## Sunday, December 27, 2009

### Spells in Chainmail/ D&D

Hey, I just realized for the first time that all of the spells in Chainmail were converted to spells in OD&D, with the "complexity" of the former turning exactly into the "level" of the latter.

With one exception: Darkness, which didn't appear until D&D Sup-I, and then at a different level. Huh.

## Thursday, December 24, 2009

### Gygax on Miniatures in D&D

I don't usually employ miniatures in my RPG play. We ceased that when we moved from CHAINMAIL Fantasy to D&D.

I have nothing against the use of miniatures, but they are generally impractical for long and free-wheeling campaign play where the scene and opponents can vary wildly in the course of but an hour.

The GW folks use them a lot, but they are fighting set-piece battles as is usual with miniatures gaming.

I don't believe that fantasy miniatures are good or bad for FRPGs in general. If the GM sets up gaming sessions based on their use, the resulting play is great from my standpoint. It is mainly a matter of having the painted figures and a big tabletop to play on.

- Gary Gygax on ENWorld, 2003 (
http://www.enworld.org/forum/1263669-post6.html)

I've heard in the past that Gygax didn't use miniatures in D&D, but it's interesting to hear it in his own voice. "We ceased that when we moved from CHAINMAIL Fantasy to D&D." This makes sense in a lot of ways.

One of the things it helps make sense is how the rules for use of miniatures in AD&D don't (to be frank) make single lick of sense. Consider how miniatures don't physically fit on a map at 1" = 10 feet scale, and the truly crazy stuff on DMG p. 10 (make maps at 1" = 3⅓ feet). The reason? Well, Gygax had ceased actually using them as soon as the RPG itself came into existence. The ranges and movements are copy-and-pasted from Chainmail, but he wasn't actually using them directly. In other words, the use of minis became a vestigial, unusable appendage in D&D.

Consider stuff like this. A fireball in Chainmail & OD&D has a fixed range of 24". In AD&D that gets changed to a caster-dependent range of 10" + 1" per level. Repeat that for every spell's range and area in the entire book. Why the enormous increase in complexity (requiring math on the fly just to find any spell's area and range)? Especially when Gygax wasn't using miniatures or a game map in any way himself?

Knowing how Gary would write, I can almost hear how he'd answer this. "It's self-evident that more powerful casters will have greater efficacy, and rules for minatures were included for the kind of person who would enjoy that sort of thing." Something like that. Kind of dodging the fact that AD&D is shot full of complicated rules, everywhere, that he neither used nor playtested; looking good on paper but not playing out so well. (Funny, too, that he's licensing and promoting "OFFICIAL ADVANCED DUNGEONS & DRAGONS miniature figures" [DMG p. 11] simultaneously with abandoning their use in his own play.)

Now, there are other things that this does helps rationalize. One is that it's an excellent point that, in a game with lots of random encounter tables, you really would be hamstrung if you have to go running for different types of miniatures every time a new encounter pops up. Another thing is the need for AD&D rules to now specify random contacts in combat. "Discharge of missiles into an existing melee is easily handled... Assign probabilities to each participant in the melee or target group according to sheer numbers." (DMG p. 63). "As with missile fire, it is generally not possible to select a specific opponent in a mass melee. If this is the case, simply use some random number generation to find out which attacks are upon which opponents..." (DMG p. 70). That sort of stuff.

But the one thing this egregiously overlooks is the interaction of area-effect spells (fireball and all the rest). If melee is an entirely abstracted, Pigpen-like dustup, how do you determine who gets hit by an area-effect spell? Everyone, friend and foe? Whoever you want? Just the bad guys? Random determination? To-hit rolls or Intelligence checks? In all of OD&D and AD&D, I'm pretty sure there's not a single line addressing this question, leaving it entirely ambiguous.

A critical history of D&D would include the following -- Start with Chainmail historical mass rules at 1:20 scale (1 turn = 1 minute, 1" = 10 yards); this includes catapult-fire where players declare the range shot without measurement. Then Gygax develops man-to-man combat, including jousting and the fantasy supplement (using the moves and ranges from 1:20 scale, but never addressing what the new scale is or what should change in that regard); a wizard's fireball simply refers back to the catapult rules.

Now OD&D comes out, and in large part it refers back to Chainmail for combat. "Special Ability functions are generally as indicated in CHAINMAIL where not contradictory to the information stated hereinafter", stuff like that (Vol. 2, p. 5). Of course, the game creator himself is not using miniatures anymore. Questions of scale are given only the most cursory treatment: the combat turn is still 1 minute (fixed from Chainmail's 1:20 mass combat), and not until Vol. 3 are we told, "In the underworld all distances are in feet, so wherever distances are given in inches convert them to tens of feet." (Vol. 3, p. 8). Perhaps that's all the attention you need to the issue if combat has been entirely abstracted at this point.

If I had been more observant, a few years ago when Gary was still with us and generously answering questions in several different Q&A questions online, I really wish I'd asked him this: "What do you do in D&D to adjudicate the effect of area spells like a fireball, et. al?" Are we to assume that OD&D's reference back to Chainmail Fantasy, which in turn references back to Chainmail mass combat's catapult rules, requires declaration of shot range? (In neither of the former cases is it explicitly stated.) Or are we to assume that since miniatures are no longer actually in use on a map, that the determination is done by caster fiat or some random method?

Once I noticed this, it seems funny how much ink is spent in AD&D covering the new hit-the-caster-lose-the-spell rules, and never once addressing who-gets-hit-by-the-spell in its new, purely abstract combat system. Take-away here is two things, I think. (1) Gygax never actually played the game with miniatures at the alleged 1" = 10 feet scale (or 1" = 3⅓ feet, or the stated ranges for moves, missiles, and spells, or anything else), and (2) Area-of-effect spells are left entirely unaddressed in classic D&D, and definitely require some novel, independent adjudication on who gets hit by each individual DM.

Addendum: Another Q&A post by Gygax rules that targets for a sleep spell would be randomly chosen, so perhaps that aims us in a suggestive direction. ( http://www.enworld.org/forum/1972519-post68.html )

Virel: Say a sleep spell is cast at a group of ten characters... Can the caster specifically select the six creatures or six levels he or she wants to be effected?

Gygax: No. Six of the 1st level NPCs would be affected at random.

## Monday, December 21, 2009

### Gygax on Chainmail's Fantasy Scale

Regarding Chainmail's Fantasy man-to-man scale, here's an exchange between Gary Gygax and our friend RFisher, from ENWorld in 2005 ( http://www.enworld.org/forum/2069195-post152.html ):
RFisher: A couple of Chainmail questions: When the combat tables say "1 die per man", do they mean 1 die per man (20 dice per figure) or 1 die per figure (1 die per 20 men)? (I've known people to interpret it both ways.)

Gygax: Read "man" as "figure" and you have it. One die is just that...

RFisher: Under Heroes, does "They have the fighting ability of four figures" mean that they are equivalent to 4 men or 80 men?

Gygax: Heroes are used only in Man-to-Man play, so one is equal to four normal men.

RFisher: I understand that hero v. hero would be resolved on the Fantasy Combat Table. Hero v. normal forces would be resolved on the regular Combat Table. (The hero being classed as heavy foot, armored foot, light horse, &c. as fit the particular hero.) But were heroes & other things from the Fantasy Supplement ever used with the man-to-man rules? If so, how?

Gygax: I am quite at a loss to answer that, as the Hero and all the other Fantasy supplement figures were employed only in the play of Man-to-Man games, never in the mass system where one figure equalled 20.

And just so we don't forget, Gygax was very consistent on this point over the years. From the Swords & Spells Introduction in 1976 (p. 1):
The FANTASY SUPPLEMENT written for CHAINMAIL assumed a man-for-man situation.

From the original Dungeons & Dragons Vol. 3, Land Combat in 1974 (p. 25):
The basic system is that from CHAINMAIL, with one figure representing one man or creature.

And from Wargamer's Newsletter #127 in 1972, where early play of the game is discussed purely in terms of man-to-man play:
http://grognardia.blogspot.com/2009/12/1972-gygax-article.html

And also from The Strategic Review #2 in 1975 (p. 3):
CHAINMAIL is primarily a system for 1:20 combat, although it provides a basic understanding for man-to-man fighting also. The "Man-To-Man" and "Fantasy Supplement" sections of Chainmail provide systems for table-top actions of small size.

It's funny how many of us (definitely me included!) were tricked into the illusion that Chainmail Fantasy apparently supported mixed 1:20 and 1:1 scale play, when it really doesn't.

### Saves as Severity

Saves in classic D&D come in 5 categories, and the exact categories evolved a bit from OD&D to AD&D, BXCMI, etc. Some thought has gone into tracking the different save categories, how they were meant to be distinguished, what they "mean", etc. Here's an observation I haven't seen expressed before: The save categories in OD&D are most easily interpreted as just levels-of-severity. Consider the following:

The first category is "Death Ray or Poison", and receives a +4 bonus in comparison to generic Spell saves for fighters (which we'll take as our baseline). Obviously, this is a category which represents instant death. In order to give our characters a fighting chance, a fairly hefty bonus is given.

Second is "All Wands -- Including Polymorph or Paralization". The emphasis on polymorph & paralyzation is interesting: these are effects that don't cause literal instant death, but do render the victim effectively helpless and subject to a follow-up coup de grace. Hence a relative +3 bonus is given to avoid these effects.

Third is "Stone", i.e., turn-to-stone (petrification). Similar to the preceding, a victim of stoning is immediately and permanently hors de combat. However, the victim is not quite so immediately subject to death, as the stony form doesn't allow an immediate dagger death-stroke. Presumably some amount of labor could break up the stone form, but that's a far more involved process. Bonus is +2 here compared to baseline.

