Friday, January 19, 2018

Races and Rations

Real-world spreads suitable for various RPG races on the go:

Monday, January 15, 2018

Spell Areas on a Grid in the d20 System

In AD&D 1st and 2nd Edition, miniatures rules were optional or even vestigial. Gygax wrote, “I don't usually employ miniatures in my RPG play. We ceased that when we moved from CHAINMAIL Fantasy to D&D” (link).

With D&D 3rd Edition and the d20 System, the new designers worked to make a closer connection with miniature play on a grid (and collection of said miniatures). However, in its first appearance (2000), there were no hard-and-fast rules for such things as measuring distances or placing spell areas on the grid. There is a section in the DMG on “Using Miniatures and Grids” (p. 67-69), but it counsels, “Realize ahead of time that you will have to make ad hoc rulings when applying areas onto the grid.” None of the guidelines there appear in the 3.0 PHB or the Open-Gaming SRD core rules document. (In fact, the text suggestions and illustrations are at many points contradictory.)

These rules became more solidified in the D&D 3.5 Revision, the SRD, and the later Pathfinder game. A first formalization was, “The point of origin of a spell is always a grid intersection.” This was suggested in the 3.0 DMG, but appeared nowhere in the 3.0 PHB or SRD, and was contradicted in the PHB illustration for the meteor swarm spell, for example. A second formalization was, “When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on.” Note that this rule appeared nowhere in the 3.0 text, and the text that does exist subtly contradicts it (see: “majority of a grid square” rule, DMG p. 69; and do the integral calculus).

In the somewhat ambiguous era of 3.0, this author wrote an essay on the different possible interpretations at the time, and put forward three different options to make the system well-defined.  With greater perspective, it is now easier to interpret the 3rd Edition designers’ intent along the lines of the 3.5 rules (which do in fact match the 3.0 DMG spell illustrations, if not the text). While this authors’ graphics for spell templates proved to be quite popular (continuously the top download on the Superdan.net site through 2017!), it seems due time to make them more concise and easier to locate.

Area Accounting

Below is an accounting, for both 3.0 and 3.5, of how many times each of the areas is referenced in the given spell listings. In theory, this highlights which areas would be the most used, necessary, and recommended for having a physical template.


Coloration indicates inclusion in the new document: Green items are included at scale for printing; Yellow included but cannot be at tabletop scale; Red are excluded from the document. Generally, 3.5 reduced variation in its areas: The one-off types in 3.0 (burning hands and meteor swarm) are removed in 3.5. Whereas 3.0 used circles of any radius 5 to 40 feet freely, 3.5 mostly only uses 10, 20, and 40 feet. The variable-range, triangular-style cones in 3.0 were replaced by fixed-range quarter-circle cones in 3.5.

Another important category is not included above: the many conjuration-type spells (such as summon monster) which have a restriction like, “no two of which can be more than 30 ft. apart”. Now, this is not exactly the same as a 30-foot circle, but it’s very close (we can place 3 creatures each 30 feet apart, and require a 35-foot radius circle to enclose them all). There are 44 such spells in 3.0, and 58 such spells in 3.5. So this would suggest that one should have a 30-ft circle on hand for such castings.

Large-Scale Implications

One may note that the implication of the 1-2-1-2 diagonal metric is that for any quarter-circle, the far edge gets shorter by one box for every 2 steps taken – in different directions on each side of the diagonal line itself. This means that in the limit, normalizing for scale, our circles really look like octagons on the grid. Below is an example for a 100-ft radius circle (center and edge only shown) as per this rule. However, this is a larger radius circle than any actually specified in the game, so this behavior will usually not be apparent to players.


Other Options

Disclosure: The d20 System rules provided an enticing mathematical subject of investigation. That said, I haven’t actually played a d20 System game, or use these rules on a grid, in many years. Generally I play classic D&D where miniature usage is relatively rare, and when it does happen, the movement rules are very rough and casual (I may let people count each diagonal as “one”, or else hand out a ruler, depending on mood).

Likewise, for spell-effect areas, I wouldn’t actually use grid templates on paper, as they seem too burdensome, fussy, and difficult to place with miniatures in the way. What I have used in the past are either an ink-pen compass, or a set of brass rings of appropriate sizes, which I found to be much easier to use.

Brass ring

Ink compass

Links

Click the link below to access the document on revised spell areas on a grid for the d20 System.


