Friday, August 5, 2016

A Quick Note From GenCon: Ken St. Andre and Metamorphosis Alpha

It's been an interesting couple of days at GenCon!

On Thursday, I managed to speak to Ken St. Andre and ask him when they began to use saving rolls in T&T with other attributes than Luck. He says that the idea occurred to him between 2nd and 3rd editions, which would would place it in 1977; originally, 'saving rolls' had been based only on Luck, and had been used purely for avoiding danger. During that time, however, he realized that the mechanic could be applied to other attributes... and that in so doing, it could be used to resolve active actions as well as reactions.

(2nd and 3rd edition were 'missing links' for me - I have the 1st edition reprint and one of 4th edition, but haven't had access to either 2nd or 3rd.)

He also says that he didn't get the idea from any other game, and that he's rarely looked at other RPGs, except for Runequest, which he had to read completely through while working on Stormbringer.

Given the timing, and that the version of the rules in Monsters! Monsters! didn't have the concept, it looks like Steve Jackson and Ken St. Andre may both have invented the idea of attribute checks independently.

Ken also stated that he suggested the idea of using percentile dice for resolution to the creators of Runequest.

Also available at the con was Metamorphosis Alpha, the first science-fiction RPG. I've picked up the "Collector's Edition", which has the original 1976 rules, errata for them, a collection of articles about MA (including a review from The Space Gamer and several supplementary bits that were published in The Dragon, The Dungeoneer, and The Space Gamer), and commentary by James Ward, Tim Kask, and Jon Petersen.

Since TSR took MA off the market after Gamma World was introduced (apparently feeling that two science-fiction RPGs involving mutated people, animals, and plants would be too many), all I've seen of it before this is the articles from The Dragon about it. I'm looking forward to digging into it!

Tuesday, July 26, 2016

Toward a History of RPG Mechanics, Part 12: The Fantasy Trip - Melee

In the mid-1970s, Steve Jackson (the US one, not the UK one) was working for a game company called Metagaming. At the time, he was "playing a lot of D&D", and, like other people playing D&D, found that combat in the game was unsatisfying to him - too abstract, with no real tactics involved. He was also working on a game for Metagaming called Monsters! Monsters! - an adaptation of the Tunnels & Trolls rules for campaigns where the players would play monsters (later acquired by Flying Buffalo). However, the combat system of M!M! was even more abstracted than that of D&D.

So he wrote a simple (by wargame standards) man-to-man combat game, which he called Melee. Steve realized that it could be the basis for a new RPG, and Metagaming was very interested in getting into the RPG boom. Thus, even before Melee was first published, plans were already underway to create a full RPG based on it: Sword and Sorcery.

Unfortunately, SPI announced that they were going to be releasing a board game titled Swords & Sorcery, so Metagaming had to find a different title to use, and the one chosen was The Fantasy Trip.

TFT: Melee was released in 1977. It was a "micro-game" allowing players to create warrior characters and have them fight each other in arena combat. Melee was packaged as a small booklet (24 pages, roughly 4" x 8"), a hex grid sheet that could be used for the 'arena', and counters. A year later, TFT: Wizard was released as a fully-compatible micro-game of wizardly combat in an arena. It took another two years before In the Labyrinth, the GM's book, was released... but we'll talk about Wizard and ITL later. For now, let's talk Melee!


The first big innovation in TFT was in character creation: the first fully point-based character creation system for an RPG. In Melee, this is extremely simple, due to the narrow focus of the game: characters had only two attributes to set (Strength and Dexterity, abbreviated ST and DX). Each character started with 8 points in each, and an additional 8 points to divide as they wished. A third attribute was Movement Allowance (MA); this, however, was set by creature type, with humans having MA 10.

Players also selected armor and weapons for their characters. There was no system for purchasing these in Melee - instead, the available weapons were limited by ST, and armor reduced effective DX.

That's it to creating characters in Melee, although the game does advise players that "giving each figure a name and background adds interest, especially when miniature figures are being used as counters." We're told that the sample character created is "Ragnar the Impetuous", and that he's a Viking. Various other character names are used in examples: Astrid, Bjorn, Rolf, and Tark.

There's also a full example of combat, which is treated in an interesting way: it's given in a story format in the game's Introduction, then repeated at the end of the rules - but this time, written as a turn-by-turn breakdown, showing how the mechanics work in a complete, if short, fight.


Almost all actions in Melee (and in the rest of TFT) have their success or failure resolved through a single mechanic: the saving roll. We've seen this term previously with Tunnels & Trolls, and it seems likely that Steve Jackson was influenced here by it, through his work on Monsters! Monsters!

The basic concept is the same: one of the character's attributes is tested, with a varying difficulty. The specific method is different, though: instead of being 2d6 + attribute vs. variable threshold, the TFT saving roll is an attempt to roll less than or equal to an attribute score, rolling a variable number of dice. Most commonly, this is 3d6, but easy rolls are 2d6, difficult ones 4d6 (and, in the fuller TFT rules, there would be rolls of even higher difficulty).

Other elements that seem likely drawn from T&T include strength requirements for the use of various weapons, the use of Strength to double as Hit Points (T&T used Constitution for this, but TFT's Strength doubles as an indication of physical health), and armor absorbing damage instead of making characters harder to hit (although TFT armor does not ablate the way T&T's does). More similarities are seen in Wizard, but we'll cover those when we talk about it.

Unlike T&T's highly abstracted combat system, however, Melee was quite detailed. Movement was performed on the hex grid, and the chance for a hit was adjusted for facing (e.g., a foe facing away from you is easier to hit), position (standing, prone, etc), and other factors. A character could choose to Defend or Dodge as an action. Armor reduced effective DX and MA, creating a tradeoff: heavy armor makes it harder to hit your own opponents, thus prolonging combat, while allowing you to take many more hits than you could otherwise.

Some influence from The Perrin Conventions may be visible here as well. The combat round (called a 'turn' in Melee) is similarly short (5 seconds here instead of Perrin's 10), there is an 'engaged' status in melee, characters who move more than half their movement can't do anything else (indeed, there's a whole set of rules for what sort of actions can be combined with what sort of movement, depending on whether the character is engaged or disengaged), and effective Dexterity is used to determine when attacks take place. Attacks can force a target to move back, and hits that do more than a certain threshold of damage cause the target to take a penalty to their effective DX the next turn.

