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Bring out the bardic depth charges!

Over the past few months I have been involved in a roughly fortnightly series of adventures to play-test a new RPG, 13th Age. Since play-testing is over and the product is now at a kind of first draft stage, I thought I’d give my thoughts on the system. My thoughts, however, will be heavily tainted by the experience of the group I am gaming with, which consists of an excellent and energetic bunch of players and a brilliant GM, whose achievements I have noted before.

13th Age was co-developed by Rob Heinsoo and Jonathan Tweet, I think, two quite famous figures from both inside and outside of D&D. It was billed to me as old school gaming with indie flair, or something along those lines, and is based extremely loosely on the fundamentals of D&D3.5. The blurb on the website says:

Our goal with 13th Age is to recapture the free-wheeling style of old-school gaming by creating a game with more soul and fewer technical details. …13th Age makes the play group’s campaign the center of attention, with a toolkit of rules that you can pick and choose from based on the kind of game you want to play. The mechanics draw from classic games as well as newer, story-based games.

I’m not really convinced that there is a “free-wheeling style of old-school gaming” but to the extent that “free-wheeling” in gaming can be encouraged by the rule system, I think that 13th Age does a very good job, and I think that its simple and flexible rules do encourage a rough and ready approach to gaming that is more adventurous than one would find in Pathfinder or D&D. On the surface it feels like classic d20 D&D, but in actual play it behaves quite differently, for a variety of reasons. It has some mechanisms in place to enable PCs to step outside their niche using skills, but the skill system itself is very light; it has redesigned all characters along the lines of 4th edition powers, but has included more old-school spell rules as well; and it has incorporated some elements into character creation that make it very easy to generate story arcs and plot-based gaming, but in such a way that they can also be jacked for immediate effect outside of plot arcs. This makes the basic rules very flexible. I’ll summarize some of the key changes here.

Character classes are very “4th Edition”: PCs have powers that operate daily, per battle, or at will. They have recoveries (i.e. healing surges) and feats that can be used to enhance specific powers. Interestingly, AC is determined by class + armour type – specific choice of armour is not relevant, only its weight and the character class. Thus some classes are constrained to operate best in specific armour types. Saves are very 4th Edition: roll over 11 or over 16 to save, with no modifiers. Looking at my character sheet, it’s a 4th Edition PC sitting there looking at me.

Background defines skills: At creation, each PC gets 8 points (or is it 10?) to spend on backgrounds of the PCs choice, which can have a maximum rating of +5. There are no skills in this game, and every time a PC attempts an action that requires a skill check they roll d20, add their level and an appropriate stat bonus. Then, if they can convince the GM that one of their backgrounds is relevant, they can add the rating of their background to the roll. So when we need to track someone, our insane Dwarven axeman uses his Tribal Dwarf background to add 3 to the roll; when we need to investigate insane arcane phenomena, my PC (Raucous Rella the Tiefling Bard) calls on the fact that she is the Reincarnation of a Famous Wizard (+5). For lying, cheating and fast-talking we have Raucous Rella’s Wandering Troupe (+5); for stealth we have the halfling’s … halfling-i-ness. And so on. If you can convince the GM that it applies, you get the bonus. This means that instead of having a wide range of specifically applicable skills, the character sheet contains a couple of lines for backgrounds, and that’s that.

Icons and Relationships: Perhaps in something of a nod to Japanese gaming (whether they know it or not), the creators have included a section in the rules for the relationship between the PCs and a set of 12 (I think) powerful figures that vie for supremacy in the world of the 13th Age. These “Icons” are not necessarily gods, but they have great status and power and their machinations in the world play an important role in shaping the destiny of nations. The PCs can have positive, negative or conflicted relationships with icons, and can use these relationships as resources in-game. These relationships may thus play the role simply of contacts or social tools, or they can be hooks and levers to get PCs into complex campaign stories. Over time relationships can change, of course. So far we have only used a relationship once – the rules for this seem to be quite vague and hard to operationalize, but the Icons’ presence in the world has been crucial to our understanding of power plays going on in the background of a couple of adventures, so make for excellent plot hooks. Perhaps in a way they function as a more accessible and temporally influential form of alighnment.