Thursday, January 11, 2018

Insanity Cards Crowd Sale

I'm incredibly fortunate that my good friend Paul Siegel is also one of the finest GM's and game designers that I've ever had the opportunity with whom to game. See here at Paul's Gameblog for some of his writings (which he's massively ramped of late, I might note). He's also the designer of the OED Deck of Spells, compatible with the OED rules Book of Spells (see sidebar).

Now, his latest production in that vein is a work called Insanity Cards. This is a variant add-on to any game that calls out for a Sanity mechanic: I've seen it used in D&D, Call of Cthulhu, Savage Worlds, etc. It's a pretty nifty mechanic: the basic idea is several "suits" of insanities, and as a player stacks more cards on a given suit, they take more aspects of a given type of insanity. This gives players a little bit of agency over exactly when and in what fashion they go insane. But insane they go. This does warm my heart as a pretty good middle ground.

The other thing Paul is testing out is a Crowd-based print run program on The Game Crafter, which he uses for production. The idea is something of a reverse Kickstarter: the product is already completely designed, extensively playtested, and available for purchase. The only remaining variable is: the more people who can commit to the initial print run, the more the price goes down. Sounds like win-win to me; in my own mind, this solves a lot of the conceptual problems and risk around crowdfunding projects. In fact, I'm rather eagerly looking to see how this works, and may release products of my own the same way in the future (whereas I've scrupulously avoided crowdfunding products to date).

Check it out at the link below. Complete rules are in a free document at the bottom of the page. I believe the Crowd Sale program ends this Sunday, Jan-14 (end of day). Consider telling us how you like them in comments below!


Monday, January 8, 2018

On Support and Upkeep

Let's look at some old-school rules regarding PC support and upkeep expenses.

Original D&D

Gygax in Vol-3 says this (p. 24):
Player/Characters must pay Gold Pieces equal to 1% of their experience points for support and upkeep, until such time as they build a stronghold. If the stronghold is in a wilderness area all support and upkeep costs then cease, but if it is in a village or town not controlled by the player/character then support and upkeep payments must continue.
Here we have a fairly simple rule to simulate cost-of-living expenses for the presumably high-living adventurer; including a built-in incentive for one to build a stronghold at the topmost levels. The rate of the expense is not explicated, but we can assume it to be monthly, as it is in both the AD&D DMG and the Dalluhn manuscript (the early draft for OD&D; see the post on the OD&D boards by user aldarron here). One obvious, small gap with this rule: a 1st-level adventurer starts with 0 XP and therefore pays zero upkeep so long as they stay that way.

AD&D 1st Edition

Gygax in the 1E AD&D DMG changes the rule to this instead:
Each player character will automatically expend not less than 100 gold pieces per level of experience per month.  This  is simply support, upkeep, equipment, and entertainment expense. These costs are to be deducted by the Dungeon Master automatically, and any further spending by the PC is to be added to these costs. Such expense  is  justified by the "fact" that adventurers are a  free-wheeling and high-living lot...
The expense calculation is greatly simplified (a linear multiplier by level), and in so doing, enormously reduced in the long run (i.e., after 8th level). The other detail is that the saving from having a stronghold seems to be removed; the passage goes on to establish a 1% stronghold value cost per month, in addition to the preceding cost.

AD&D 2nd Edition

Dave Cook in the 2E AD&D DMG adjusted the rule to give players a choice of living conditions:


Even though this choice is given, as is the idiom for 2E, there are no specific in-game results of this decision; only some vague role-playing suggestions:
"The only direct game effect of living conditions is the expense involved, but living conditions can also determine some role-playing events and conditions in your game. Your player characters' lifestyles even can be used as a starting point for many different types of adventures."

D&D 3rd Edition

The 3E D&D DMG has a "Variant: Upkeep" in a sidebar (p. 142 of my copy), much in the spirit of the 2E rule. Here the options expand to 6 categories, and again, some soft role-playing suggestions attached to each are given, but no hard-and-fast rules. One change is that all of the category expenses are fixed values, including the topmost ones, such that none of them scale by level. The categories in question are: Self-Sufficient (2 gp/month), Meager (5 gp), Poor (12 gp), Common (45 gp), Good (100 gp), Extravagant (200 gp).


Basic D&D

To my knowledge, no version of Basic D&D ever included a rule of this sort. Searching Holmes Basic, Moldvay B/X, Mentzer BECMI, and the Allston Cyclopedia, I was unable to find any reference to "expense", "upkeep", or "support" in this context.