As with many wargames, however, Melee separates "initiative" from "attack order". Opponents roll for initiative, rolling 1d6, with the higher roll winning. No mention is made of how to resolve ties. Initiative is rolled for each turn. The winner chooses whether to move first or to move second; all movement is done, and then combat takes place, with the order of attacks dependent on effective Dexterity, independent of the initiative roll.

This is similar to Chainmail's initiative, but I personally doubt that the inspiration comes from there. Firstly, such initiative systems are common in wargames, which often divide up "movement" and "combat" into separate phases. Secondly, as we've seen in a previous column, Chainmail's combat system was much more detailed than the "alternative" system that was presented in Dungeons & Dragons. If Steve Jackson had been using it, he likely would have felt less frustration with D&D combat.

Ranged weapons are divided into two types; thrown weapons and missile weapons. Range decreases accuracy, with effective DX being at -1 for each hex of distance for thrown weapons, or for each 3 "megahexes" of range for missile weapons. (A TFT "megahex" is a hex of hexes - that is, one hex and its surrounding six hexes. These are marked on the map, which does create some oddness with ranges and such. Megahexes become more important in Wizard, where they are used for areas of effect of some spells.)

Other Concepts

A number of concepts that would later become popular in RPGs show up here for what is, to my knowledge, the first time:

"Shifting" when engaged. The term "shift" is used, and as in the much later d20 System, it is a move which engaged figures can make, limited to one 'space'.

Critical hits and fumbles exist. Since 3d6 is the normal attack roll, a natural 5 or less is considered to always hit. A 4 hits and does double damage; a 3 hits and does triple damage! Since a one-handed "broadsword" in the game does 2d6 damage, and most characters will have less than 16 ST (doubling as hit points, remember), such hits stand a good chance of killing a foe. Even plate armor with a large shield can only block 7 hit points of damage, so criticals with reasonably heavy weapons are quite deadly. For further comparison, a giant will have a ST of "AT LEAST 24; it might be 40 or 50 if he's a tough one." (Emphasis in original.) A triple damage hit with a broadsword will average 21 hits, nearly enough to take down a weak giant, and can do a maximum of 36 hits!

Conversely, a natural 16 is always a miss; a natural 17 is a miss and results in dropping any weapon the attack was made with; and a natural 18 breaks the weapon the attack was made with! (Characters are allowed to carry a dagger in addition to whatever weapons they normally wield, but that's it - no having a "spare sword" in Melee!

In addition, Melee makes it possible to hit your own allies with thrown or missile weapons. If allies are in the way, or if a ranged attack misses and allies are along the "flight path" beyond the original target, the attacker may have to "roll to miss" them. This works like a roll to hit, but in reverse... meaning that a low DX attacker may actually be more likely to hit an ally than an enemy! The rules therefore also specify that you cannot "roll to miss" an enemy.

Characters can defend and dodge. Defending is used by engaged characters, against melee attacks, and requires a melee weapon in hand; dodging is used by disengaged characters, against ranged attacks. In either case, the character cannot attack, but those attempting to hit them with the appropriate sort of attacks must roll 4d6 and try to roll under their effective DX, instead of 3d6. Critical and fumble rules are also adjusted: 5 or less is an automatic hit (but does not double or triple damage!), 20 and above is an automatic miss, with 21 or 22 causing a dropped weapon, and 23 or 24 a broken weapon.

Shields can be used offensively, for a shield-rush. This is used to knock down a foe, but does no damage.

Lastly, Melee begins the long tradition of special grappling rules in RPGs. Here, it's called "hand-to-hand combat", or "HTH". To enter it, you move into the enemy's space (the only time you normally can share a space with an enemy). If the enemy can't move away, agrees to HTH combat, or you're entering for their blind side (side or rear hexes), HTH combat begins. Only a dagger can be used as a weapon; other weapons and shields are dropped, and the characters are assumed to be rolling around on the ground struggling with each other... which makes them very vulnerable to attacks by others. However, if someone attacks into HTH combat with a weapon and misses, they must then "roll to miss" any allies they have in the grapple! Thrown or missile attacks simply hit a random target out of those struggling, making it tend to be a very bad idea.

(There's considerably more to HTH combat - about two pages worth - but the exact details are less important than the fact that Melee appears to be the first RPG to devote a whole subsystem to it. The first edition of Boot Hill has rules for grappling, but they're integrated into the system for melee combat - you can't really choose to grapple in Boot Hill.)

These various options do interact in some interesting ways - for example, you could shield-rush someone to knock them down... which would then make it easier to enter HTH combat with them while they're knocked down!

Character Experience

Of course, character growth is an important part of almost all RPGs. In Melee, it's via Experience Points (EP), which are gained through combat (since it is a combat game, after all!). Interestingly, however, there are different gradations:

Combat to the death gives 50 EP to each survivor, or 70 if the enemy side was significantly superior.

"Arena Combat" goes until the enemy side is defeated, with all of them being dead, unconscious, or choosing to flee through the door they entered the arena from. The winners get 30 EP each; defeated survivors get 20 EP, or 10 EP if they fled without first being injured. If one side is significantly stronger, survivors on the other side get +10 EP... so it's possible for the loser of an unfair fight to get as much experience as the victor!

Lastly, Melee allows for "practice combat". No missile weapons are allowed, and other weapons are blunted, doing only half damage. You must surrender when reduced to 3 ST or less. Those on the winning side who are not taken out get 10 EP. The game notes that it is possible to die in "practice" - remember how deadly those critical hits can be!

When a character gains 100 EP, they can raise either ST or DX by a point. In Melee, there are no other ways to spend experience.

Other Foes

To provide a bit of variety, Melee gives statistics for bears, wolves, giant snakes, giants, orcs, hobgoblins, and goblins. Orcs are designed to be balanced with 'normal' characters, but the others are not. Rules for making elves, dwarves, and hobbits are also included; elves and dwarves get slight advantages compared to humans (elves move faster, dwarves get +1 damage with hammers or axes); hobbits are created with only 20 total attribute points, but get +3 DX with missile and thrown weapons, and +1 to damage with them.

Wrapping Up

While TFT's popularity wasn't enduring (possibly due mainly to Metagaming going out of business for largely unrelated reasons, and Howard Thompson then asking $250,000 to sell the rights to TFT back to Steve Jackson; Steve decided to instead create GURPS), it was very popular in its day, and influenced many other RPGs.

In particular, Melee's rules on movement and engaged status seem to have influenced 3e D&D, and through it the "d20 System". Indeed, the similarities are enough that when I first described 3e combat to friends from my old gaming group, I described it as "D&D cross-bred with The Fantasy Trip".