Characters are Heroic: PCs are intended to start as heroic adventurers, and they gain power rapidly as they increase levels. They also (aside from my bard) start off with a fair amount of power, and are intended to be able as a group to take on fairly challenging opponents. Combat intensifies rapidly, and PCs have lots of ways of doing significant amounts of damage in combat. Our rogue and barbarian, particularly, do ferocious amounts of damage. There are also some cute mechanics involving additional effects on dice rolls – if, for example, Raucous Rella rolls an even number and hits she can give off a battlecry that gives one nearby PC a chance to save against one ongoing effect. These kinds of things make for rich combat decisions and avoid reducing every battle to a chain of hit rolls.

These characteristics in total lead to a fast-paced, flexible and free-flowing gaming experience, where all mechanics are aimed at encouraging PCs to jack their characters to handle the situation, and GMs are encouraged to play to the moment. The system, by being designed for flexibility and speed, encourages esoteric choices, stunts and improvisation. In some areas the system is too vague (particularly with the icons and relationships, which sit there on my character sheet seeming mostly pointless) and when it strays too close to D&D it can be frustrating – using d20s to resolve actions really annoys me because of its unrealistic effects, for example, and my bard being able to cast Charm Person only once a day is a classic piece of Vancianism. But it has just enough extra elements to relieve the game of some of D&D’s more stultifying effects, and not to feel like just another flavour of D&D.

If you’re looking for something that feels close enough to D&D to pick up quickly, but has more flavour and incorporates some of the better ideas from outside the world of D&D, and if you like a game that encourages innovation and fast-paced action through its rules, then this is the game for you. If you’re really wedded to a game without daily powers or skills, or if you need a game that doesn’t contain any elements of story and plot development (even if only coded in as options) then I would avoid it. If you need detailed simulationist rules to float your boat, this is also not the game for you, but otherwise I think it can appeal to most players. I think it might be a system best suited to experienced GMs, because its flexibility raises the risk of GMs walking into big mistakes that can damage adventures or campaigns, but if you’ve enough experience to handle those risks (or haul your arse out of the fire after you make the big mistakes) then I strongly recommend giving this system a go to see how well it supports your creativity. It’s a good effort and well worth a go!

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After taking account of comments here and on the Paizo messageboards, I have adapted my simulation programs to allow for purposive attribute scores, feats and races, and re-analyzed the survival data for a smaller sample of more carefully designed fighters. In this second round of analyses Gruumsh the Bastard doesn’t acquit himself well, but neither do some of the PCs who went against him. This post reports on the updated analyses.

Update (3rd July 2012): In editing my code to incorporate some minor changes, I noticed that I didn’t actually pit 100,000 fighters against 100,000 randomly-generated orcs – I pitted 100,000 fighters against Gruumsh, who only has 6 hit points. Against a full range of Orcs one gets very different results – I will report on this today (3rd July 2012). This post has been edited to remove references to 100,000 randomly-generated orcs.

Introduction

Previous analyses of survival in Pathfinder have relied on randomly generated ability scores assigned in order, and have not incorporated feats, race, fighting styles or weapon types. In this post the analyses are updated to allow for a range of basic feats, four races, purposive rather than completely random assignment of ability scores, and three types of fighter: strong, fast and tough. Survival is compared against Gruumsh again, and results analyzed for insights into possible character creation decisions.

Methods

A sample of 100,000 randomly generated fighters were pitted in battle against Gruumsh, who is still not ferocious. The fighters were generated so as to fall into three types, defined by ability scores, armour and weapon types, and feat choices:

  • Strong fighters: strength was determined randomly from a uniform distribution between 13 and 18, and the fighters were equipped with scale mail and a two-handed sword. Human fighters had three feats: power attack, weapon focus and desperate battler. Humans placed their +2 ability score bonus in strength. Non-human fighters dropped power attack
  • Fast fighters: dexterity was determined randomly from a uniform distribution between 13 and 18, and the fighters were equipped with studded leather armour, a heavy wooden shield and a rapier. Human fighters had three feats: improved initiative, dodge and weapon finesse. Non-humans dropped weapon finesse, and humans put their +2 bonus into dexterity.
  • Tough fighters: constitution was determined randomly from a uniform distribution between 13 and 18, and the fighters were equipped with chain shirt, wooden shield and longsword. Human fighters had three feats: toughness, shield focus and weapon focus. Non-humans dropped toughness (because two of the races already had +2 constitution), and humans put their +2 bonus into constitution.