Fourth is "Dragon Breath", which is not instant elimination from a failed save, but (obviously) pretty bad, major business. Bonus is effectively +1 in this case.

Fifth and finally you have "Staves & Spells" which is in some sense "everything else", i.e. non immediate death or incapacitation. This is our baseline, hardest to avoid, i.e., +0 bonus in similar terms.

Now, the counter-argument to all this is the position of "Wands" and "Staves" on the chart with the former (weaker) given an easier save, and the latter (stronger) given a more difficult save, which is counter to the observations above.

But more generally, you could use these principles for judgements on the fly about the severity of effect: basically you're awarding between +0 and +4 to the save, with more heinous effects given a more generous save (again, just to give the characters a fair, fighting chance). For example, I would consider giving the save for sleep (recall, "no-save" language doesn't yet exist in the OD&D LBBs) the same category as "paralization", since the effects are so similar. A bad falling-stone trap might be worth a save vs. dragon breath, whereas an instant pit-into-lava trap should be worth a save vs. death. Et. al.

## Friday, December 11, 2009

### No Scale in Man-to-Man Combat

I've said it before, but I've had it highlighted for me again recently. There are no scales given in Chainmail Man-to-Man Combat (corollary: same for the Fantasy Supplement), and I think that it's Gygax's single most fundamental oversight in the design of the original game. In any other miniatures context he's careful to specify the key 3 scales (figure, distance, and time). But the whole issue is conspicuously absent from the Chainmail Man-to-Man rules.

This caused a lot of grief over the years, IMO. First of all, the lack of figure scale made it unclear that the Chainmail Fantasy Supplement was actually for man-to-man action only (1:1), not mass combat, and thereby contributed to the faulty notion that original D&D had a mass-land-combat wargame included. Secondly, the lack of a distance scale precipitated a pretty short-sighted hack to OD&D that 1" = 10 feet (an evolution of Chainmail's 1" = 10 yards); this resulted in 25mm miniatures not actually fitting into a proportional space on a map, and really crazy convolutions like AD&D's DMG p. 10 (where it is specified that when using miniatures, ground scale should actually be mapped out at 1" = 3⅓ feet!). Thirdly, the lack of a time scale likewise caused Chainmail's mass combat turn (1 turn = 1 minute) to be carried over directly to D&D; and while this was entirely reasonable for Chainmail's 1:20 scale, it was frankly entirely unreasonable for man-to-man (1:1) swordplay and bowfire, again resulting in long-winded and unconvincing justification attempts in places like AD&D's DMG p. 61.

As much as I try to give priority to the original versions of the D&D rules, and hew to them as closely as possible, this trio of scaling issues is the #1 item that I simply cannot accept in OD&D and/or AD&D. It's the principal reason that miniatures never really worked all that well in classic D&D tactical play. I do feel that Holmes went in the right direction with a 1 round = 10 seconds time scale, and 3E was in fact a relief to allow 1" = 5 feet ground scale, thereby matching the miniatures we've always used. If Gary had only considered the issue more carefully when writing the original 2 pages of Chainmail Man-To-Man Combat, or sometime shortly thereafter.

## Tuesday, December 8, 2009

### No Heroes In War

I want to expand on a few things I mentioned in the last blog.

First of all, just so it's clear, the primary point of the last post was this: There are no endgame rules presented in either Chainmail or Original D&D, and that goes for either fantasy mass-warfare or dominion management. It's not specifically my point that that's either a good thing or a bad thing. But clearly the impression of such is given, when it's not truly available. (Again, see OD&D Vol. 3 p. 25, as an example.) If we want to be charitable, we could call this impression a "teaser" of things that could come later. If we wanted to get really cranky about it, we could perhaps call it "deceptive advertising" or somesuch. (Of course, I prefer the former.)

Now, as a very minor corollary to that observation, we've also discovered another, somewhat more specific piece of common wisdom that was also erroneous, and that's what I'd like to further highlight here. Throughout D&D mass-warfare writings, we're given the impression that higher-level fighters and monsters can, acting alone, stand against masses of normal troops. ("These fellows are one-man armies!" as per Chainmail p. 30.) This is incorrect, and what I'm interested in here is the proactive effort that was needed to obscure this rather key fact. Here are some case studies.

Case 1 -- Chainmail Fantasy Supplement. Note again that these rules are only for man-to-man action (1:1 figure scale). There is simply no provision available to adjudicate a high-level fighter acting against large masses of troops. Of course, this fact wasn't made explicit in Chainmail, and you have to look to the Introduction of Swords & Spells years later to see it in print from Gygax.

Case 2 -- Swords & Spells. Consider this example from the Introduction (p. 1):

At the scale of these rules a single man can be represented by a single figure on the table. So if one opponent has a lone hero (4th level fighting man) facing several figures of men-at-arms (or orcs or similar 1 hit die creatures), an actual melee can take place. The hero will inflict .40 of the damage shown for a 4th level creature on the combat tables and sustain damage until sufficient hits are scored upon the figure to kill the hero.

Now, there's no need to leave you hanging here, when we can calculate in advance exactly when the hero in question will be killed. And that is (taking reasonable assumptions): In one full turn of melee against one opposing figure. Proof: Assume the hero has average hit points (4.5 x 4 = 18), and is wearing full plate & shield (AC 2). Average damage is shown in the combat table on p. 24 (or, take d6 damage and compute 4/20 x 3.5 x 10 = 7). Note that one full turn in S&S allows 3 melee rounds of attacks (p. 17) and you have 7 x 3 = 21 points of damage against the hero, killing him in one single turn. If you like, feel free to add some hit points for Con bonus, and I'll add the plural "figures" from the quote above to dispatch the hero even more quickly.

Gygax doesn't spell out exactly when the 4th level fighter gets killed (namely: immediately), nor does he explain later on the page why "the admonition regarding single creatures is important" (namely: so they don't get killed immediately). But he could have.

Case 3 -- Battlesystem 2E. (Side note: I love Doug Niles Battlesystem 2E book. It's a really beautiful work, and if it weren't for some very small but critical flaws I wish I could use it all the time.) Consider the same quote I pointed out last time (p. 106):

From a mathematical perspective, the attributes of heroes in a BATTLESYSTEM scenario are inflated beyond those of the creatures in the units surrounding them. However, the conversion is based on the assumption that there is an intangible quality to heroism that exceeds in importance the hero's worth as a fighting machine.

Well, why not spell out exactly the factor by which hero attributes have been inflated? Let's see: A standard figure represents 10 men and is given a "Hits" value 1; hence each "hit" really represents 10 HD total (or more; see p. 105 or my posts from last month, which are comparable). Meanwhile, "All monster types, and characters of the fighter class, receive 1 hit for each 2 Hit Dice or experience levels." For example, a 10th-level fighter or monster (~10HD, comparable to the total hit dice for a normal 1-hit figure), is given 5 hits by this system. In other words: Heroes in Battlesystem have been quintupled over their actual D&D-scale health values. This is to say nothing of their attack values, which are more complicated to compute, but given similar inflation factors.

Niles could have spelled this out, as well, be he chose not to. (The Battlesystem boxed set came with special lead figures for use as heroes/ commanders, and I guess it would be raining on someone's parade if Niles were to suggest that they weren't going to be at all effective standing alone in mass land combat.) Even so, heroes and lone fantastic monsters can be quickly dispatched in Battlesystem by racking up just a few hits on them.

Now, there are a few narrow exceptions to all of the foregoing. One is if the hero's AC is so good that no normal man can hit them. In OD&D this point occurs at AC -2 (plate & shield with +4 total bonus), which is pretty difficult in core OD&D (impossible with a literal reading?), but becomes more likely with Greyhawk and other supplements. (This is possibly countered if you use AD&D's combat tables, count a natural 20 as always hitting, or strictly apply rear/flanking situational bonuses, but that discussion becomes highly edition- or house-rule-specific.) Second would be if the hero/monster is only hit by attacks of a special sort, such as silver or magical weapons, et. al. In these cases a hero figure obviously really could wade through armies of men untouched, until some enemy hero decided to give him chase. But still there is no real contest to play out; the specially-protected hero could automatically massacre an unlimited number of normal men without any threat whatsoever.

Again, I want to clarify that I'm not saying that this affair is either good thing or a bad thing in itself. (In fact, I guess I'd have to say that the realization is refreshing compared to my prior thinking. Numerous new possibilities open up.) Maybe given completely free design capacities you'd choose to have the interaction of heroes with masses one way, or the other. But clearly the impression that heroes can stand against masses doesn't, in general, bear out in play for either D&D or any of the mass-combat games that were later based on it. And that's an error that could have easily been avoided.

## Saturday, December 5, 2009

### The Problem with the Endgame

These rules are as simple and straightforward as I could devise for a game system which involves "magical" and fantastic factors. The FANTASY SUPPLEMENT written for CHAINMAIL assumed a man-for-man situation. While it is fine for such actions, it soon became obvious that something for large-scale battles was needed.

- Gary Gygax, "Swords & Spells" Introduction, 1976

As old-school D&D'ers, I think that many of us share the intuition that there is an "endgame" in which high-level PCs wind up managing castles, baronies, and leading fantasy armies in battle. It seems a little frustrating that the endgame seems to have been "lost" somehow over time.