There was a definite movement toward "more realistic" combat in the 70s and 80s, which we'll see more of with The Arduin Grimoire and RuneQuest. TFT was one of the leaders of that charge, with a system that still holds up well compared to modern RPGs.

One of the biggest differences in TFT, though, is very hard to show in a description like this: Steve Jackson was used to professional board wargames, which tended to have much more cut-and-dried rules than miniature wargames. Thus, Melee was written in a very different, much clearer style than either Dungeons & Dragons or Tunnels & Trolls. Even though the booklet is very short, it contains a good table of contents, fairly copious examples, and rules broken down into separate cases, with much use of emphasis and section headers to make it easy to find things. There are illustrations to help with points that can be made clear more easily in a visual fashion (e.g., a diagram with several counters on a hex map, illustrating the visibility rules) and a summary page of the various DX adjustments in the system (which includes several that are actually from Wizard, for easier use when combining the two games).

Compared to other early RPGs - and even to some today - Melee is a model of clarity and well-organized explanation... and its release seems to have prodded other companies to improve the layout and writing of their own games.

Next time, we'll be talking about the TFT magic system, with Wizard!

Tuesday, May 31, 2016

Toward a History of RPG Mechanics, Part 11: The Perrin Conventions

As discussed previously, Dungeons & Dragons spread far beyond the wargaming audience that TSR initially aimed for. In Playing at the World, Jon Peterson speculates that D&D may have spread so because its setup didn't focus on 'war' in the sense of large-scale battles. The counterculture of the late 60s/early 70s was strongly anti-war, and, indeed, some within it went so far as to protest wargame conventions and wargames in general.

D&D did have combat, but it tended to be on a smaller scale, and the universe it posited, like that of Tolkein (who the counterculture of the time also seized on), featured a clear-cut morality that the members of the counterculture could no longer believe in with regard to conflicts in the real world.

There was also a hearkening back to 'simpler times' in much of the counterculture, and the medieval setting of D&D played to that. Of course, D&D wasn't the only thing that the counterculture seized on that did so - another was the nascent Society for Creative Anachronism, or SCA, which had initially formed in the late 1960s. Some of the SCA's founders styled it as a "protest against the 20th century", and the Society often describes itself as recreating the Middle Ages "the way it should have been".

Naturally, then, many of those in the already-existent SCA found themselves interested in D&D. These people were already practicing faux medieval combat with padded weapons and armor, and found D&D's wargame-based combat rules to be quite unlike their own experience.

Thus, players in the San Francisco Bay area began to create their own modifications to D&D combat. In 1976, Steve Perrin typed up and copied a set of such modifications, which he named "The Perrin Conventions", and distributed to the attendees at DunDraCon I, a D&D convention held in Berkeley.

Copies of the Conventions were borne back from DunDraCon to groups across the United States, and the Conventions were further spread by being included in the second volume of All the World's Monsters, an early 'universal supplement' for fantasy RPGs. Steve Perrin went on to be the primary creator of the rules for RuneQuest, which bears many obvious similarities to the Conventions.

So, what were the Conventions, exactly? Well, you can find them here, but these are what I consider to be the most interesting points:

1. The melee round was reduced from D&D's one minute to ten seconds. Similarly short melee rounds are seen in many later games - including Holmes' Basic D&D and its descendants.

(As a side note, the reduction to a ten-second melee round, with 'normal' movement being 120 feet per round, works out to a speed of about 8 miles per hour... which is also the same speed as D&D's standard outdoor running movement rate of 240 yards per 60-second round. This contrasts to D&D's own combat rules, where characters fighting indoors move at 1/3 the rate of those doing so outdoors because of the difference in scale.)

2. Rather than being randomly rolled, initiative was determined by Dexterity. There is, however, mention of the possibility of adding a random factor, and of allowing someone with a longer weapon to strike first against a foe with a shorter one. Dexterity could also be modified by armor, for both this purpose and other purposes. Holmes' Basic D&D also adopted this rule, although later versions of BD&D went back to traditional randomly-rolled initiative.

3. Characters who moved more than half their movement allowance were not allowed to make melee attacks. This is seen later on in Melee, and in the action system in the d20 System underlying recent versions of D&D.

4. The idea of using a "Dexterity roll" to determine success at actions such as changing a weapon, jumping over something, and so forth. Original D&D made no mention of the idea of directly using ability scores in this way (although Peterson's Playing at the World indicates that Dave Arneson's proto-D&D used ability scores for rolls... and also differed from the published D&D in many other significant ways).

5. Combatants could be knocked back or knocked down by blows, with an increasing probability as they lost hit points. These conditions each carried different penalties.

6. The Conventions had the idea of characters being "engaged" in combat (although not using that term). Withdrawing from combat with an opponent once engaged required an opposed dexterity roll, and carried the possibility that the opponent could get an attack in as you tried to break off.

These ideas were carried forward into many other RPGs. Steve Perrin says that he did not originate all of them, but gave the collection he created the name "The Perrin Conventions" because they were the ones he was choosing to use and was writing up together.

Overall, the modifications proposed by the Conventions make things much easier on GMs. A melee round which is a full minute long allows for a huge amount of movement in the course of it: presuming people can jog at about 8 mph (the "running" movement rate in classic D&D), they can cover more than the length of a football field in one round!

Such long rounds therefore make missile weapons much less useful than they are with shorter rounds: with the one-minute melee round, an attacker can move from being out of bowshot to melee range in one round. Further, since D&D without the Conventions doesn't prevent someone who has moved their full movement from attacking, they can then immediately attack! Depending on the GM, then, a warrior in non-Conventions D&D might close against a bowman and attack before a single arrow can be shot!

The Conventions change this greatly. The distance that the warrior closed in one round before (240 yards outdoors) now takes six rounds to close. This is the same 60 seconds of in-game time, but the bowman gets twelve shots off in that time! This makes missile weapons far more effective for defense. This in turn tends to make numbers more important. A dozen bow-wielding goblins become a much more significant threat!

The requirement to not move more than half your movement in order to make a melee attack also changes things a bit, and the concept of becoming engaged with a foe does it even more. All in all, these changes provide a GM with rules support to keep PCs from just running past foes, and enable some tactical considerations in movement. More limited movement makes it easier to form up lines to protect a target, makes formations such as combat wedges work better, and so on.

(This also makes horses actually useful in combat: in the standard D&D version, you can already close from out of bowshot to a bowman in one round. Unless you're facing opponents using catapults or other weaponry that can't be used by a single man, riding a horse provides no tactical advantage from speed. In the Conventions, however, a horseman can close from out of bowshot in 3 rounds instead of six, halving the number of chances the bowman gets to hit them!)