All other physical stats were generated with 3d6, but scores below 9 were reset to 9. Mental stats were generated using 3d6 in order, but nobody cares if their meat shield has read Shakespeare, so the details aren’t reported here. The hapless 100,000 were then thrown against Gruumsh, with the promise that anyone who survived would get to meet Salma Hayek. Needless to say, I lied: for unknown reasons, Hayek only dates bards. All fighters with power attack were assumed to be using it for every strike, and you would too if you met Gruumsh.

Results

After incorporating racial bonuses and feats, and assigning ability scores purposively rather than randomly, overall survival increased significantly: only 20% of the newly trained fighters died. However, variation in survival was significant and depended heavily on race and fighting style. Table 1 shows the mortality rates by race and fighter types.

Table 1: Mortality Rates by Race and Fighter Type
Race Strong Fast Tough
Human 17.1 26.5 0
Dwarf 11.1 21.8 1.1
Elven Ponce 27.3 46.9 16.4
Halfling Loser 21.2 45.3 8.3

From Table 1 it is clear that elves and halflings are not good fighters, and Dwarves are excellent in this particular role. The small difference in mortality between humans and dwarves is probably due to the reduced number of feats that dwarves have relative to humans. In fact, once feats and purposive ability score selection are included in character development, constitution becomes an extremely important score: 0% of fighters with constitution bonuses above 3 died. This is probably because CON bonuses of 3 or more guarantee a fighter cannot be killed in a single blow by an Orc (maximum damage 12) and the increased damage and hit stats of these fighters mean the orc will not survive to deliver a second blow. This is indisputably a good thing.

It is clear from table 1 that the least successful form of fighter is the fast fighter, and indeed some perverse results obtain. Figure 1 shows the mortality rate by dexterity score: mortality increases with increasing dexterity in this dataset. This is probably because higher dexterity scores are more likely in the “fast fighter” choice, and amongst halflings, both of which deliver less damage than other races and class types.

Figure 1: Mortality by dexterity score

A similar perverse result is visible with armour class. Figure 2 shows the relationship between mortality and armour class, which is positive.

Figure 2: Mortality by Armour Class

Again, it is likely that the highest armour class values are only achieved by halflings (who have size bonuses), and higher AC is associated with lower damage and attack values. Note that fast fighters have very high initiative values (up to +9!) but these don’t seem to say the battle: for fighters who start with a minimum of 8 hit points, starting the battle first is less important than being able to hit your opponent and do massive amounts of damage.

Conclusion

Dexterity is useless, and a fighting style based on light armour and fast weapons is a waste of time. As a result, weapon finesse is the ultimate wasted feat: it could have been used to get 3 more hit points, which for a first level fighter guarantees that one strike from an Orc will not be fatal. After incorporating feats, the best option for a first level fighter is to choose toughness, shield focus and weapon focus, and pour as many points as possible into constitution. 17 hit points, chain armour and a shield at first level are vastly more useful than a fancy fighting style and a leather skirt!

In most social democratic countries (that is, the UK, Australia, New Zealand, Canada, Japan, troll-infested Scandinavia and much of Europe), the government provides some state support to the arts and sport, either directly through grants and training or indirectly through subsidies for community participation and activity. Let’s consider a few examples of these from around the world that I know.

The UK

Before the 2008 Beijing Olympics the UK invested heavily in amateur sports that would be represented in the Olympics, and in that year for the first time in a long time its sportspeople performed at a level that one would expect for a country of its size: this was preparation for the UK Olympics of 2012, where it’s expected they’ll do even better and, in a remarkable turnaround, will repeat the 2008 performance of beating Australia in sports we’re usually good at (I think they beat us at swimming in 2008). The UK also famously maintains free access to its public museums, which is a great thing (though my god they are crowded).