Conclusions

I think it reasonable to have some (simple) rule for simulating mundane cost-of-living expenses to the resting adventurer. I am really not fond of the 2E/3E expression of a choice with no real in-game ramifications. One way of resolving this would be to draft a more full-fledged set of rules with some kind of concrete results from that choice -- like modifiers to abilities, checks, hit points, reaction rolls, different encounter tables, etc. (Somewhat in the vein of the infamous "carousing" rules.) Another path would be to say we're not really that interested in mundane details, and just strike out the whole system in favor of an earlier, simpler, choice-less accounting.

One thing that's interesting to note is that -- once again -- if we convert the OD&D rule to a silver standard, and assume 1 sp = 1 groat (i.e., 1/3 of a shilling), then the results are somewhat surpringly more in line with reality than we first might guess. Check the following table:


Example expenses are taken by looking at the Medieval Sourcebook: Medieval Prices (currently here). They actually track quite well, as around Name level the expense resembles that of a Baron's estate, etc. The 1E DMG rule would not work this well, as its linearity does not reflect the exponential curve seen in a real economy, such as in the Sourcebook above (but nicely modeled by the OD&D XP charts, fortunately).

So for my OED campaign I expect to use exactly the OD&D rule, as shown here. This removes any choice from the player and abstracts out the expenses to something we don't have to role-play around every month (indeed, it presumes our adventurers are a hard-drinking, hard-experimenting, and/or hard-tithing lot, with more rooms and servants as time goes by). It's reasonable to set a minimum 10 silver/month expense to fill in the gap for low-XP PCs (economically we could defensibly set this at 20 sp/month, but I think the round number is easier to remember and distinguishes from the 2nd level tier). I've also got a rough rule that if the PCs refuse or cannot pay this cost, then a −1 modifier to all ability scores is taken (but I'm open to some more refined, if equivalently simple rule on this score).

Monday, January 1, 2018

Halfling Weapons Through the Ages

Here's a "small" issue that gives me fits any time I try to analyze it. Halfling preferred weapons varied wildly across different editions of D&D. Let's look at that. (Also: Happy birthday to J.R.R. Tolkien, who was born on Jan-3.)

Tolkien

Nonetheless, ease and peace had left this people still curiously tough. They were, if it came to it, difficult to daunt or to kill; and they were, perhaps, so unwearyingly fond of good things not least because they could, when put to it, do without them, and could survive rough handling by grief, foe, or weather in a way that astonished those who did not know them well and looked no further than their bellies and their well-fed faces. Though slow to quarrel, and for sport killing nothing that lived, they were doughty at bay, and at need could still handle arms. They shot well with the bow, for they were keen-eyed and sure at the mark. Not only with bows and arrows. If any Hobbit stooped for a stone, it was well to get quickly under cover, as all trespassing beasts knew very well.
This is the key paragraph on Hobbit martial prowess from the Prologue to the Lord of the Rings ("Concerning Hobbits", 18th paragraph). Interestingly, what takes priority here is first and foremost the bow (and only secondarily stone-throwing). And this is underscored elsewhere, too: the only assertion of historical Hobbit military action outside the Shire emphasizes the same thing (3 paragraphs prior): "To the last battle at Fornost with the Witch-lord of Angmar they sent some bowmen to the aid of the king, or so they maintained, though no tales of Men record it."

In the Lord of the Rings, we see Hobbit archers in action only at the very end. Perhaps more memorable for most readers is the major combat in Chapter 8 of The Hobbit, in which Bilbo, alone and invisible, holds off at least 50 giant spiders by throwing stones at them (one-shot killing at least the first two he targets). Tolkien writes:
Bilbo was a pretty fair shot with a stone, and it did not take him long to find a nice smooth egg-shaped one that fitted his hand cosily. As a boy he used to practise throwing stones at things, until rabbits and squirrels, and even birds, got out of his way as quick as lightning if they saw him stoop; and even grownup he had still spent a deal of his time at quoits, dart-throwing, shooting at the wand, bowls, ninepins and other quiet games of the aiming and throwing sort—indeed he could do lots of things...
So we can forgive most readers if foremost in their minds are the scenes of Hobbit stone-throwing, instead of archery. If you search online, you'll find quite a bit of confusion and debate as to the source, context, and meaning of these passages (e.g., here and here). But if we read carefully in each case, Tolkien indicates that stone-throwing is but one instance of a broad family of similar skills. In the Prologue to Lord of the Rings, it is clear this is due to their being "keen-eyed and sure at the mark". Likewise in The Hobbit it is emphasized at many points that Bilbo has significantly better eyesight than any of the dwarves, e.g., even in the darkness of the Mirkwood ("for by now they knew Bilbo had the sharpest eyes among them", Ch. 8).