These movement restrictions also interact with the changed initiative system. While initiative is more fixed, the ability to gain first attack by preparing a missile weapon allows a tactical way around it. However, the Conventions also make it so that switching weapons is not "free"!

The addition of new combat states (being knocked back and knocked down) have significance as well. Knocking someone back or down allows disengaging from them with little risk, and provides a way to break up combat formations! They also make formations more important, by allowing for more situations where one character might need the help of another during combat.

Overall, these changes make combat much more tactical - there are many more significant decisions for players to make. While Tunnels & Trolls had actually abstracted combat even more than D&D, most subsequent fantasy games in the rest of the '70s would follow the lead of the Conventions toward more detailed combat.

In addition to the changes in combat, the shorter rounds mean that it's considerably easier to judge how much someone who's not engaged in combat can get done during a round. For example, in 60 seconds, I can walk through my house, not particularly hurrying, open the door to every room, and look into each and every one (not including closets). Pretty much no D&D GM would allow a party to check 9 rooms for opponents in one round! With ten-second rounds, allowing me to check one room per round would result in it taken 90 seconds... which is a bit longer than it actually took (58.65 seconds on my stopwatch), but not too bad. Thus, a shorter round makes it much easier for a GM to reasonably judge how much a character can get done.

We'll see the impact of the Conventions in our next game - The Fantasy Trip, which we'll be touching on in a few days!

Thursday, May 26, 2016

Toward a History of RPG Mechanics, Part 10: Finishing Early D&D

Last time, we discussed the Greyhawk supplement to Original D&D - the supplement that made OD&D into something that players of later editions would much more readily recognize. We closed with a discussion of the race/class rules that Greyhawk introduced, focusing in particular on the level limits for non-human races.

To modern players, level limits of 9th level and below probably seem extremely low - especially to those used to computer RPGs. Classically, though, D&D was largely played at such low levels. Indeed, in his article "D&D Is Only As Good As the GM" (The Strategic Review, April 1976), Gygax wrote that 
"It is reasonable to calculate that if a fair player takes part in 50 to 75 games in the course of a year he should acquire sufficient experience points to make him about 9th to 11th level, assuming that he manages to survive all that play."
And that last bit is important - character mortality was quite high in older versions of D&D, especially at low levels! A typical 1st level character would be killed by one or two hits from a monster. In the AD&D1 DMG (1979), he wrote:
"The acquisition of successively higher levels will be proportionate to enhanced power and the number of experience points necessary to attain them, so another year of play will by no means mean a doubling of levels but rather the addition of perhaps two or three levels. Using this gauge, it should take four or five years to see 20th level. As BLACKMOOR is the only campaign with a life of five years, and GREYHAWK with a life of four is the second longest running campaign, the most able adventurers should not yet have attained 20th level except in the two named campaigns. To my certain knowledge no player in either BLACKMOOR or GREYHAWK has risen above 14th level."
This would seem to indicate in turn that the rules for higher level characters in OD&D and AD&D1 had not been well playtested, if indeed they were playtested at all. For example, judging by this, no PC in either campaign had yet become capable of casting 7th level cleric spell, nor 8th or 9th level magic-user spells... even those had been introduced three years previously, in Greyhawk.

We can also see the focus on low level characters in the level titles of OD&D and AD&D1. A fighter becomes a Lord at level 9; a magic-user takes a bit longer, becoming a Wizard at level 11. Moldvay's version of Basic and Expert D&D similarly covered levels 1 to 3 (in Basic) and 4 to 14 (in Expert). A "Companion" set was promised to cover levels 15 to 36, but this would not be released until after Basic and Expert were revised a few years later.

My own experience with first edition AD&D was similar, with us considering "low levels" to be 1 to 4, "mid levels" 5 to 8, and 9th level and higher to be "high level" characters. We considered the "sweet spot" for adventuring play to be levels 3 to 8. Below that, characters were too easily killed, and above that, they should be settling down and beginning to establish their own domains. Such high-level characters we would usually retire, to bring out for rare "high level" adventures.
Thus, the level limits for non-human characters didn't seem so onerous; they were within the "sweet spot" that we considered to be D&D's best play experience, and thus, didn't really feel limiting. We also kept Tunnels & Trolls style "stables" of characters. Before starting a new adventure, the GM would normally announce what level range it was for, and players would either use existing characters they had of those levels, or, if they had no character in that range, would create one. The fact that a dwarven warrior couldn't get above a certain level thus wasn't a problem - it just meant you'd have to play a different character if your dwarven warrior wasn't high enough for a particular adventure.

The Rest of OD&D: Blackmoor and More

While Greyhawk brought D&D into the same basic form it would continue to have until around third edition AD&D in 2000, it was not the last of original D&D. Blackmoor came out in 1976, but most of its bulk was devoted to an adventure, and new 'things' - the Monk and Assassin classes, new spells, new monsters, and new magic items. Its expansion of the rules in general was smaller and less successful. Six pages were devoted to a hit location system, which was not carried forward into any future version of D&D. Seven pages in the rear gave brief rules for underwater adventures, diseases, and NPC specialists.

Eldritch Wizardry  came out later in 1976, and added Druids as a class, along with spells for them, more monsters, and more magic items. Artifacts were introduced here, but the only additional rules for them consisted in the idea that their powers should not be known by players, and so various lists of possible powers were given instead of set powers for them.

The largest rule addition in EW was psionics - but while the various psionic abilities introduced were carried forward into future editions of D&D, the methods used for determining what abilities characters have changed greatly between EW and AD&D's Player's Handbook, which came out two years later.

A Dexterity-based initiative system was introduced as well, which cut the one-minute melee round into six "segments" of ten seconds each. As with the hit location rules introduced in Blackmoor, however, these initiative rules were not carried forward into future editions of D&D.

Lastly came Gods, Demi-Gods, and Heroes, which gave game statistics for various gods and monsters, but added no new rules of significance, and Swords & Spells, which brought D&D full circle back to Chainmail, as it was a D&D-based system for conducting fantasy battles. While S&S introduced a large number of new rules for this, most of those were either straightforward extensions of what already existed in D&D (for example, units did damage computed from their chance to hit, number of attacks in D&D, and how much damage each of their attacks did in D&D), or were carryovers from Chainmail. In any case, S&S did not sell well, and its rules were not carried forward into future versions of D&D either.