Australia

Australia has a long-standing practice of funding sports at many levels, including a cricket academy and soccer academy. State and local governments also maintain a very large number of public sports grounds that see heavy use: this community participation is the main reason Australia has four healthy football codes, one more than the UK and three more than the US. Women’s soccer in Australia is also booming and in fact the main break on its growth was the limited availability of grounds, which put women’s soccer into competition for resources with men’s soccer. Given the nature of a soccer ground, this kind of problem is often only resolved through public funding (to make more park space available). Australia also maintains a very well-organized system of political support for sport, which is manifested through e.g. the martial arts accreditation scheme and state-sponsored inquiries into the management of elite soccer. This sort of stuff is necessary to maintain momentum in the growth of new sports. Australia also maintains a system of grants for artists (the Australia Council) which fund any kind of new art through a supposedly competitive process. In addition to separate funding for the major elite arts (like opera and orchestras), Australia’s most famous landmark building, the Sydney Opera House, was built from public funds. So the arts at many levels are funded well by the state, through our taxes.

Japan

Japan maintains a network of public halls, kominkan, which are available for use for any cultural pursuit: flower-arranging, book groups, role-playing groups, you name it. The Japanese prefectures and city offices also maintain special martial arts buildings (budokan) for the practice of all forms of combat sport – you can book rooms in these halls to practice your own. Sumo is supported through public funding to some extent, I think (a source of much dissatisfaction to many Japanese when they see match-fixing and gambling scandals, and notice that the best-behaved sumo wrestlers are the foreigners!) Japan’s public schools and universities also maintain a heavy level of sports participation through clubs. I’m sure there’s other types of arts and cultural funding over here too, if I care to look.

Of course before the modern state this type of subsidy also existed, in the form of noble or religious patronage, but this subsidy came with the rather sad downside of requiring its recipients to either directly sing the praises of their patrons, or to at least look the other way from their worst flaws. So subsidy is not new, even if it is more systematized and conducted under more complex institutional arrangements in the modern world.

Since the mid-70s, however, the developed world has seen a flowering of cultural activities that were almost exclusively developed in the private sphere and/or through private sector initiative, without a skerrick of direct state subsidy. As a few examples: plane- and train-watching; martial arts; various forms of collecting; computer gaming[1]; lego and meccano; wargaming; and, of course, role-playing[2]. These cultural activities have developed over a long period of entirely private investment and support, in the sense that there was no government support for them as cultural activities either on the corporate side (in setting up companies to sell the activity); the individual side (in turns of subsidization or support for involvement); or the community side (in, e.g. special halls or facilities for them). Indeed, famously, after 9/11 the state intervened actively (though not deliberately) to make plane-spotting a good deal harder than it was.

Would the government have saved us from 4e?

One obvious question that this raises is whether these activities would have been more or less successful, or even different at all, if they had received state support as burgeoning cultural activities. Looking at the history of TSR, for example, it appears to have folded or near-folded several times, and gone through all sorts of weird product-redesign and marketing strategies to save itself (plus there was all that internal nastiness). Would the company’s history, and thus the game’s development trajectory, have been different if in the period from, say, 1972 to 1985 it had been able to receive some small quantity of government support as a cultural activity? One argument would be that with “handouts” supporting it the game would have disappeared up its own arsehole, becoming some post-modern weirdness disconnected from its market of gamers; the other is that with a bit of basic financial support the designers would have been freed up to focus on quality product rather than chasing the next bonanza, or at least able to spend a few years producing a coherent game system without worrying about matching their production activities to whatever marketing scheme they thought would save the company. I guess this argument comes down to one about industrial policy (should your government pick winners like Japan and the USA do, or should it foster competitiveness like Australia and New Zealand do). But I think we can boil this issue down to one simple question: would TSR have needed to make 4th Edition if they were receiving a government subsidy[3]?

What sort of subsidies would be appropriate?