We might think that the halflings should therefore get some bonus to finding secret doors or traps or somesuch, but they do not in any edition of D&D; in contrast to elves with their secret-door detection, and dwarves with their stonework traps detection, etc.

Chainmail Fantasy

They can fire a stone as far as an archer shoots, and because of their well known accuracy, for every two halflings firing count three on the Missile Fire table.
Unfortunately, in Chainmail (hobbits/halflings being the very first entry in the list of fantasy creatures), the weapon being described is ambiguous: "fire a stone". This is might be throwing (although "fire" is a slightly unusual verb for that; Tolkien does not use it). Or it could be slings (but there is no reference, statistics, or fire rate given for slings anywhere else in Chainmail). Or it could possibly be crossbows (some crossbows fired stones instead of quarrels). It seems like the only thing it couldn't be is the self-bows highlighted by Tolkien. The three-for-two attack rule means that halflings get a boost on the normally mass-attack Missile Fire table, with any group likely scoring an extra hit as a result.

Original D&D

In Vol-1 (Men & Magic) we see this:
... they will have deadly accuracy with missiles as detailed in CHAINMAIL.
This shares the ambiguity of Chainmail itself. Is this meant to be throwing, slinging, and/or crossbows, as it might be in Chainmail? Could it be a blanket bonus to all things that count as "missiles"? Furthermore, handling the numerical bonus gets murkier as we shift from mass combat to man-to-man. (This was written, presumably, shortly before the "Alternative" combat system using d20's.)

On that point, after Sup-I (Greyhawk), we get a Corrections sheet that says this:
Hobbits:  All hobbits add +3 to hit probabilities when using the sling.
Now we have the first clear specification, giving the preference to slings (and only to slings). The bonus of +3 is both odd and surprisingly hefty (equivalent to the melee attack bonus from 18/75 Strength in these same rules, say). But consider this: Against an opponent in chain mail (AC 5, e.g., most humanoid types), a 1st-level fighter hits on a 14 or more (that is, 7 in 20, or 35%). The chance to get at least one hit from n such attacks is given by P(n) = 1 − (1 − 0.35)^n. For 2 attacks we have P(2) = 0.58, whereas for 3 attacks we have P(3) = 0.73. The difference between these chances is 0.15 = 15%, or precisely 3 pips out of 20; so the +3 attack bonus is a reasonable translation of the advantage given in Chainmail.

AD&D 1st Edition

We will see that across AD&D, different books in the same edition always expressed contradictory ideas about the halfling attack bonus. (Perhaps as one was updated and the other lagged one edition behind?) In the 1E PHB, we see no reference whatsoever to any attack bonus in the section on Halflings (9 across paragraphs on p. 17). But the 1E MM says this in the monster entry for Halflings:
SPECIAL ATTACKS: +3 with bow or sling
This is in the statistical summary block (p. 50), with no further explanation in the text. This seems to be a retention of the +3 bonus from the Greyhawk correction, expanded by Gygax to be more in line with Tolkien's original depiction. The illustration of halflings in this book features one in action with a bow (see top of this article); their weapon frequency table shows 20% with short bows, and 20% with slings. However: we will see that this is effectively the one and only time that a D&D editor thought to call out halfling specialization with the bow. (Side note: at this time Thieves cannot use bows, but in the later Unearthed Arcana they will be given permission to use short bows.)

AD&D 2nd Edition

The 2E PHB says this:
Halflings have a natural talent with slings and thrown weapons. Rock pitching is a favorite sport of many a halfling child. All halflings gain a +1 bonus to their attack rolls when using thrown weapons and slings.
Notice that the preference here is different from the 1E MM, shifting from slings/bows to slings/thrown (emphasizing the final line from Tolkien about stones, and overlooking his thoughts on archery). The bonus is dropped from the hefty +3 to a measly +1 (but see also the B/X rules, which the author Dave Cook worked on previously -- this may be from whence his numerical sensibility for the issue comes from). On the other hand, the 2E MM still says this:
They are very skilled with both the sling and the bow (receiving a +3 bonus on all attack rolls) and use these weapons to great advantage in battle.
Note that the weapons and bonus value both contradict the 2E PHB, but are still in line with the 1E MM (likely a copy-paste mistake from that prior edition).