Finishing Up

This concludes our coverage of "official" OD&D. Next time, we'll be looking at The Perrin Conventions, a set of early 'house rules' for OD&D that were highly influential, and at Melee, initially released as a combat system to use with other RPGs, but which formed the basis for another early fantasy RPG, The Fantasy Trip.

Saturday, March 26, 2016

Toward a History of RPG Mechanics, Part 9: Greyhawk

When Dungeons & Dragons was first published, its creators had no idea that it was going to be as successful as it was. Indeed, Gygax didn't even bother to register a copyright for the original printing!

It was also not expected that D&D would far outsell Chainmail, with the result that the vast majority of players were using the "alternative combat system". Under this system, the weapons characters used were irrelevant: the chance to hit was completely determined by the level and class of the attacker and armor class of the defender, and all weapons did the same damage (1d6). The Chainmail combat system handled weapon differences by giving each weapon type a unique profile of chances to hit different armor types, and by a set of initiative rules that were highly dependent on the weapon being used. This was all lost with the alternative combat system, though - indeed, D&D didn't even have an initiative system of its own, and one was supplied in the very first D&D FAQ, presented in The Strategic Review, volume 1, issue 2.

A fix for all this was one of the major changes to the D&D system in Greyhawk, the first supplement to be produced for Dungeons & Dragons. Gygax took a two-pronged approach: first, he introduced variable damage by weapon type, establishing the classic D&D weapon damages: 1d4 for a dagger, 1d8 for a long sword, and so forth. Monsters were also given different damage values for their attacks. Second, he added a table of "to hit" modifiers by weapon type vs. armor type, bringing some of Chainmail's sophistication in that regard into D&D. At the same time, the "alternative combat system" was declared to now be the official combat system of D&D in TSR's house organ of the time, The Strategic Review.

The second major change was to fix the progression of hit points and hit dice. Originally, D&D used only six-sided dice for determining character hit points. This resulted in some... shall we say, 'interesting', hit die progressions.

In Greyhawk, this was replaced by the much simpler expedient of using different types of dice for the different classes. Thus, magic-users now rolled a d4 each level, adding the new result to their existing hit points, so that hit points could only ever go up. Fighters used a d8, and clerics a d6.

A third major change was to how ability scores were used. Instead of providing adjustments of +1 or -1 to various things, they provided larger adjustments, ranging up to +3. Strength especially was expanded on, with high strength giving bonuses to hit and to damage, to how much weight could be carried, and to the chance to open dungeon doors.

Even more was added than that, however: Fighters (which was the name now primarily used in Greyhawk instead of the official class title of "Fighting-Man") who were lucky enough to have an 18 Strength could roll percentile dice for "exceptional strength", with a 50% chance of increasing their Strength even above the bonuses granted by an 18. With a roll of 00, the fighter would gain a massive +4 to hit and +6 to damage.

The use of Intelligence for magic-users was also expanded on, with  those of below 17 intelligence unable to use the highest levels of spells (on a sliding scale, so that a 17 was required for 9th-level spells, but only an 11 for 6th level spells).

Charisma acquired no new functions for the general run of characters, but fighters with a 17 or higher score could become Paladins if they were of Lawful alignment. The paladin gained a number of other special abilities. At low levels, these were not very significant, but as the paladin advanced, they became more significant.

Constitution had its bonuses increased, to a potential +3 hit points per hit die.

A Brief Aside/Rant

Why was the significance of ability scores changed so much? I would suggest that Gygax realized that while a +1 or -1 was quite significant in the Chainmail combat system, which relied on 2d6, it was much less important in the alternative combat system, based on 1d20. With 2d6, the increase in chance to hit varied from 5.56% (if a 12 was needed to hit), to 16.67% (if an 8 was needed). With 1d20, a +1 always increased the chance to hit by 5% - less than the minimum possible in the 2d6-based system. A +2 was comparable, but simply making the modifiers -2/0/+2 probably felt non-intuitive... leading to the +1/+2/+3 progression, to allow those with the highest ability scores a little something extra.

However, the net effect of all these changes was to make players' luck when generating characters much more significant. In original D&D, one needed a 12 or higher to get a +1 from an ability. On 3d6, the chance of rolling a 12 or higher is 37.5%. Since you'd roll 6 abilities, the chance that you'd have a bonus in at least one was 94%... so your character was almost certainly good at something. The changes, however, moved the improvement points up: with Strength, at least a 13 was needed to get any bonus; with Constitution, a 15 was now needed to get a bonus. These may not seem like a big difference... but on 3d6, the chance of getting a 13 or better is 26%, compared to the 37.5% for a 12... and to get a bonus to hit comparable to what a 12 gave originally, a 17 Strength was now needed... which only about 2% of characters would have. Meanwhile, the Constitution change meant that the chance of getting a hit point bonus was only about 10%.

Worst of all, though, were the 17 requirement for Charisma to become a paladin (again, a 2% chance on 3d6), and exceptional Strength for fighters. 1 in 216 characters were even eligible for the latter. Those lucky enough to get an 18/00 Strength - 1 in 21,600 - gained huge bonuses. A +4 to hit, equivalent for attack purposes to an extra six levels as a fighter, coupled with a +6 to damage, more than doubling damage output for a typical fighter.

Even without the 100 roll, the +2 to hit for an 18 Strength was equivalent to about 3 fighter levels for attack purposes, and the +3 damage would nearly double damage output.

Compounding this were the experience point adjustments for high ability scores... so not only were these lucky few much more effective in play, they also would increase in power faster.

Later additions to D&D would continue this trend of what I like to call "piling rewards on the lucky". Players of fighters began to feel that they couldn't compete without having at least a 17 (in either Strength, giving them a significant attack and damage bonus, or Charisma, giving them access to the paladin option). This led to the adoption of various alternative methods of character generation, from the famous "4d6, drop the lowest" method, to such variations as "everyone gets to make their highest score into an 18". Eventually, this ability score inflation would culminate with the character generation method given in Unearthed Arcana for AD&D, where the player would roll 9d6 and keep the best 3 for their most important ability, 8d6 for the next most significant, and so on.

The Thief

Of much more importance to the history of D&D, however, Greyhawk introduced the fourth of D&D's classic "core four" classes: the Thief. This class was given a d4 for hit points, like the magic-user; however, it rose in levels faster, so that at low to middle levels, a thief would tend to have more hit points than a magic-user playing in the same game.