For probably 30 years I've been trying to scratch this itch and find the proper solution to the reputed endgame. Once again I've been attacking the problem recently, having had an opportunity in the last year to become familiar with Chainmail, OD&D, re-reading Swords & Spells and Battlesystem, etc. Personally, I need my mass-war system to have the same statistical expectations as if you actually played the RPG rules out man-to-man (i.e., it's no good to have X beat Y in RPG rules, but Y beat X in mass-war rules; I'm looking at you, War Machine.)

Here's my new observation: The endgame never actually existed in original D&D. It was sort of an illusion all along, which caused a lot of personal frustration.

Let me be specific: In neither Chainmail nor OD&D is there any provision for handling fantasy battles between opposing armies of hundreds of men (or monsters). It looks like there is, but there really isn't. Consider the quote at the top of this post (emphasis mine). Indeed, the Chainmail fantasy rules were in their entirety only meant to work on a 1:1 scale, not a mass scale, i.e., they're a continuation of the "Man-to-Man Combat" section that immediately precedes them. In other words, OD&D is in some sense just a somewhat revised edition of the Chainmail Fantasy Man-to-Man rules, not a totally different game.

Let's think about this a little more, because you get conflicting signals/ advertising from Chainmail itself. Conflicts would include: (1) Chainmail in general is at a 1:20 mass scale, and the Fantasy section never says explicitly that anything has changed in that regard. (2) The opening to Chainmail Fantasy says that it can be used to "refight the epic struggles related by J.R.R. Tolkien, Robert E. Howard, and other fantasy writers," which is not truly the case at 1:1 scale. (3) The language for Super Heroes asserts that, "these fellows are one-man armies!", when in fact they are only able to counter 8 normal men, not a whole army. (4) Combat chances between fantasy creatures and men refer back to the standard (mass) Combat Tables, not the Mam-to-Man Melee Table.

So, these assertions in the past led me to think that Chainmail Fantasy was at 1:20 scale, which caused all kinds of collisions with the standard D&D rules. I would think, "How can Super Heroes be worth an army in Chainmail (8x20 = 160 men), but only 8 men in D&D?" (Or, "Is every individual catapult/ giant boulder/ fireball really killing 100-300 men per shot?") Furthermore, you would have all these situations in D&D indicating the action of hundreds of men or monsters (such as [a] monster number appearing stats, [b] guards in castles, [c] clerical faithful followers, [d] crew numbers on naval ships, etc.) And let's pile it on one more time with OD&D Vol. 3, p. 25, which has a very brief (as always) reference to "Land Combat" which says this:

The basic system is that from CHAINMAIL, with one figure representing one man or creature. Melee can be conducted with the combat table given in Volume I or by the CHAINMAIL system, with losses equalling a drive back or kill equal only to a hit. Battles involving large numbers of figures can be fought at a 20:1 ratio, with single fantastic types fighting at 1:1 or otherwise against but a single 20:1 figure.

Now, we can see that the first part of this is an honest description of the Chainmail rules (man-to-man). The second part is not so honest, making it sound like Chainmail has the capacity to handle a 1:20 fantasy scale, when the truth is it really doesn't. As much as we'd all like it to, Gygax included. The last sentence with its waffle-y "or otherwise" is really more of a thought-experiment or a proposal than an actual rules reference. The fact is, we really have no pre-planned way in either Chainmail or OD&D to deal with those hundreds of wandering orcs, castle guards, faithful soldiers, or ship crews. (Nor the hundreds of guards in the barracks of Sup-II's Temple of the Frog.)

The conjoined problem is that any single hero-type will, if we honestly look at the statistics in OD&D, get chewed to pieces by dozens or hundreds of 1st-level opponents. Even a D&D Superhero in plate & shield (HD8, AC2) will get hit by normal men 20% on each strike (req. 17+ on d20). Surrounded by just 5 normal men at a time -- ignoring flank/rear bonuses -- the Superhero can be expected to take 1 hit per round and go down in 8 standard rounds (or less). Even with their fearsome number of attacks and morale effects from Chainmail, the Superhero will be dead in just a few minutes of standard D&D combat. (In OD&D it requires AC -2 to become immune to the attacks of normal men; of course, this immunity is taken away by the AD&D combat tables with their repeating 20's.)

So, I find that for the first time in 30 years I fully understand Gygax's Introduction to Swords & Spells. It's a fascinating read. He knows that there's a problem with mass Land Combat in D&D and he's trying to provide a solution. He knows that the presented ruleset is only a partial solution at best (using all expected-value hit point calculations, with no dice or randomization of combat results whatsoever.) In fact, having recently drafted a forward for my own similar work, I find that Gygax anticipated most of my initial comments 33 years ago, working on an equivalent project.

Some extra-curricular way must be added to allow our D&D heroes to survive on the battlefield, when they really shouldn't according to the stock rules of D&D. Gygax writes in Swords & Spells, "The admonition regarding single creatures is important: If they meet, or are simply near each other, they should seek combat with each other rather than inferior opponents, and this combat should be fought at 1:1 in the normal D&D manner". Yep, that's one way to keep them alive (i.e., force them to avoid masses of normal men whenever possible).

Likewise, Doug Niles writes in the Battlesystem 2E book p. 106: "From a mathematical perspective, the attributes of heroes in a BATTLESYSTEM scenario are inflated beyond those of the creatures in the units surrounding them. However, the conversion is based on the assumption that there is an intangible quality to heroism that exceeds in importance the hero's worth as a fighting machine." Yep, that's another way -- just arbitrarily boost the hero's stats on the battlefield to keep them alive.

An interesting problem, and some highly interesting reads when you lay out the entire sequence of mass-land combat in D&D. The truth is, there were no rules even intended for mass combat in fantasy D&D until Swords & Spells, and later Battlesystem, and these were only limited successes at best. OD&D hinted at an endgame that wasn't really ever there in the first place.

(Special thanks to James & Jervis for recently getting the 1972 Gygax letter on fantasy wargaming posted on Grognardia, which jogged my thought process a bit more on this subject.)

## Friday, November 27, 2009

### More Hit Dice Stats

In the prior post, I presented some numbers for the average hits required to take down different HD creatures. Of course, that was done by random simulation, so it will have some small amount of sampling error in the numbers.

I wanted to double-check these numbers with a closed-formula, direct probability calculation. Even that takes some heavy-duty processing power (with permutations, combinations, convolutions, and such). Fortunately, it turns out that the numbers do in fact check out very nicely. Exact statistics and code below if you're interested.

## Tuesday, November 24, 2009

### Are All Hit Dice Created Equal?

Here's a D&D math puzzle. Consider a 4HD creature versus a 1HD creature -- say, an OD&D Hero versus a Veteran. (For this discussion we assume that all hit dice and damage are uniformly d6's.) On average, will the 4HD creature take 4 times as many hits to kill as the 1HD creature?

You might assume so -- I know I did, and that assumption is more-or-less built into the bridge that connects Chainmail to D&D. But somewhat surprisingly, that turns out not to be the case. Consider the following table (PDF): www.superdan.net/download/CompareHD1.pdf

What you'll see is that on average, any creature takes about HD + 0.5 successful hits before being eliminated. That is, there will usually be a little bit of "wasted" damage, perhaps as the creature is reduced to 1 or 2hp, and still requires another full hit before being struck down. And what this is means is that, as a proportion of overall HD and hit points, the 1-HD creature types will be "wasting" more damage and more hits than higher-HD types.

In the second and third columns of the table, you'll see things like this: Whereas a 1HD creature takes an average 1.5 hits per HD, a 4HD creatures only takes 1.1 hits per HD. In short, a 4HD creatures actually only takes 3 times as many hits as a 1HD creature (on average). And this grows progressively more severe: an 8HD creature only takes 6 times the hits of a 1HD creature, and a 15HD creature really only takes 10 times more total hits than a 1HD creature!

This might be merely a mathematical curiousity. Or, it might be something we have to make decision about if (to pick a random example) we wish to construct a set of mass-warfare rules which replicate D&D results with high statistical fidelity. Should we honor the actual hits-to-kill-over-1HD (as in D&D above), or should we more simply use the HD as hits-to-kill (as in Chainmail)?

Follow up -- More Hit Dice Stats (checked by closed probability formulas).

## Saturday, November 7, 2009

### OED: Book of Spells

We just published a volume on Lulu, entitled Original Edition Delta: Book of Spells. It's a concise, comprehensive collection of magic spells for use with the "original edition" fantasy game rules (as published by Gygax & Arneson, 1974-1975).

Personally, I always wished that the magic spells were set aside in their own booklet (instead of filling up the basic player's book), and now we have that. It uses the OGL to extract the bare-bones original rules back out of current, freely available source material.

Myself, I plan to print one of these out for each of the wizard players in my games (or whatever subsection they need: for example, the 1st-level spells all fit on one page again, so I just hand new players that and tell them it's their entire spellbook). I also made some minor edits to particular spells after playing with them for 30 years, which may or may not outrage you personally. :-)

It's 18 pages, with interior art on about 1/4 of the text pages where it fit. Available on Lulu as a download for $3.50 or printed with extra cover art for$7. Tell us what you think!