Taking as read that social democratic societies will continue this practice of funding cultural and sporting activities, what sorts of things would be suited to RPGs if they were included under the rubric of “cultural activity”? Here are a few things I’ve thought of that I think actually would help to make gaming more widespread, more enjoyable, and perhaps more diverse:

  • Sponsorship of conventions: this would enable the conventions to be held in better locations, to have budgeted conference dinners, prizes, and possibly pay for attendance by renowned designers or GMs. It would also enable the game to spread outside of its heartland areas a little.
  • Recognition of some games as cultural icons, and their preservation either in print or digitally for common use: for example, the UK government might declare Warhammer Fantasy Roleplay 2 an iconic game and provide funds to maintain it in print or in an online archive, thus ensuring that it didn’t disappear. Some games that I think this would be a really good idea for include ICE’s Middle Earth Role-Playing, some form of OD&D, WFRP2, and the original Shadowrun. This wouldn’t preclude the companies from making new versions of these games, but it would mean that games of cultural significance were retained. Look at the effort the OSR puts into producing variants of OD&D as an example of the benefits of retaining these games in print or online.
  • Funding and research support for those elements of, eg, the OSR that are trying to piece together the history of the game, for example through funds to travel and do interviews, support in archiving and organization, and specialist research tasks (including translation)
  • Greater support for academic study of gaming, for example through research grants
  • Support for copyright issues: no gaming company can afford the rights to Harry Potter, I suspect, but a Harry Potter game would really help to spread RPGs around. If the government fronted up the money for the rights, then maybe this could happen – even a flawed Potter game would be a huge benefit to the gaming community, I think. More generally, access to the rights for game settings and art connected to them could help the industry a lot
  • Support for culture-specific games: e.g. the Australian government could hold a contest for development of a game setting that was uniquely Australian in feel, or the US govt could give out grants for the development of culturally-sensitive Native American game supplements
  • Technical support: development of online platforms, more research into the complex probability models used in some games, better editing and book-binding or just provision of support to overcome barriers to entry into new media would be really useful for diversifying the style and types of game and gaming methods
  • Establishment of an independent, high-quality magazine: most gaming magazines are owned by the publishing houses and have been for a long time. A genuinely independent magazine with high production values and an industry- and community-wide remit will never flourish in such a small culture industry, at least not in print, but I think with government subsidies it could and it would be interesting
  • Support for the online community: Prizes for bloggers, financial support for annual physical meet-ups, perhaps technical support in the form of grants to expand the use of the internet for gaming collaboration. Also, money for me.

None of these ideas seem to fundamentally change the basic modern business model of gaming, but I think many of them would help start-up gaming companies with both the cultural background of their activities, and access to some of the technical matters that can help a game work out. Other funding ideas here are largely about supporting the community that the gaming industry is built from, because as a cooperative activity role-playing needs more than just our private money. The RPG hobby only flourishes when individuals have the space, time, money and inclination to come together to make games happen, and it’s (rightly) difficult for private companies like TSR to build this by themselves. It’s easy for us as individuals to put in the basics – our money, our time and our living rooms – but when it comes to the deeper, more complex aspects of maintaining the hobby, perhaps we could do with the same support that recognized cultural activities obtain. Communities may not require support to maintain but it certainly helps, and governments are ideally placed to provide that support.

What do you think?

fn1: I include computer gaming in this list because although in some times and places the computer game companies have received state support as start-ups (e.g. in Australia), this state support is through industry development funds, as a pure business enterprise, not as a cultural activity per se. i.e. you can approach the government of a social democratic nation (in some times and places) and say “I want to start a business selling X” and they’ll fund it even though it’s a kooky hobby; but the same funds don’t seem to have been available for “X” as a cultural activity.

fn2: My reading of the early history of role-playing in the UK suggests a lot of the early games did actually happen in public facilities, like community halls. But a lot of these were church- or school-run, and when I was gaming in London these halls didn’t seem to exist, so I think this aspect of state subsidization of community art in the UK has died off in the past 20 years. I guess this is because public halls have been defunded, and since certain religious issues arose in connection with D&D it’s hard to ask to rent a church hall for an RPG convention.

fn3: And the related question: if you were a benevolent dictator subsidizing TSR, would you have let them?

