp
6 hp
7 hp
8 hp
2.7
3.6
4.6
5.7
6.9
8.2
9.6
10.2

That gives the expected number of survivors as 51.5 out of a starting group of 100.

That’s actually an interesting number. It shows that for one hit die or 1st levelish creatures with moderate armor, if you (as a low level character) fight them for three rounds, you are likely to have reduced their numbers by about half. That’s another morale break point, I think. Low level OD&D combats shouldn’t last very long.

We can rewrite the results using percentages (by dividing the results by 51.5%). Drop the %’s and you have the number of Orcs in each hit point category out of 100 surviving ones:

1 hp
2 hp
3 hp
4 hp
5 hp
6 hp
7 hp
8 hp
5.2%
7.0%
8.9%
11.1%
13.4%
15.9%
18.6%
19.8%

These numbers are closer to those of the original blogger at the high ends (though not at the low ends), though they are still not quite as pronounced.  So replace

Only 13% should have 3 or less. Nearly half, 45%, should have either 7 or 8 hit points.  More than three quarters, 77%, should have 5 or more.

With

Only 21% should have 3 or less. Over a third, 38%, should have either 7 or 8 hit points.  More than two thirds, 68%, should have 5 or more.

Keep in mind, though, that raising the to hit chances to 40% helps the original blogger’s case. The numbers would be even more off if we had stayed with 35%.

Finally, you can rerun the numbers using the new proportions—5.2, 7.0 etc. vs. 12.5, 12.5, etc.—to find results if the surviving Orcs decide to fight additional three round battles. Sure enough, if you fight enough three round battles—3 actually—the wimpy 1 hit point Orcs will be reduced to that magic 1 in 100 number.
  

# Battles
1 hp
2 hp
3 hp
4 hp
5 hp
6 hp
7 hp
8 hp
1
5.2%
7.0%
8.9%
11.1%
13.4%
15.9%
18.6%
19.8%
2
1.9%
3.4%
5.5%
8.4%
12.4%
17.5%
23.9%
27.0%
3
0.6%
1.5%
3.1%
5.8%
10.4%
17.4%
27.9%
33.5%


But these numbers are quite different from those originally claimed:


hp
surviving after three battles


1
1 in 11,248 (!!! -ed.)
2
1 in 252
3
1 in 46
4
1 in 15
5
1 in 6
6
1 in 3
7
4 in 7
8
2 in 3

Again, see here.

Extra credit: instead of computing probability formulas, you can simulate Orc battles using the RANDBETWEEN and IF functions of Excel.

For the first to hit roll on a d20 it’s a1=RANDBETWEEN (1,20), then to compute damage you go b1=IF(a1>=13, RANDBETWEEN (1,6), 0). Do that three times and then add the “damage cells” to determine whether you have a kill. If f2 is the number of starting hit points, then the formula is =IF((b2+d2+e2)>=f2, 1, 0) where 1 is a kill and 0 is a survival. Of course starting hit points can be determined by =RANDBETWEEN(1,8). Or one can simply start out with 12 or 13 in each category. For successive battles featuring survivors, you can use a more complicated RANDBETWEEN or even RAND function using the new proportions.

If anyone has ever done something like this in Excel, you know that once you have the formulas set up, you just have to touch a random non-used cell (or fill it in) to simulate another battle and thus get a different result. It takes less than a second.

Probability can be weird. On only my fifth battle I had a situation where the 1 hit point Orcs actually survived in greater numbers than the 8 hit point Orcs.

More power to them!

Final note: I could of course have made all sorts or errors. If any readers would like to try their hand at identifying them, I would of course be interested and not offended. But please, no four-letter words, Alexis.