## Tuesday, September 29, 2009

### Death Statistics in D&D: 1978

This is an excerpt from a short article by Lyle Fitzgerald in Dragon #20 (November 1978, p. 26). I find myself mentally returning to this glimpse of the past rather frequently.
Our campaign is primarily a wilderness one (as the statistics reflect), although huge dungeons do exist. The 600 deaths listed include deaths of playing characters and their advanceable hirelings, not mercenaries or other non-playing characters. We started compiling these statistics 2 to 3 years ago...
• Goblin races (61) 10.1%
• Dragons (45) 7.5%
• Giants (34) 5.7%
• General Combat (26) 4.3%
• Lycanthropes (24) 4.0%
• Execution/ torture, sacrifice (23) 3.8%
• Bandits/ pirates/etc. (20) 3.3%
• Giant insects (20) 3.3%
• Assasination/ treachery (18) 3.0%
• Giant rocs (18) 3.0%
• Fireballs/ lightning (17) 2.8%
• Trolls (16) 2.7%
• Turned to stone (14) 2.3%
• Guards, military patrols (13) 2.2%
• Evil high priests (13) 2.2%
• Man-eating vegetation (13) 2.2%
• Related dragon species (13) 2.2%
• Cursed items/ booby traps (12) 2.0%
• Giant animals (12) 2.0%
• Falls (12) 2.0%
• Gnolls (11) 1.8%
• Gargoyles (9) 1.4%
• Hell Hounds (8) 1.3%
• Demons (8) 1.3%
• Elementals (8) 1.3%
• Griffins (8) 1.3%
• Kindred races (elves/dwarves)(6) 1.0%
• Misc. spells (6) 1.0%
• War (6) 1.0%
• Misc. causes (85) 14.6%

## Sunday, September 27, 2009

### A Trite Expression

From a column this week by Jim Rossignol at Offworld.com:
Games don't necessarily have to be fun to be engaging. Indeed "fun" seems like a trite expression in the face of some contemporary projects: games can provoke more than simple enjoyment. Look at the terrifying crypts of Stalker, or the strange sadness of Shadow of the Colossus. To realise that games ride on more than fun only takes a quick glance at the bigger picture.

Sing it, brother! Of course, this is just prelude to an interesting article about other new developments, highly recommended. Plus, discussion at Slashdot.

## Saturday, September 26, 2009

A recent post on Grognardia features a player reminiscing about playing in Gygax's Lake Geneva campaign in a solo expedition to Castle Greyhawk (as a 1st-level magic-user, no less). It brought to mind what I've long considered a potentially really great untapped market -- solo adventures, specifically for Thieves.

It's always seemed like there's a bit of awkwardness around having "thieves" working with adventuring parties, when they're presented as likely to cheat and steal from the very party they're working for. On the other hand, I've had lots of occasions in my life where I it would be great to run a game with the one single player I had available. It seems like "solo thief" scenarios would be an ideal solution (ostensibly two problems cancelling each other out).

I actually had a lot of fun once running module "O1: Gem and the Staff", which is the one dedicated solo-thief module I can think of. It also offered a really nice opportunity to run a "mini-tournament" game where I ran each person in my regular gaming group through it individually, and then compared scores at the end -- among other things, this got a little "quality time" with each player to see their personal reactions and preferences.

As much as I'd like to see scenarios like that, I know I'm not the one to make them -- I think you need someone a little more steeped in noir, crime drama, Lankhmar and Thieves' World traditions than I am (which is to say, practically none whatsoever).

## Tuesday, September 8, 2009

### On Light

I played a short game of D&D this weekend with some good friends (OD&D with OED interpretations). Played very well with 2 first-time players, my beginner-level girlfriend, and an almost 30-year veteran at the table (who gave me a great compliment about his suprise at how well the game worked sans clerics).

One thing that popped up is how far a torch illuminates, which isn't specified in OD&D. I started researching this, comparing across different rulesets, and the results were interesting. Partly this will be a critique about how games evolve towards greater abstraction over time, from realistic beginnings to nonsensical endings. It seems that the inertia, the infatuation with the game system itself takes over and late-version designers wind up working in an echo chamber. (And it's not just D&D: I've seen the exact same thing happen at games I worked on at a few video game companies. Perhaps it's true for other media as well, like books, TV, and movies.)

Question: How far does a torch let you see in reality? Consider this snippet from a Scientific American Supplement: "Torches consist of a bundle of loosely twisted threads which has been immersed in a mixture formed of two parts, by weight, of beeswax, eight of resin, and one of tallow. In warm, dry weather, these torches when lighted last for two hours when at rest, and for an hour and a quarter on a march. A good light is obtained by spacing them 20 or 30 yards apart." This indicates a bare minimum radius of visible illumination of 30 feet (half of 20 yards), maybe 45 feet (half 30 yards); possibly even 60 or 90 feet (20 or 30 yards itself) depending on how liberal the above usage of "good" is taken.

Question: How far does a torch let you see in D&D? In OD&D, the issue is seemingly not addressed; without directly comparing them to torches, the light spell is given a 3" radius, and the continual light spell a 12" radius (ostensibly 30 and 120 feet). In the AD&D 1E PHB a torch is given a 40-foot radius (p. 102, quite compatible with the research above), and the light spell is described this way: "The light thus caused is equal to torch light in brightness, but its sphere is limited to 4” in diameter." (Note that the second clause highlights the fact that while brightness is torch-like, the range of the magic spell is distinctly and intentionally shorter: just a 20-foot radius.) The continual light spell is reduced to a 6" radius, yet "its brightness is very great, being nearly as illuminating as full daylight".

Let's skip ahead to 3E D&D. Clearly some designer wanted to synchronize all of these effects and make them identical, a pretty reasonable motivation. If a light spell has been compared to a torch, why not make it equivalent to a torch in all ways, for brevity's sake? Well, the problem arises when this late-era designer doesn't do any research, and takes as his basis (looking solely from inside the rules) the effect of the magic light spell, and revises the effect of the mundane torch to match it. Thus in 3E you have both normal torches and the various light spells illuminating only a 20-foot radius.

Now, not only is the 20-foot radius torch unrealistic (whereas it formerly was), it's also extremely awkward from a gameplay perspective. The torch bearer only lights up 4 spaces (3E) away; routinely you'll have the front-line party member in darkness, or the front-most enemy in direct melee unsightable, or the extent of most rooms indeterminable during routine exploration, if you adjudicate this literally. (Now in 3.5E both light sources were given a new rules category of "shadowy illumination from 20 to 40 feet", but don't even get me started about trying to adjudicate that.)

The truth is that I'd recently been looking at the 3E SRD spells listing with its 20-foot radius torch, and so made a similar ruling in my game this weekend, and did get a look of disbelief from at least one of my players at the awkwardly short range of the party's light. And, I see now, he was right (in both realism and gameplay), my being led astray by late-era D&D rules-mechanic navel-gazing. At this point I have half a mind to say that torches give "good enough" light up to 60 feet away, illuminating most rooms in their entirety, and just using a whole 12" ruler (at 1"=5 feet) if we ever need to check it in play.

A rule-of-thumb I discovered over 10 years ago at one of my game programming jobs, and refreshed at times later on (even while building miniature models not long ago): If stumped by a particular design problem, ask yourself "What solution is used in the real-life situation?" In my experience, the answer is usually immediately applicable as a solution in your game rules. I'd guess that only a fetish for over-abstraction in a game would lead one away from this principle. I'll say again that we don't want realism-for-realism sake (see DMG p. 9), but for pre-existing gameplay problems, it often provides the most elegant fix.

There's other stuff about the interaction of light in published D&D that's bugged me over time (like the effect of the darkness spell, SKR's absurd-but-successful rant "infravision and why it should be destroyed" in 3E, etc.) That may have to wait for another posting.

## Thursday, September 3, 2009

### OD&D Saving Throw Charts

Here's a series of charts I compiled, comparing the various OD&D saving throw categories (click image to expand).

These graphs chart the saves at every individual level in OD&D, and also insert linear regression lines ("trend lines", or "lines of best fit"). They incorporate all the data from levels 1 to 15. I think this highlights certain patterns which are not obvious in the tables (granted the differing ways the class levels are grouped), and may even disabuse a few common misconceptions.

One of the first things to be seen is how the class save values are grouped (Fighters in blocks of 3 levels, Clerics 4, Wizards 5). Some of us would like to smooth this out from the table values, permitting a small improvement every level or so (as suggested for fighter to-hits in the AD&D DMG, or the Lakofka/Gygax Dragon article noted here) -- so the trend lines are useful for that.

A second thing is that wizards (magic-users) tend to have a shallower trend line, improving more slowly than the other classes. This is partly because there is another higher-level category for wizards (levels 16+) which is not shown here. Ultimately wizards end up with saves as good as (or better than) the other classes, but that doesn't occur until the very high levels off these charts.

Now for some more specifics. Fighters and Clerics are extremely close in almost all their values and trends, to the extent where I'll simply regard them as effectively the same. Similarly, in the last chart, saves vs. Spells are practically identical for all the classes at all levels; at most a difference of +/-1 in the trend at any level. Saves vs. Stone are somewhat more mixed; the trend lines actually cross (Fighters start out the worst, then become the best), but are so closely packed that we may as well treat them as basically the same, as well.

Finally, some differences. Wizards (and hence Thieves, as per Greyhawk) are clearly, consistently deficient in their Death and Wands saves from levels 1-15. Also, while starting out fairly close, Fighters have a particularly steep (beneficial) trend line in Breath saving throws. Therefore on average, wizards are at -3 when compared to Fighters across all these categories (Wands, Death, and Breath; technically average -2.67, -2.67, -3.47 respectively). Even clerics are at a -2 average penalty when compared to fighters in the category of Breath saves (-2.33, to be exact).

It's interesting that if you take Fighters as the basic character class (including all monsters), the baseline saves differ, on average, by precisely 1 point per category. That is, starting with the last category of Spells, Breath is at +1, Stone at +2, Wands +3, and Death +4 (again speaking in terms of the trend line intercept parameter; you can also see it immediately in the top row of the OD&D table itself).