D&D 3rd Edition

3rd Edition can be credited with somewhat better organization, finally synchronizing the rule between PHB and MM. The 3E PHB says this, and the MM agrees:
+1 racial attack bonus with a thrown weapon: Throwing stones is a universal sport among halflings, and they develop especially good aim.
This is different from the 2E PHB rule, and is the most restrictive version seen in any edition (thrown only, no slings or bows). It's also the most likely interpretation to come from someone who primarily remembers the combat between Bilbo and the Spiders in The Hobbit, say.

D&D 3.5 Edition

From the 3.5 PHB and MM:
+1 racial bonus on attack rolls with thrown weapons and slings.
This backs off the hyper-restrictive rule in 3E, and returns the skill with the sling (so: exactly matches the rule from the 2E PHB).

Basic D&D

Here we check in with the Basic D&D line, which branches off temporally after OD&D, but has its own distinct rule. Holmes Basic says this (p. 7):
Halflings are extremely accurate with missiles and fire any missile at +1.
According to Zenopus Archives, this bonus is exactly what Holmes put in his original manuscript (before an editing pass by Gygax; link), which is totally different from any other ruleset. Compared to the prior OD&D Greyhawk, it seems to massively expand the preferred weapons (from only slings to all missiles), while severely reducing the bonus (from +3 to +1).

What was the motivation for this? Well, let's imagine for a moment that Holmes was looking only at OD&D Vol-1, and didn't have the Greyhawk Correction sheet in sight when he wrote this rule. As we saw above, Vol-1 fails to explicate either the exact weapons or bonus applicable for the present ruleset ("they will have deadly accuracy with missiles as detailed in CHAINMAIL"); even if you looked back in Chainmail the weapons are ambiguous, and the bonus is totally not in terms of the present ruleset. So you might very well interpret "missiles" as "all missiles", and some kind of undefined bonus as +1, in all probability. But perhaps more importantly: if you have expert familiarity with the writings of Tolkien, re: Hobbits being "keen-eyed and sure at the mark" with bows and other weapons, then this might be the most faithful expression of that conceit.

This "any missile at +1" was kept unchanged through all later editions of Basic D&D: it is the same in Moldvay-Cook B/X, Mentzer BXCMI, the Allston Cyclopedia, etc.

Conclusions

Below is a table summarizing the always-changing status of the halfling attack bonus across different editions of D&D:


I also asked the question as a poll on the Facebook 1E AD&D group. Interestingly and unusually, the 1E rule (neither of them) did not come out on top, with a strong preference for the 2E/3.5-style rule highlighting slings and thrown items:


Recall once more that Tolkien himself emphasized use of bows, and secondarily thrown items. In the history of D&D, this latter item seemed to get the focus of attention: an ambiguous rule in Chainmail/Vol-1, with the Sup-I correction translating it to slings, around which the rule orbited from then on (and reflected in the poll results above). Yet amusingly, in some sense the sling was the only missile weapon that Tolkien didn't call out by name as favorable for Hobbits.

At this point in my OED house rules I have the benefit to halflings listed as +2 to all missile attacks (the least-popular option in the poll above, but one). It would seem that if we want to be in any way faithful to Tolkien, we must give the bonus to at least bows and thrown weapons; and then the most concise rule is to just wrap in slings on the side and make it "all missiles". Moreover, if Tolkien attributes this to being "keen-eyed and sure at the mark", then by all rights it should benefit all types of ranged attacks. The value I set at +2 as the mean between the +1 and +3 bonuses seen in various editions above (also: I have a rule-of-thumb that I don't want to deal with any situational modifiers less than +2). However: I've juggled that benefit around in OED I-don't-know-how-many-times, so based on that, it might get adjusted again in the future.

What is your preference for the Halfling attack bonus, in terms of both numerical value and preferred weapon(s)?

Thursday, December 28, 2017

Oscillating Rotation to Order Dice

Diego Maza, et. al.,  Physical Review Letters: An experiment using oscillating rotation to order a container of 25,000 dice, which is seen to be greatly more efficient than tapping or shaking methods.


Hope you have a happy New Year!

APS Physics.

Monday, December 25, 2017

Dice-O-Matic

Have I not posted GamesByEmail's Dice-O-Matic before? Here it is. Merry Christmas.