Of course, with the thief came the concept of thieving skills. In Greyhawk, these were

open locks
remove traps
hear noise
move silently
hide in shadows
climb sheer surfaces

and "strike silently from behind" - the ability that would later be known as "backstab" (and still later, "sneak attack"). This last was the thief's best attack ability, giving a +4 to hit (on 1d20), and doubling damage done (moving up to triple damage at 5th level, quadruple at 9th, and so on).

The existing player races were all allowed to be thieves, giving dwarves and halflings a second class option (both were only able to be fighting-men in original D&D). Elves could choose to be purely a thief, or to be a fighter/magic-user/thief, in which case they were required to divide experience evenly among all three classes. None of these races had a level limit as thieves.

Greyhawk also introduced increased level limits for non-human characters with high ability scores. Where previously dwarves had been limited to 6th level as fighters, they could now reach 7th if they had a 17 Strength, or 8th with an 18. Elves could reach 6th level as fighters (with 18 Strength), and 9th as magic-users (with 18 Intelligence).

Dwarves and elves could also become clerics... but only as NPCs. All dwarven clerics were fighter/clerics (with the term "fighter" being used, instead of "fighting-man"). Elven clerics were fighter/magic-user/clerics.

While halflings couldn't be clerics at all, those wanting to be clerics did have a race option other than human - the newly introduced half-elf. Like elves, they could be fighter/magic-users, but their limits as such were lower than those for elves. For their clerical option, well, let me quote the rules:
"There are no helf-elf clerics, for in this regard their human side prevails. However, half-elves with a basic Wisdom score of 13 or more may also become clerics. If they so opt all experience will be divided in equal proportions between fight, magic use, and clericism. Half-elves may work up as high as the 4th level (Vicar) clerically."
(And yes, "helf-elf" is what is actually written. My copy is the 4th printing.)

I'll note that there is no mention of thieves in the half-elf description at all. This makes me wonder whether "There are no half-elf thieves" is what was intended... but what does "for in this regard their human side prevails" mean? That doesn't seem to make sense for either clerics or thieves, since humans can be either!

In any case, though, the strict three-way division of experience is interesting here and with the elven fighter/magic-user/thief. Given that AD&D would require all multi-classed characters to divide their experience evenly, and that when the Basic line branched off, its elves would effectively do the same, I have to wonder whether Gygax became unhappy with the elf's ability to switch back and forth between the two classes in original D&D.

Next Time

These level limits probably seem ridiculously low to those used to more modern versions of D&D - a maximum of 9th level for elven magic-users? Maxing out at 6th level as a fighter? Why would anyone play an elf at all under these restrictions?

We'll discuss this next time, as this post is getting a bit long, and the next part of Greyhawk's changes - those to experience point awards - really invites some comparison among editions. So, join us next time as we talk about Experience and Levels in Early D&D!

Tuesday, October 20, 2015

Toward a History of RPG Mechanics, Part 8: Boot Hill

Boot Hill, TSR's third RPG (and second system, if we count Empire of the Petal Throne's system as a variant of D&D's) is very different from D&D. First off, it uses percentile dice almost exclusively. (One subsystem, for brawling, uses 2d6.) Second, it eschews D&D-style classes and levels completely - a character's capabilities are defined by their attributes, and by how many gunfights they have successfully survived.

This makes Boot Hill a major first: the first RPG without classes or levels. It's also another major first: the first RPG to be based in a historical setting, without any fantasy or science-fiction elements.

The character attributes in Boot Hill are:

Personal Bravery
Personal Accuracy (thrown weapons)
Personal Accuracy (fired weapons)

While these are set by rolls of percentile dice, these percentile values are not what is used in play (although they are recorded for use in the experience system). Each has a table that gives varying values. For example, for Personal Bravery, we have:

01-10  Coward
11-20  Cowardly
21-35  Average
36-65  Above Average
66-80  Brave
81-90  Very Brave
91-98  Fearless
99-00  Foolhardy

Similarly, Speed and Personal Accuracy have 10 and 11 rankings, respectively, and Strength has 13, which are assigned numbers from 8 to 20, as well as descriptors.

Now, there's some argument over whether the original Boot Hill should be classed as an RPG. Some argue against it on the basis that the mechanics focus almost entirely on gunfighting, with no real rules for anything else. My perusal of the rules, however, makes me disagree with this - although gunfighting is covered by far in the most detail, there are rules for brawling, grappling, tracking, forming a posse, gambling, intoxication, campaign-level movement, hourly movement for long-distance chases, aging of characters, and sample prices and wages given.

To put it another way, Blume & Gygax seem to have made an effort to supply rules for what they considered to be the important parts of running a Western campaign and adventures. There's a lot of territory that they didn't cover - but there's also a lot of territory that original D&D didn't cover, and Boot Hill was working with a much shorter page count!

A second objection is that the original Boot Hill explicitly calls for players to play multiple characters, rather than each player playing one and only one character. However, Boot Hill does specify that each player should have a "personal figure" that is their primary character. This "personal figure" is given a boost in character generation, getting to add 10 to each die roll that is an 01-50, and 5 to each result of 51-70. Thus, looking at Personal Bravery above, we see that a personal figure is never a Coward. The actual results become:

01-10  Cowardly
11-25  Average
26-60  Above Average
61-80  Brave
81-90  Very Brave
91-98  Fearless
99-00  Foolhardy

Thus, personal figures will have higher bravery than the average NPC 75% of the time, and will generally be Above Average or Brave (those two results being 55% of all results).

These personal figures are arguably the "player characters" of the players. This argument is boosted by the fact that early versions of D&D also tended to have the players each controlling multiple characters, via the concept of having "henchmen" and "hirelings". Indeed, it was quite common for one of a player's henchmen characters to become their new PC, if their PC died! Likewise, Tunnels & Trolls briefly mentions that individual players may have multiple characters as well, and such "character stables" were common with it, by what I've read from those who played it in the '70s and '80s.

As with many versions of D&D, Boot Hill assumes the use of miniatures. Ranges and movement rates are given in inches, as in early versions of D&D. These are fairly close to D&D movement rates, with people being able to "run and dodge" 12 inches or run 24 inches, and horses having a maximum "gallop" movement rate of 32 inches.

"Initiative" is called "first shot determination" in the rules, and is handled by calculating a total based on the character's Speed attribute, their Weapon Speed (six categories, from Very Slow to Very Fast, plus an additional one for "Already Aimed", which is regardless of weapon), Surprise Factor, their current Movement, how badly wounded they are, and modifiers for drawing two guns and/or hip shooting.

All these are totaled, and the character with the highest total shoots first, with shots then proceeding from highest to lowest. Wounds taken during the current round do affect order, so a character's ranking can drop before their turn comes up.