The trend lines move downward with an average slope of -0.6 over all saves and classes (with a range of from -0.45 for the shallow wizard lines to -0.8 for the quickly advancing fighters vs. breath saves). If we think about smoothing out the curves with a simple formula (instead of using the tables directly), we might think about giving a bonus of half-the-level as a pretty good estimate. Of course, in my OED rules editorial, I felt even that was too complicated, and simply rounded it off to d20+level (beat 20+), plus the various modifiers noted above.

## Monday, August 31, 2009

### Quick Dice Average

Quick way to find the average (expected value) of dice xDy: Take half of x, add one to y, then multiply the two. This is equivalent to what some refer to as "Gauss's formula" for summing a series. For example:

8d6 -> 4*7 = 28
12d4 -> 6*5 = 30

## Friday, August 21, 2009

### OED Reincarnate

I've been working on a compact collection of spells for Original D&D-style games. Here's one example -- actually the very last one I completed, the longest, and possibly the one that caused the most difficulty to find the proper balance.

Keep in mind that in my games, there are no clerics. That might seem to preclude raising dead characters, but recall that our wizards fortunately still have the 6th-level reincarnate spell:

Reincarnate
Range: Touch
Duration: Instantaneous

With this spell, the character brings back a dead creature in another body, provided death occurred no more than 1 week before the casting of the spell and the subject’s soul is free to return. The magic of the spell creates an entirely new young adult body for the soul to inhabit from the natural elements at hand. This process requires 1 hour to complete. When the body is ready, the subject is reincarnated.

The recipient of the spell must make a saving throw to return in the same body type as before (same race and abilities, appearance may change). If failed, the DM should instead choose a random humanoid race of the same alignment for the new body type (re-roll abilities, up to ogre size). It's quite possible for the change in the character's ability scores to make it difficult for the character to pursue his or her previous character class. The character’s level is reduced by 1.

A few comments. You'll see that the standard "stat block" elements are just range & duration; nothing else is really necessary for the majority of old-school spells. The first paragraph is just copied directly from the 3E SRD as provided by the OGL.

The second paragraph is text written by myself. Since this is our only raise-dead type spell, I wanted to have some chance that the character returned fundamentally unchanged and still playable. Is the saving throw the proper mechanic? I think so. On the other hand, I wanted to retain the chance that the character is lost in the process, and returning as a random humanoid makes it likely to be the effective case (perhaps socially speaking) -- although restricting it to humanoids makes it easier to run in play if the DM so wishes. The probability is generally similar to 1E "system shock" rolls for Constitution, but folds into the standard save mechanic. The character-level loss is retained from the SRD to make sure this doesn't become a routine (or cyclical) procedure. Other than that, there's quite a bit of flexibility for the DM to adjudicate this spell in the best fashion for his or her campaign.

The spell text above is designated open game content under the terms of the Open Game License v1.0.

## Tuesday, August 11, 2009

### OED Update (v0.5)

Minor update to the Original Edition Delta house rules (version 0.5). Mostly just editorial cleanups, I felt it was important to fit on 4 pages (i.e., one folded sheet of paper). Took out some details on spells and monsters that seemed unnecessary here. Revised exploration movement back to the core rules.

http://www.superdan.net/oed/

## Tuesday, July 28, 2009

### The Gray Zone: Convention Games

Let's consider three different contexts for playing D&D:

1. Home campaigns. Here you'll be playing with the same players & characters over an extended period of time. Characters will almost certainly be generated individually to player taste; they will advance and explore the world over time. Old-school “sandbox” style play basically requires this context.

2. Convention games. This is a one-shot adventure, possibly limited to a 4-hour time slot or something similar. Characters may be pre-generated or custom-made (consider RPGA point-buy rules or the old DMG Appendix P, which I still use). The characters won't advance in any mechanical way.

3. Tournament play. This is also a one-shot adventure, but in a competitive context. There will be multiple (possibly very many) playgroups run through the same scenario, with an eye towards scoring the best and picking a “champion”. Characters are almost certainly pre-generated (so as to give a level playing field to the competition).
Notice that I distinguish here between “convention games” in general and “tournament play” in particular (even though they have many coarse similarities, and tournaments are generally run within a convention gathering). Convention & tournament games are similar in that they both feature short one-off adventures, and they avoid any usage of the character-advancement rules. But they differ in that one is competitive and the other is not. Simple convention games, perhaps, have more of an incentive to let the players “win” (sometimes they are run as product-release promotions or trials, and have good reason to want the players to leave the table feeling like they “had fun” with the experience and the product).

Tournament games, meanwhile, have an excellent reason to be tough meat-grinders where the majority of the players “lose” (by acting as a strict filter, they make it easier to identify the one “champion” in the event that made the most progress; whereas if many people uniformly “win” it will be difficult to make that distinction). Compare to an interesting quote from recent cyberware games at West Point: the attacks designed by the NSA were made "a little too hard for the strongest undergraduate team to deal with, so that we could distinguish the strongest teams from the weaker ones." And this also explains why the earliest D&D published adventures all had a "killer DM" feel to them: they were all originally developed for competitive tournament situations.

Okay, so getting closer to my point -- Having considered the different kinds of play contexts I've seen for D&D, two of them have seemed the most compelling, and one is rather more frail for me. We might ask the question, "Why are we playing; what do we gain at the end?" Two of these situations have a meta-reward, outside the game itself, that makes the experience deeper and more compelling. In case (1) Home campaigns, the meta-reward is largely character advancement; levelling up, accessing new powers and magic items. There's also exploration of a larger campaign world over time, but let's face it -- The #1 revolutionary, addictive development that D&D brought us was the idea of persistent, advancing characters over many game sessions, and this is almost solely accessible in terms of a home campaign. In case (3) Tournament play, the meta-reward is the competition with other teams playing in parallel to yours, and seeing one team at the end awarded with honor and a trophy (or somesuch). Personally, I love playing in a tournament, and love the heads-down, high-proficiency play that I see in that context.

So that leaves case (2) Convention games, and frankly, I can't figure out what the meta-game "point" is to them anymore. When I run one, I'm left a little bit bewildered at the end about what the payoff is. It seems very awkward if there's a TPK at the end, and it seems almost equally awkward if time simply runs out after a certain number of rooms are successfully looted.

One suggestion is that there needs to be a specific "quest" in a convention game -- The players are given an explicit (or obvious) assignment at the start, and if they can succeed in the time alloted, they are declared to have "won". A few problems here: (1) It's difficult to estimate in advance a perfect set of encounters that lead to a "win" at exactly the 4-hour mark. (2) The setup manages to frustrate the classic D&D architecture of open-ended exploration, multiple paths, resource management, wandering monsters, treasure and XP rewards, etc. (3) There's still no meta-game reward from this in-game "victory".

Now, I have a good friend Paul who recently ran an exceptional convention game a few weeks back. Philosophically, we tend to disagree about many of the high-level "whys and wherefores" of D&D, but I think we almost always agree about whether a given game we just experienced was good or not (sort of an "I know it when I see it" experience). In the past we simultaneously co-DM'd a campaign, and at least once our differing styles stomped ugly all over each other (Ettin-style?). He may run a better convention game than I do; the one he ran the other weekend was one of the most fun D&D sessions I've had in a long time -- hilarious characters, great encounters, well-paced, filthy humor (which I like), great ending. I was mulling over my troubles with convention games on the ride over, and lo, my friend snaps off one of the best such games in my memory.

Anyway, Paul wrote up his notes on that adventure on his blog over here. The thing I was surprised and a bit unsettled by was that the quest, locations, and NPCs were all being invented and moved around backstage on the fly, which is how our investigations managed to lead us to saving the girl at almost exactly the 4-hour mark. Made for a great, nigh-perfect gaming session -- and it's not something I think I'd ever be able to bring myself to do, as it goes against every grain I've been trained in as a game designer, thinking more in terms of published tournament-style adventures that we'd prefer to keep fixed, replicable, and fair if multiple groups are run through the same adventure over time.

So, what to do? Should I just give up on running one-off convention games (granted that they frustrate all the meta-game rewards that are the hallmark of D&D), and leave them to better narrative DMs? Is there any way to interface the classic rewards of D&D in an isolated, one-shot experience? Troubling questions, since at this point in my life the only opportunities I have for play are the infrequent one-off convention games: the "gray zone" in the middle, if you will.

## Thursday, July 16, 2009

### What is the Best Combat Algorithm?

Throughout the history of D&D and RPG's (and more generally, any action/ wargame), there have been a host of different algorithms to determining success in combat and other feats of skill and luck. For example: to-hit-tables, THACO, compare to increasing AC score, etc.

Within some very small tolerance for error (say +/-1 difference), all of these systems have been mathematically equivalent (i.e., result in "hits" for the same rolls of the d20 die). But which is the best algorithm? That is, treating the tabletop gamer's brain as a kind of natural "computer", which is easiest/ fastest/ most efficient/ least error prone? Is it one of the aforementioned algorithms, or something different?

First, let's establish the different components of the basic D&D "to hit" (or anything else) roll. They include: (1) a d20 die roll, (2) a basic attack proficiency, by class or hit dice, (3) the armor of the defender, (4) miscellaneous modifiers (positive bonuses being good for the attacker), and (5) the "baseline" chance to succeed at hitting, irrespective of other modifiers #2-4.