I have always found it impossible to play magical cyberpunk outside of Shadowrun; I can’t imagine adapting the Shadowrun system to play, say, space opera or high fantasy. Similarly, I can’t imagine playing high fantasy with Traveller rules, or cyberpunk with D&D. Something about these classic games prevents them from being used outside of their genre remit, which is why I don’t naturally turn to D&D Modern, though no doubt it’s perfectly capable of the task. This is probably partly because they’re the games I grew up with, and back in that more innocent age I adhered to the setting constraints they gave me and then when I grew up I couldn’t escape them; but I don’t think I’m alone in this feeling, and I think there’s a more fundamental artistic achievement here than merely capturing the attention of a 13 year old boy when he was vulnerable. Even now I can remember what it was like to open the AD&D Player’s Handbook (I think first edition, with the badly-drawn wizard on the front), and smell the very special smell of the paper, and see that densely written text; read Gygax’s strange (and in many ways wrong) prose, and appreciate the spells and monsters and actions described therein. There’s something very specific and powerful about the way that game is presented, like it contains its own lexicon and cosmology, right there in those 200-odd pages. The style of the game determines what you can do with it, and the presentation of AD&D, along with its gaming style, is so particular that you can’t just strip out the spells and monsters and use the system to run a space opera. I’d wager no one ever has, or if they have, they’ve slowly regressed.

I was reminded of this today by this excellent review of The Name of the Wind and The Children of Hurin, which compares the modern style of one genre novel (The Name of the Wind by Richard Rothfuss) with another, more suited to its task (The Children of Hurin, by Tolkien). The reviewer says about style:

style—the language and form of the novel—is seen as an unimportant adjunct to the “story.” It is not. A bourgeois discursive style constructs a bourgeois world. If it is used to describe a medieval world it necessarily mismatches what it describes, creating a milieu that is only an anachronism, a theme park, or a WoW gaming environment rather than an actual place. This degrades the ability of the book properly to evoke its fictional setting, and therefore denies the book the higher heroic possibilities of its imaginative premise.

I think this applies to RPGs as well. Creating style in RPGs isn’t just about the book (though the AD&D 1st edition is a great example of how this is done) but about how the gaming environment is constructed. Fiddly dice and tabletop mapping (AD&D); fiddly cards and tokens (WFRP3); miniatures and maps (D&D 3rd); starmaps and starships and sparse use of props (Traveller) – these are tools to create an environment that invokes a style. In some games this style is very carefully evocative of the nature of the game, and in others it is sterile (Aria) or actually versatile (Rolemaster/Spacemaster/MERP/Cyberspace). But without creating this specific environment – in the rules, in the aesthetic of the book, in the gaming environment, and in the nature of challenges and dramatic process – the game will fail to impress. Maybe this is why generic systems tend to be less successful than genre systems, and maybe also why some setting-specific games fail (because they don’t match their style to their setting).

The reviewer gives an example of this with Tolkien, contrasting the modern 20th century style of Rothfuss with Tolkien’s genre-specific style:

It’s a book by a man who knew intimately not only the facts and paraphernalia but the mindset, values, and inner life of his relevant historical period—more Dark Age than medieval, this time, but assuredly not modern. The most obvious, although certainly not the only, level on which this registers is that of the style, which actually does approach the classic elevation that Wollheim wrongly identifies in Rothfuss. The Children of Húrin‘s syntax is compact, declarative and unafraid of inversion (“Great was the triumph of Morgoth”). Its vocabulary is almost entirely purged of words not derived from Old English sources: so much so that the occasional Anglo-French term—for instance, the phrase “Petty-dwarf” with its petit-derived qualifier—jars a little. More, it is a prose written with a careful ear for the rhythms of English; a prose with a very satisfying balance of iambic and trochaic pulses, sparingly leavened with unstressed polysyllables (it reads well aloud)

This shows well the numerous tools that a writer can use to invoke effect, beyond just plot and ideas.The task of RPGs isn’t just to provide a distracting few hours of your life (as the reviewer so dismissively characterizes Rothfuss) but to provide a means of escape to another world. You don’t get this by slinging together a skill resolution system and a character sheet. You need a style for your game, a bridge between the imagination of the players and the mechanism by which they play it out interactively. Is this more difficult than constructing a good genre novel? I’m not sure, but I’m fairly confident it’s less financially rewarding. In any case, there’s a lot to be said for the stylistic achievements of the early gaming world, even if the systems themselves were crap and we eventually moved on to better ones. And I think the linked review gives some powerful examples of why these early games held our attention despite their flaws, through the comparison of two fantasy novels.