Note that there is no random factor in this determination: initiative order is deterministic, although one's ranking can vary according to what you are doing in the current combat turn. The best possible result is 35, for someone with "Greased Lightning" speed who has already aimed. (Hypothetically, it could be 38, but it seems reasonable to assume that "hip shooting" does not matter when one has "already aimed". Remember, early RPGs tend to assume that players and GMs will interpret the rules according to logic and common sense, and not blindly follow them.) Conversely, the lowest possible value is -70, for a Slow individual drawing two Very Slow weapons, who is running, completely surprised, and has taken wounds lowering their current Strength below 1/2 of maximum.

When a character gets to shoot, their chance to hit is calculated. The base chance is 50%, with modifiers for Range, Firer Movement, Target Movement, Individual Accuracy, Wounds, Personal Bravery, and Personal Experience. There is also a table of miscellaneous modifiers, for such things as shooting from the hip, concealment, resting your weapon on a solid object to steady it, and so on.

Personal Experience, in the form of how many gunfights the character has survived, makes a very large difference. A character who has not been in a gunfight before is at -10, and parity (in the form of a 0 modifier) is achieved after surviving three gunfights. At maximum, those who have survived eleven or more get a +20 modifier, boosting them to a base hit chance of 70% - almost double the 40% of someone who has never been in a gunfight!

It's possible to have a greater than 100% chance to hit. This gives nothing special, beyond the fact that this will help greatly if trying to fire multiple shots, since each additional shot gives a -10 to all the shots fired!

When a shot hits, the hit location is determined. This is either by the "fast method", which takes one roll, and simply determines whether the hit is a "light wound" (-3 to Strength), "serious wound" (-7 to Strength), or "mortal wound" (instant kill). The "exact hit location chart" requires two rolls: the first determines the hit location, and the second determines the damage done, based on that location. Damage amounts are the same as in the "fast method", but the chances vary by location. Thus, leg, arm, and hand wounds are never mortal, but shots to the head have a 60% chance of killing.

When using exact locations, hits have other effects as well - for example, a light wound to an arm gives -25 to speed and accuracy with that arm, while a serious wound prevents use of that arm for shooting at all.

Cover is handled through the hit location system - if the area hit is behind solid cover, no damage is taken. Concealment of more than half the body gives a -10 to the chance to hit.

Brawls are handled through a separate Brawling Chart, which consists of a Punching Table and Grappling Table.  Initiative is decided by the characters' unmodified Speed attributes, or by surprise. The opponent with initiative may make two punches; the slower opponent may do so if they have an advantage over the foe (gained from results in previous rounds of brawling).

Either one can try to grapple, but if they do, that is their only action for the round. Similarly, knives, clubs, chairs, gun butts, and other weapons allow only one attack in brawling.

2d6 are rolled for each attack, either on the punching table or the grappling table, as appropriate. The result indicates how much (if any) Strength the target loses. Punches are affected by whether the right or left hand is being used. The rules don't actually specify how to determine this, but presumably when two punches are allowed, it's one from each fist, and a seriously wounded arm can't be used to punch, just as it can't be used to shoot.

Results can also include modifiers to your opponent's next attack, and/or to yours. The grappling table has a few 'special' results - if a held opponent manages to gouge your eyes or knee you, they break the hold instead, and an armlock on an opponent gives them a -1 to punch attempts with that arm and to all grappling attempts. If an opponent chooses to pull a gun and shoot, any minus they have from punching and grappling is multiplied by 10 and applied to their chance to hit with the gun.

When grappling, once a lock is established, the attacker can continue it automatically each round, until the held party breaks free. Breaking a hold is done on the grappling chart. Exactly how this works isn't described, leaving it open to some amount of interpretation.

In any case, though, an opponent reduced to zero Strength by brawling is only knocked out, and will wake up 5 minutes of in-game time later. Bludgeoning weapons subtract 1 or 2 from the attack roll, but add the same amount to damage; knives are treated like punching, but if a hit is made, the rules for gun damage are used instead.

The advanced rules allow some interleaving of movement and combat (in the basic rules, all movement happens before shooting, so someone running from cover to cover cannot be shot at unless it's too far to move in one combat turn). It also allows Indians (and only Indians, by a strict reading!) who are using bows to arc their arrows over cover under some circumstances. Morale rules are added for minor characters (which includes those controlled by player who are not their "personal figure").

Optional rules add a determination of how many shots a character can fire before another character gets to start shooting. In the basic game, someone whose weapon has a rate of fire of 3, for example, gets to fire all three shots before the next character fires any, even if their calculated First Shot Rating only differs by one point. Further options allow characters to be stunned by attacks, be intoxicated, add a "gambling rating" for gambling contests, and rules for the use of dynamite, misfires (which is handled as a separate roll each time a gun is fired), stray bullets (allowing misses to hit someone else in the line of fire), gatling guns, and cannons.

The Campaign rules have turns that last a month or a week. When a turn results in characters meeting up in a potentially hostile situation, chases and tracking can then be played out, possibly resulting in fights. Aging is added as well. Characters starting age is determined with 5d10 (so they could be as young as 5!). Those under 25 improve with age; those over 35 lose points with age.

Experience also matters in campaigns. In addition to the built-in improvements in accuracy for surviving gunfights, each successful showdown allows the winner to add to Speed (+2 if under 51, +1 if under 81), Bravery (+2 if under 66, +1 if under 91), and Accuracy (+3 if under 26, +2 if under 51, and +1 if under 86). A note is made that these should be multiplied based on odds - that is, if one character defeated two, they improve twice as much, or only half as much if the winners were the side with two people, and so on.

Actual Play

To get a feel for the system, my friend Julian and I made up a couple of characters and played out two gunfights - one a short-range pistol duel, and the other a longer-range fight with rifles. We then played out two brawls, one with only our personal weapons available (i.e., knives), and the other a bar-room brawl with chairs, bottles, and so forth.

We got a few observations from this:

First off, combat is deadly and random. Even though one character had a clear advantage in stats, that didn't seem to matter much. Your "hit points" are merely your character's Strength, varying from 8 to 20... but that doesn't make a huge difference when 15% or 22% (depending on whether you're using the "fast hit location method" or the "exact hit location chart") of hits are instant kills. Two "serious wounds" will kill an average person; two and a light wound will kill 90% of PCs.