Let's look at one example, say, the THACO mechanic from 1E-2E. In the form of an inequality, the basic algorithm is:

THACO ALGORITHM: d20 + mods ≥ THACO* - AC

* The THACO was itself determined (pre-game time) from tables in the core books. But in essence, for fighter and monster-types, this incorporated the "baseline" success chance (Normal Men need to roll ~20 vs. AC 0) and a +1 bonus per fighter/monster level. In other words, THACO = (~20 - level). Let's substitute and see all 5 terms plainly:

THACO ALGORITHM: d20 + mods ≥ 20 - level - AC

Now, if we proceed to search for other, variant algorithms, we can apply the basic algebraic "rebalancing" operations to make any of these terms appear on either side of the inequality that we wish. For example, we could add a "level" term to both sides (canceling it on the right and appearing as an addition to the left). Or, we could subtract the "mods" from both sides (thereby appearing as a subtraction on the right).

In fact, since there are 5 terms, and each can appear on either of the 2 sides of the inequality that we wish, there are in fact 2^5 = 32 different formats for this inequality (by the fundamental principle of counting) that we could consider. Here are just a few of those 32 possible variations:

TABLE ALGORITHM: d20 + mods ≥ (20 - level - AC)
[Encapsulated in table]

THACO ALGORITHM: d20 + mods ≥ (20 - level) - AC
[Encapsulated in THACO]

d20 SYSTEM ALGORITHM: d20 + mods + level ≥ (20 - AC)
[Defined as New AC]

"SUBTRACT ALL" ALGORITHM: d20 ≥ 20 - level - AC - mods

"ZERO BEATS ME" ALGORITHM: 0 ≥ 20 - level - AC - mods - d20

Etc...

Now, obviously, those last few were for humorous illustrations only, and I assume not many people would want to use those systems. But what criteria can we use to choose the "best" possible system? Let's consider the following as guiding principles (and we'll back each of them up with results from experiments in cognitive psychology as we proceed):

(1) Additions are easier than subtractions.
Although mathematically equivalent (and using fundamentally the same operation in digital computing systems), most people find subtraction significantly harder than addition. For example, see the paper by MacIntyre, University of Edinburgh, 2004, p. 2: "Addition tasks are clearly completed in a much more confident manner than the subtraction items, with over 80% of the study group with at most one error on the items. Subtraction items appear to have presented a much bigger challenge to the pupils, with over 50% having 3 or more of those questions wrong."

(2) Round numbers are easier to compare than odd numbers. In other words, when comparing which of two numbers is larger (the final, required step in any "to hit" algorithm) it will be easier if the second number is "20" than, say "27". This follows from the psychological finding that it's faster to compare single digits that are farther apart; see Sousa, How the Brain Learns Mathematics, p. 21: "When two digits were far apart in values, such as 2 and 9, the adults responded quickly, and almost without error. But when the digits were closer in value, such as 5 and 6, the response time increased significantly, and the error rate rose dramatically..." In our case, setting the second digit to zero would maximize the opportunity for a large (and thus easy-to-discern) difference between the numbers.

(3) Small numbers are easier to compare than large numbers. This has also been borne out by a host of psychological experiments over the last several decades. Again from Sousa, p. 22: "The speed with which we compare two numbers depends not just on the distance between them but on their size as well. It takes far longer to decide that 9 is larger than 8 than to decide that 2 is larger than 1. For numbers of equal distance apart, larger numbers are more difficult to compare than smaller ones." Again, this is true for human computers only, not digital ones (ironically, the digital processor "compare" operation is really just an application of the same "subtract" circuitry).

Okay, so let's think about applying these principles to find the cognitively-justified best tabletop resolution algorithm. Applying principle #3 means that we'd generally prefer dealing with smaller numbers rather than larger. Before considering anything else, it's clear that it will be hardest for people to mentally operate in a d% percentile system, easier in a d20-scaled system, and easier still on a d6-scaled system. We should pick the easiest of these that gives the fidelity necessary to our simulation, and the d20-scale does seem like a nice medium.

We can also apply principles #2 and #3 to discard a key change brought about to D&D in the 3rd Edition: Ascending AC numbers. While it has its proponents (and is of course mathematically equivalent to all the other 32 permutations of the core mechanic inequality), it forces us at the end of our algorithm to run a comparison against a relatively large, and frequently odd, number, such as AC15, or AC27. By using instead descending ACs, they will always be a single digit (and therefore easier to manipulate according to finding #3), and we'll also see below that we can arrange a rule such that the final comparison is always run against a fixed, round number (and therefore preferred according to principle #2 as well).

Applying principle #1 indicates that we'd prefer to have all of our operations be additions, and do away with any subtractions (as in the THACO system). Returning to our 32 different options for presenting the basic resolution inequality, this is easily accomplished: simply add back all the terms on the right-hand side of the inequality, and all those terms become simple additions on the left. Having done this, we'll see that we're left with a nice round number to compare that addition to (fortuitously complying with principle #2, as mentioned above). We'll call this the "Target 20" algorithm:

TARGET 20 ALGORITHM: d20 + level + AC + mods ≥ 20

Now, you may have guessed where I was going with this if you'd read previous blog entries of mine supporting the idea. While never presented this way in TSR/WOTC core rulebooks, I'm quite confident that this is the most mentally efficient representation of the core d20-based resolution mechanic: Add d20, your fighter level, your opponent's single-digit descending AC, and miscellaneous bonuses; a number equal to or greater than 20 then indicates a "hit". It satisfies all of our 3 psychologically-verified guiding principles: (1) additions are easier than subtractions, (2) round numbers easier to compare than odd ones, and (3) small numbers easier to manipulate than large ones (particularly in the form of single-digit, descending ACs).

Like a lot of things in our hobby, the Original D&D rule was pretty close to optimal, but not quite perfect in this sense. If I won the lottery it might be interesting to definitively prove which method is best by running a series of psychological experiments; but since the result just follows from already-proven principles, I'd also want to set up a betting pool and recoup some of my money from the WOTC chief designers of the last several years.

## Tuesday, June 30, 2009

### The Golden Rule

Comments on the last post made me once again recall what I consider to be the most important passage in all of Gygax's writings on D&D. I use the following as my "golden rule" when thinking about game design for D&D:

ADVANCED DUNGEONS & DRAGONS is first and foremost a game for the fun and enjoyment of those who seek to use imagination and creativity. This is not to say that where it does not interfere with the flow of the game that the highest degree of realism hasn't been attempted, but neither is a serious approach to play discouraged.
- DMG p. 9: "The Game: Approaches to Playing Dungeons & Dragons"

Now, in the interest of being as clear as possible, allow me to unpack the latter two clauses and clean up the double negatives. If we do so, we read this:

(1) The highest degree of realism has been attempted (so long as it does not interfere with the flow of the game).

Again, the double-negatives make the slightly hard to parse on first viewing. In fact, we do seek the highest degree of realism -- claims that D&D has "never been realistic in any way" are totally false. Purely abstract systems are not of interest to us. However, if a conflict arises, then what must take precedence? Definitely, the flow of the game. Both elegant gamesmanship and realistic modelling, working in synergy, are the zenith of game design; but if those goals come into conflict, then gamesmanship must clearly, (narrowly) win out.

(2) A serious approach to play is encouraged.

We can allow ourselves to be serious about our gaming. Claims that "you're thinking too hard about fantasy" can generally be ignored as meaningless. And at the same time, if some of our friends are most interested in the fantastical, phantasmagoric, and even comical elements of our gaming, then that should be seriously respected, as well.

## Saturday, June 27, 2009

### Games-Within-Games

Here's an important aspect of early D&D I've been meditating on lately: the propensity for it to be an ongoing construction of games-within-games. Let's consider a few exemplary examples that spring to mind, starting with D&D and some of my most-favorite computer games:

(1) Dungeons & Dragons. In some sense, OD&D can itself be thought of as the “discovery” that the CHAINMAIL rules contained an even more interesting sub-game with its fantasy combat at the man-to-man scale (not to mention its even more refined system for jousting competitions). In the initial “White Books” you had both the standard dungeon exploration, as well as separate and distinct rules for large-scale wilderness exploration, castle-building, aerial combat, and ship-to-ship naval engagements.

What do I consider some of my most memorable D&D adventures? How about module X10, with its unique strategic-level world-warfare game (in parallel with PC-based diplomacy/adventure scenarios – including possible sidetracks to other X-series modules). Or M5, with a points-based diplomacy roleplay between imperial powers at the adventure's climax. Or even module S3, with its special system for trying to manipulate high-tech artifacts (among other things).

(2) Sid Meier's Pirates! Man, did I play a lot of this game on my cousin's Commodore 64 one summer. In some sense I consider it to be the near-perfect game – and, a lot of my design efforts wind up looking like attempts at replicating this classic. One of the strengths is that it has a completely different sub-game for each skill you might perform in your career as a privateer in the Carribean. Strategic sail navigation, taking a sun-sighting, fighting by cannons, personal swordplay on the deck, invading towns, choosing crew and cargoes, puzzling over map fragments, and wooing the daughters of prominent mayors, are all simulated in distinct sub-games. And almost all of them are both flat-out wonderful, and interface perfectly with all the rest (to the extent that only at this late date can I recognize them as sub-games at all).

(3) Mechwarrior. The original Mechwarrior was another game I played and re-played a whole lot of times. It's the first game I played that had both (a) “sandbox” play, and (b) “plot” based threads. The “sandbox” allowed you to progress as a mercenary captain, taking randomly-generated combat missions, improving your team and equipment over time. The “plot” (for lack of a better word) allowed you to follow up on clues that you were the member of a deposed royal family, and potentially win back your family's home. Some great (and dare I say Gygaxian) aspects of this: (1) you could play the mercenary sandbox indefinitely, (2) it was actually fairly hard to discover that there was a “plot” based mystery to follow up on in the first place, and (3) you still had to do some random mercenary missions in order to build up the strike team you needed at the end of the plotted scenarios. The exact time and sequence of events is impossible to predict in a game of Mechwarrior.

