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.
Exact numbers: www.superdan.net/download/CompareHD2.pdf
C++ code to generate table: www.superdan.net/download/CompareHD2.cpp
Friday, November 27, 2009
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)?
(C++ code to generate the table above: www.superdan.net/download/CompareHD1.cpp )
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)?
(C++ code to generate the table above: www.superdan.net/download/CompareHD1.cpp )
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!
http://www.lulu.com/content/paperback-book/original-edition-delta-book-of-spells/7871266
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%
- Undead (21) 3.5%
- 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:
Sing it, brother! Of course, this is just prelude to an interesting article about other new developments, highly recommended. Plus, discussion at Slashdot.
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
Solo Thief Adventures
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).
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.
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.
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