(Side rant: one would think that game designers would make sure that alternative systems that are supposed to be equivalent have equivalent results, especially when the math isn't very hard. However, in this case, the "fast" method gives a hit breakdown of 50% light wounds, 35% serious, and 15% mortal, while the "exact" method gives 35.25% light, 42.75% serious, and 22% mortal, making it considerably more deadly. This is compounded by the fact that the exact system also gives penalties based on wound locations. For example, a light wound to a leg halves maximum movement, and one to your gun arm gives -25 to speed and accuracy. Thus, if anything, if would make more sense for the exact method to be less lethal, since it adds in penalties for being wounded!)

Even without guns, combat feels very random: your character's statistics literally make no difference whatsoever in the brawling rules, except for Strength determining how much damage one can take before going unconscious. On the bright side, the results given by the tables are all given names, such as "glancing blow", "jab", "head lock", etc., making it easy for a GM to colorfully describe a fight (or even for colorful fights without a GM!). However, since it's basically a random dice-rolling exercise with almost no strategy or tactics, it can be quite frustrating as a player. And if someone pulls a knife, combat turns very deadly!

Something else we noticed, in looking over the sample scenario and through early articles in The Strategic Review and Dragon for Boot Hill (notably, the writeups of Western heroes and characters from Western movies and TV shows) is that your characters, while likely to be slightly above average, are by no means 'heroes'. The writeups of those heroes almost universally have far above-average stats. For example, Wyatt Earp in the sample scenario is given Speed 97, Gun Accuracy 96, Bravery 97, and Strength 99, plus 9 gunfights worth of experience. Only one listed character in that scenario has an average of less than 70 in their stats, and most are better than that: the average stat across the 11 characters given in the sample is 82!

A quick check with shows that about 2% of characters will have an average of 80 or better, taking only the four stats given for the scenario characters. To add insult to injury, since the experience system caps the abilities it does improve (at 81, 91, and 86), and never improves Strength, it's not even possible for a character to work their way up to the level of the 'legendary heroes'. You either luck into being that good, or never get it at all.

Even then, advancing requires surviving a lot of gunfights (brawls don't count, by the rules as written)... which, given the lethality of the rules, isn't too likely. Since one cannot increase Strength (and thus hit points), and there is no defense skill or attribute to improve, lethality to all characters is likely to simply increase over time as everyone gets more accurate.

Final Analysis

Boot Hill is an interesting departure, and presages many things that other games would do later: percentile-based mechanics, hit locations, wound penalties, and a classless system all make their first appearances here. Unfortunately, the Western genre was already well past the peak of its popularity, and the realism of the system likely did not appeal. With it very unlikely that one would get a 'heroic' character, no reasonable way to advance characters to such levels of skill, and low survivability, it was poorly suited for long-term roleplaying by people who became heavily invested in characters. With quick character generation and fast mechanics, it could have been well-suited to one-shot games, but genre limited its appeal.

Tuesday, September 29, 2015

How Much Does a Dragon Eat?

Obligatory Joke: As Much as it Wants!

But seriously... the other day, my daughter and I were talking about dragons. She'd been re-reading Wizard of the Coast's "Practical Guide to Dragons" series, and, well... let's just say that while the art is great and the writing is good, the books could be used as poster children for the "Writers Cannot Do Math" trope.

They thankfully don't even try to give amounts that dragons eat. So, when she asked about how much that might be, my physics/computer science background came out, and I started doing some estimating. I started with the knowledge that a working cart horse needs 30 to 45 pounds of food a day. Estimating the horse's weight at 1000 to 1500 pounds, and looking up the Calories / pound of various foods, I estimated that an animal of the same weight eating meat would need about 1/6 as much food... for 5 pounds of food per day per 1000 pounds of body weight, of 10 pounds/day/ton.

We then decided that since dragons fly and breathe fire, they'd likely need more energy. So we decided to somewhat arbitrarily double the amount, to 20 pounds/day/ton. Given a 7-ton dragon (the weight of a large tyrannosaur or elephant), that comes to 140 pounds/day, or 980/week... that is, about a sheep a day, or a cow a week.

Of course, that's presuming the animals being eaten are 100% meat, which isn't too likely. So let's make it two sheep a day, or two cows a week. (Some of which will likely be wastage.)

However, predators tend to eat less regularly, eating all they can at a meal, then not eating for a considerable length of time. While some types of reptiles can eat their own body weight or more, most animals cannot. If we assume a dragon can consume up to 1/4 its own weight and still fly, which seems reasonable (and about matches how much a lion will consume at a meal in the wild), then our 7 ton dragon will eat about 1.75 tons at a sitting, or 3500 pounds - which is about 3.5 cattle.

That gives us a dragon who kills and (mostly) eats four cattle about every two weeks. This doesn't seem unreasonable, and would certainly make a big impact on local farmers, especially when you consider that each time the dragon feeds, it's likely to panic the herd of cattle it's feeding from, causing additional injuries (and possibly deaths), knocking down fences, and so forth.

Later on, I looked up how much predatory birds eat, thinking that would be a reasonable model for flying dragons. The relevant formula there is:

Maintenance Metabolic Rate (kcal/day) = 1.5 (78 (weight in kg 0.75))

(found at The Modern Apprentice, a falconry site)

This is adjusted for bird activity, with multipliers from 0.7 for an inactive bird, to 1.3 for a highly active bird. To two significant digits, we get 83,000 kcal / day. Now, here, we need to note that food industry Calories are actually kilocalories. Using beef's roughly 850 kcal / pound, we find that this is 98 pounds of beef / day, a bit less than the 140 pounds / day we arrived at above. However, digging into some other sources, carnivore digestion is only about 90% efficient... and, of course, we have the fact that a cow isn't pure beef. Between those, we can probably keep the above figure of 20 pounds/day/ton, and not be too far off.

(I also remembered later that Gregory Paul's Predatory Dinosaurs of the World, which I am a happy owner of a copy of, has an appendix on predatory dinosaur energetics. There, I found a similar formula, of 140 (weight in kg 0.75)).

The one thing we might want to do is use the weight 0.75 scaling factor from above, when figuring larger weights, at least. So, for a huge dragon, say weighing the estimated 90 tons of the largest titanosaurs, multiply by ( 90 / 7)  0.75 = 6.8... for a creature that eats around 25 cattle every two weeks!

Of course, if dragons hibernate, then this changes significantly. Bears depress their metabolic rate to about 25% of normal when hibernating - using that model, our huge dragon might each 25 cattle, then return two months later.

Another alternative would be to use cold-blooded animals' metabolic rates, which are about 1/10 that of warm-blooded animals... so our dragons would eat about once every 5 months. If they also hibernate, that could be every couple of years!