Now, some of this should be well-known to players of current computer game “sandbox” designs (Grand Theft Auto, anyone?), but since I don't play modern consoles, I can't comment directly on those. The thing I want to emphasize is that we don't lose the willingness to allow games-within-games in our classic tabletop RPGs.

Consider a few other examples from TSR/WOTC. In the old Star Frontiers Knight Hawks space combat game (by Doug Niles, who deserves his own blog acclaim), there was a brilliant scaling rule: for 15+ ships, use the coarse, Basic rules for the game; for 5-14 ships, use the more detailed Advanced rules; for 2-4 ships, use the Advanced rules with the individual characters' piloting & gunnery skills detailed. In the more recent d20-based Star Wars game, the spaceship rules were entirely done by analogy to the stock character-to-character system – which I was rather appalled to see when I read it.

Post-2000, there's been a bit of an over-reaction by my left-brained brothers and sisters, often times feeling that all activities in a particular game need to be abstracted out into one single universal mechanic. While this might be nice in theory, in practice I consider it be an abject failure (see the Star Wars example above). Even AD&D is not immune to criticism – when it converted overland movement rates from hexes to miles-per-day (so as to be usable with any campaign map scale; compare DMG p. 58 to OD&D Vol. 3, p. 16), it should have been emphasized that each DM really needed to manipulate those numbers and turn them back into spaces-per-turn on their personal map scale. Unfortunately, it did not. Here we see how frequently the attempt at abstraction interrupts the gamesmanship that we need at any scale of action.

Hence we have a few criticisms of the current branding of D&D: Action at different scales should have different mechanics that support the distinct flavor appropriate to each. Likewise, character classes that represent very different approaches to adventuring (magic vs. martial arts) should have different mechanics supporting each. We lose a lot when the game is reduced to a single kind of action scale (6-second moves on 5-ft squares), and the willingness to include sub- and super-games is prohibited (such as castle-building, tactical mass warfare, etc.) And, we have even more reason to avoid fetishizing character development, because we have to be willing to lose those characters abruptly if we play out an encounter at a larger scale (see 3E's Tome of Battle for the mangled result of being unwilling to allow for this).

Much of the addictive beauty of the original D&D game comes specifically from its flexibility as a model of developing games-within-games, both above and below the “normal” scale of action. It's a more interesting and more challenging enterprise than writing either "story" or "sourcebook" supplements, which add nothing concrete to our gameplay. But likewise, we should avoid being dogmatic, and try to engage our expansion systems only when it makes sense to do so (perhaps taking Doug Niles' SFKH as a canonical, concise example).

## Monday, June 15, 2009

### Defending D&D?

I keep wanting to make a connection between some defensible "essential properties" of D&D, and established legal protections for food products such as Chocolate, Champagne, Gruyere cheese.

For each of these food products (see Wikipedia), there were companies that would have increased sales and made more money, if they could have labeled their products with these names (and of course, they desired to do so). However, trade groups did manage to defend certain definitions of the products and prohibit other usages.

Most of these defenses have been seen in the form of legal restrictions in the EU. However, you've got at least one case in the US in 2007 where companies wanted to replace cocoa butter with hydrogenated vegetable oil and still label the product as "chocolate", which the FDA shot down.

I like the basic idea of that, although in each case it's a legal construct, and it's hard to see where we could take that with the D&D trademark still currently held by WOTC/Hasbro.

(This post was originally a comment of mine on James Maliszewski's Grognardia blog.)

## Thursday, June 11, 2009

### OED: Falling

There's just one more thing I realized I had to add to the OED, and that's a rule for falling:

Falling: Assess falling damage at 1d6 per 10 feet fallen (linearly). This assumes a fall onto earth or wood; decrease damage for yielding surfaces (water, snow, mud), and increase damage for very hard ones (stone, metal, etc.)

Falling has an extremely weird pedigree in D&D, and I could write at length just on that (in fact, here it comes...). Consider OD&D – Where are the falling rules located? Only in the naval combat section (for being pushed off the deck of a ship; also in passing in Vol. III, p. 5 *). And what is the rule? 1d6 damage per 10' fallen – but with a saving throw, generating only a 1-in-6 chance per 10' of taking any damage at all. For example, a 20' fall has just a 2-in-6 chance to fail the save (4-in-6 success) - and thus, two-thirds of the time, will deliver no damage whatsoever!

The subject of falling is mentioned in AD&D's PHB in only the most cursory fashion: “It is probable that your referee will simply use a hit points damage computation based on 1d6 for each 10' of distance fallen to a maximum of 20d6...” (p. 105) A pair of Dragon magazine articles later assert that this damage should be assessed cumulatively (i.e., 10'=1d6, 20'=3d6, 30'=6d6, etc.) – this being a very short blurb by Gygax in issue #69 (as part of his thief-acrobat presentation, later reprinted in Unearthed Arcana), and then a full-page article by Frank Mentzer in issue #70 (asserting a Gygax claim that the original PHB language was a typographical error; however, this does not agree with other Gygax works such as module G2).

A somewhat later issue of the Dragon (#88) had what I consider to be one of the most inspired and challenging presentations for that era. That issue carried the article “Physics and falling damage” by Arn Ashleigh Parker, wherein a “proper” falling damage system was deduced from rigorous consultation to physics formulas, gravity constants, advanced algebra, wind speed, and reference to texts on skydiving (the result being quasi-similar to the original 1d6/10', with more damage assessed earlier on). And this article came as part of a debate, with reference to its own rebuttal article in the same issue by Steven Winter, “Kinetic energy is the key”, which used other physics concepts to argue precisely for the original linearly-assessed 1d6/10' rule. Imagine that happening in Dragon today!

In some circles, the 1d6-per-10' rule was commonly ridiculed (ignoring the cumulative revision) as permitting high-level fighters to leap off 100' cliffs without much fearing for their lives. There is some reason to this, in that fighter hit dice swelled up to d10, and Constitution bonus up to +4/die, while falling damage remained the same 1d6 per level over time. However, I'm convinced that the reaction to this produced one of the most atrocious disfigurements of the system in 3E: the “Massive Damage” rule, whereby a save-vs-death was called for when any damage amount hit the magic number of 50. Most players are under the impression that this was an optional variant rule, but in 3E, it was not.

For many years I was using Gygax's cumulative system for falling damage, feeling indeed that falls should be more perilous, and I also applied the idea to other environmental factors (such as heat, cold, thirst, and starvation). In general, I felt that if higher-level hit points represented less physical stamina and more “dodging/fortune-type” factors, then they should be devalued in the context of an unavoidable fall. However, two problems with that have occurred to me recently. First, there seems little justification that someone able to dodge a monstrous blow could not also be able to roll/spring/cover their head properly to avoid the worst effects of a great fall (or simply land in a lucky spot). Second, when I looked in the DMG to compute exactly what percentage of hit points were “fortune” at any level, I was dismayed to find (on p. 82) that Gygax had stipulated a system wherein the raw physical hit points grew at precisely a constant rate every level (before abruptly ending at level 7). If this were the case, then even under my former assumption, falling damage should increase only linearly through level 7 (at least).

So now, here I am back today, opting to assess damage at the old standard of 1d6 per 10' fallen. (Perhaps if I were playing 3E I would increase it to a base 1d10 per 10'.) I'm not going to use the save from OD&D because (a) it's simply an unnecessary complication, and (b) it makes too many 20' or 30' falls entirely without injury, which really is silly. It's probably a reasonable amount of damage if most hit dice are still d6 themselves (Fighters d8, maximum Con bonus +2), and surfaces like hard, jagged stone can boost this by +1 or +2 points per die. Other environmental factors will probably also be assessed linearly from now on. We shall see.

* Edit 11/23/11: I just learned of another place in OD&D that I had overlooked: in the Aerial Combat section. "Crash -- for every 1" of height a rider must throw one six-sided die for damage occurring from the crash, i.e. a crash from 12" means twelve dice must be rolled and their total scored as points of damage incurred by the creature's rider." [Vol-3, p. 27] Thanks, Grognardia!

## Monday, June 8, 2009

### OED: Spell Changes

In addition to the section on PC Generation, the OED v0.4 rules also added a section on Spell Changes, in 3 parts. In particular:

Sleep: Roll 1d6+1 for total hit dice affected (no figure over 3HD). Duration is 12 turns; slapping/shaking awakens 2-in-6 per round.

You'll see a lengthy analysis arriving at this a few posts back. I made the die roll 1d6+1 for elegance sake (it neatly results in exactly 1-3 creatures of 2HD, for example).

Missiles: For missile spells (fireball, lightning bolt), announce a range, and then roll 2d6 over/under for exact location (read lower die, ties indicate on target).

Now we're getting into the material that you might keep unmentioned until a player throws their first fireball and discovers this during play. This is originally an optional rule from Chainmail for catapults/field guns. (The fireball and lightning bolt in those rules, of course, simply reference back to the effect of such catapults/field guns.) Therefore I think it's both legitimate under the original rules, and scratches an itch of mine that the fireball/lightning combo are generally used with suspension-of-disbelief-shattering accuracy.

If there's any question about the rule, it's this: Announce a range to fire the missile-spell (say, 10”). Roll two d6 of different colors (say a red one for “over” distance that comes up 4, and a white one for “under” distance that comes up 2). Apply the result of the lower die (in this example, 2” under the declaration, placing the spell 8” from the caster in the desired direction; if the dice were tied then the shot would be exactly 10” away).

Permanence: Spells under 5th level cannot be permanent. Those without a listed duration fade after d6+6 weeks (such as charms, continual light, etc.)

Another itch of mine being scratched. There's a whole lot of mischief that can be done if you permit low-level spells to be truly, indefinitely, permanent. Charm person allows someone to gain infinite followers over time. Continual light allows those magic-street-lamp cities (yuck). Wizard lock may as well be used by cantankerous wizards on their downtime, locking every door they encounter forever, just to be nasty.

You can also think of this as a generalization of the principle introduced in Supplement I: Greyhawk, where charm spells are given additional saves to break, assessed over some weeks of time. Why not apply the idea equally to other spells where indefinite duration allows silly mischief?

This does, however, still leave the door open to higher-level permanent spells, and we should carefully consider if there are any game-breakers in the bunch. I feel that the 5th-level spells provide in-milieu limitations: wall of stone can be dispelled (so a wizard would prefer to have a real wall constructed) and animate dead has obvious drawbacks (collecting wagonloads of bodies for an undead army invites the wrath of more heroic adventurers). The 6th-level spells need more careful handling: invisible stalkers should get more and more perilous if used in great numbers; geas spells should have some drawbacks or risk if used with abandon (c.f. the works of Vance, for example).

## Thursday, June 4, 2009

### OED: PC Generation

The OED v0.4 rules added a section on PC Generation in 3 parts. The first part says this:

Convention Play: When making a party for a one-off convention-style game, the normal level limits are not good balancing factors. Human characters should be created at +1 level. Wizards are required to have a minimum Intelligence of 10+highest spell level.

I'm thankful that my last convention game threw a high-intensity spotlight on this problem – it was the most troublesome issue I confronted, and I've been grappling with it for weeks, looking for the best solution. (I was working on a 2,000-word essay to explain it, but then I thought better to scrap that.)

Here's the issue: I'm happy to accept the OD&D doctrine that low-level powers can be balanced by high-level limitations, and vice-versa. This system creates “opportunity costs”, where early decisions have continuing repercussions over a lengthy period of time. In 3E, this was thrown out as anathema, and a demand was made that all races/classes be made equal at every possible level.

While not explained in the 3E texts, I now understand why this was done. While the level-limitations (and exponential wizards) are reasonable in a long-running home game, they are useless in a one-off convention game. For example: In my last low-level OD&D convention game, I think all of the wizards chose to be elves (gaining armor & weapon usage at no cost). Meanwhile, in my last high-level AD&D convention game, all of the characters chose to be humans, except for one dwarven thief (thereby sidestepping all level limits).

So now the dilemma is this: Do we re-write the race/class balancing mechanics so they work for any convention game, at any level? (This being the choice made in 3E; fulfilling, perhaps, a failed goal of AD&D). Or do we reserve the extra balancing rules to an appendix, for the special case of convention gaming? Obviously, after much soul-searching, I chose the latter.

Generation Order: Players should take a PC card and fill in the abilities, race, class, alignment, and money/ equipment. Then, the DM takes the card and calculates modifiers, move, AC, attacks, specials, and directs the roll for hit points. Finally, add the character to the DM's summary roster.

This here is just an observation of the most efficient way to administer the from-scratch character creation process. I'm using my pre-printed index cards for PC records. I let the DM do all the secondary calculations, both so that (a) no new player is required to know the number-crunching rules prior to play, and (b) we accomplish a character audit at the same time. Hit points require the Constitution modifier before rolling. I also keep a summary roster with: Player Name, Character Name, Race/Class, Move, AC, and Hit Points (the most important aspect being the reminder to address each player by their character name).

Magic Items: Characters should be checked for magic items at 10% per level. Checks are made by class: Fighters (2 weapons, armor, shield, potion); thieves (2 weapons, armor, ring, potion), or wizards (2 potions, dagger, scroll, ring). Items are +1 or a basic type, chosen by player; for a +2 item, roll again at 1%/level (+10%/level over 10th); for a +3 item roll yet again at 1%/level (no further bonus).

Up until recently, I was using the AD&D DMG Appendix P for higher-level party generation, in particular the assessment for magic items. Unfortunately, I found it very burdensome to mentally track all the different choices and percentages-per-level involved. Instead I thought it would easier to just batch everything up to a straight 10%/level for everything, in a few broad categories (much like the MM tables for “Men”; for NPCs, I would likewise roll at 5%/level). Once again, no table lookups required; we should be able to do this entirely from rote memory.

### OED Update (v0.4)

I've updated the Original Edition Delta house-rules to version 0.4, after incorporating some changes after the last convention game. In particular, I added a “DM's Section” at the end with a few alterations that don't affect the core system. This brings the page count up from 4 to 5; I'm likely to continue printing a 4-panel brochure to give to my players. I'll also post comments from each new section in forthcoming blog entries. (Don't forget that the Open Office ODT file has additional sidebar notes to the main document.)

http://www.superdan.net/oed/

## Wednesday, May 20, 2009

### It's Not Just About "Fun"

Let's say I'm talking to some coworker or new acquaintance about one of my many different endeavors (possibly medieval wargaming, or music, or even mathematics). Maybe we're not quite making a connection about why it's important to me. How can I make them understand why I spend time on these projects? As I struggle for a conclusion, I might say something like, “So yeah, we're having fun”. And the other person will then say, “Oh, all right then”. Apparently, they'll achieve closure from that, and walk away untroubled.

And you know what? I'm trying really hard to stop doing that, because for the most part it's just total bullshit.

I know a lot of us have the same problem. Our art and our gaming are important to us. We feel it in our gut. But when it comes time to explain it, we routinely say “It's just fun”, or “As long as we have fun,” or “The only important thing is having fun”. We wave the word “fun” at the problem of explaining ourselves and assume that it suffices.

But I hereby choose to resist that temptation. Our gaming and our art are so much more important and multifaceted than that! The “fun” explanation is really just a convenient cop-out. It leaves mute the vast majority of our experiences in any of these deeply-felt projects. Like the best literature (or theater or movies or TV), they may be: sad, scary, inspiring, informative, arousing, inflammatory, tragic, dramatic, elegiac... without necessarily being "fun".

You can see one iteration of this in the “AngryMath Manifesto”, on my math blog (over here). Most mathematicians tend to describe their work as “a play of patterns... a wonderful beauty... a crystalline serenity”. But that's not an accurate representation of our actual work in math – it's trouble, it's a problem to be solved, it's a barrier seeking destruction, and it's the jolt of relief and excitement when the light-bulb clicks on.

Consider the experience when I'm playing drums with my garage-punk band Victor Bravo (blog over here). If I'm weak-minded, I might describe the experience as “fun”, but that's not really truthful. It's hard work, and it's pre-show-anxiety, and it's also the overcoming of all that in myself. It's fast and hard-hitting, it's incredibly precise, and yet it's totally chaotic at the same time, too. We're singing songs about people's failings and disgust and destruction – and the heartfelt desire for things to be better. I'm trying to hit, I'm trying to listen, I'm trying to move my wrists and fingers properly, I'm trying to track what instruments are being damaged, and I'm trying to simply breathe properly. People are jumping and dancing and shoving each other in our mosh pit. Sometimes I'm trying to dodge stuff being thrown at us, and occasionally I'm trying to track how badly I'm being damaged (for example). That's many things, but “fun” is probably the weakest, faintest of all approximations of the experience.

Now let's come back to our gaming hobby, which is all of these things all at once. Whether players or DM, when we're at the table, we're trying to: Solve problems, support our teammates emotionally, improvisationally act out our character personalities, remember rules, crunch probabilities in our heads, decide whether to use our resources now or later, gauge risk-versus-reward, and consider a simulation of near-medieval life and technology. We're trying to manage our own emotions and come back from a bad beat or a difficult situation, and find some way to fight on (!) to victory. We're listening and parsing language and narrative descriptions for meaning. It's a puzzle and math and theater and history and a sporting event all at once. I've seen players go directly from sputtering anger to cheering joy at the roll of a single die or the discovery of a puzzle's solution (and vice-versa).

Is all of that “fun”? No, I don't think so. Much of it is heartache and uncertainty and struggle against overwhelming odds while the game is in progress. And that emotional, intellectual test is so very much more than just “fun”.

So, if “fun” is so miserably incomplete, what would a fuller explanation look like? Obviously, I can't pretend to think that I have a complete answer. But let's say, just for a moment, that we consider Aristotle's famed analysis of “Tragic Poetry” (and if he's not completely right, we can at least take this as a carefully-considered initial hypothesis). He specifies six components: (1) Plot, (2) Character, (3) Thought, (4) Diction, (5) Melody, and (6) Spectacle. Now, isn't that an almost eerily prescient description of our fantasy role-playing games? (And possibly even moreso, good rock'n'roll?) The Plot is meant to contain “reversals, recognition, and suffering... arousing horror, fear, and pity”, and meant to effect catharsis of same; the Characters are expected to “change from happiness to misery because of some tragic mistake” (see here). Is that not a fair description of our games that have no “win” condition for our avatar-selves, but only, ultimately, ways to lose?

(Now, obviously, there's another volume of Aristotle's analysis lost to us over time; but I think it's rather obvious that our RPGs are more like “Drama” than they are “Comedy”.)

Now think: Where is “fun” in this analysis? Has it been overlooked? Is it fundamentally unnecessary? Is it implied by the last and least-important item of “Spectacle”? And are the other rewards from our dramas, from our own Tragic Poetry, not immensely deeper than just “fun”? Let us be courageous and assert all of these deeper aspects, together, and not be satisfied with talking about the merely consolatory notion, which is to say, “fun”.