Incidentally, this review is also an excellent and powerful defense of Tolkien.

Figure 1: Probability Distributions for Three Different Dice Pools (Unadjusted)

Perhaps this post will be useful for any part-time game designers out there. Clayton at Kill It With Fire put up a link to his new retro-clone game, Kill It With Fire, which uses a combination of target DCs and dice pools to resolve skill checks and attacks; basically, the player rolls a number of D6, sums the result, adds bonuses, and then tries to get over a given DC. Dice can be added to the pool for various factors, and there are bonuses that apply based on level, skill training, etc. See, e.g., this paragraph:

Example: Lothar the barbarian is attacking a ghost with his magical sword. The sword’s magic grants an extra die to attacks that targets ghosts. His attack’s description says he uses his prowess trait as a bonus, and he has the ghost cornered, adding a circumstantial bonus that the referee says is worth one more die to the attack roll. So his usual three attack dice and his two bonus dice are rolled, and their result is added to his prowess and number of hit dice to see if he matched the ghost’s defense number.

In a follow-up post, Clayton asks a few questions about the mathematics, and particularly how the probabilities change with dice pools and target DCs. The nub of the matter is in this paragraph:

Actually, what I am concerned about with at the moment is math. To hit a target, I wrote that you add 10+current hit dice (which fluxuate throughout the session)+3d6.
3d6 average out to 10 themself, if I remember my Arcana Unearthed 3.5 info correctly. Meaning you may be rolling well over 20 eight times out ten when you attack. Seems a bit high.

Various suggestions have been given in comments, but since I had half a day free I thought I’d explore this in detail, so I made a spreadsheet that calculates success probabilities for 3, 4 or 5d6 dice pools against a range of target DCs, across a range of bonuses. Here I’ll present the results, and make some comments about dice pools and target numbers. Calculation details are given at the bottom of this post. First a few points about comments in Clayton’s post and the comments:

  1. 3d6 “average out” to 10.5; the most likely values to occur are 10 or 11. By “average out” here we are thinking of the expected value, that is the average value rolled over many rolls. Note that 10.5 is the same as the expected value for 1d20, which has a very different probability distribution to 3d6. By way of comparison, 4d6 average out to 14, and 5d6 to 17.5. This means that, on average, with no bonuses, rolling 3d6 you will beat a difficulty of 10.5. What this actually means in practice, I don’t know.
  2. Contra commenter Joshua, the central tendency doesn’t get stronger as you roll more dice. In fact, the probability of rolling any single value decreases, as the probability spreads over a wide range. I think here Joshua is referencing the Central Limit Theorem, which states that as the number of dice gets larger, the distribution of their sum tends to be normally distributed. This doesn’t mean that the distribution has to get sharper (which would be the requirement for a “stronger” central tendency); what exactly happens depends on the dice you’re rolling. See Figure 1 for the probability distribution of three dice pools without bonuses
  3. I approve of death spirals

In fact, it’s unlikely that these dice pools vary very much from just rolling 2d10. The crucial point is that they have a very different central tendency to 1d20, where any value has a 5% chance of occurring. Because the world is normally distributed, d20 is a terrible, terrible way of resolving probabilities of success in gaming (IMHO). Also, adding dice to a pool widens the range of outcomes, so if you rescale stats and modifiers accordingly, you get a better range of outcomes – 5d6 covers 25 possible values, while 3d6 covers 15 and 2d10 covers 18. But this is just a matter of nuance.

Success Probabilities for Given Bonuses and DCs

Figure 2 shows the probability of success for three different dice pools in the Kill it With Fire system, for a bonus of +8. That is, the PC has a bonus of 8, and the chart shows the probability that PC will be successful for DCs ranging from 8 to 37 (horizontal axis) for the different dice pools.

Figure 2: Success Probabilities for Three Dice Pools

 

As can be seen, with a dice pool of 3d6 and a +8 bonus, the PC has a probability of 50% of beating a target DC of about 19 (actually, from my spreadsheet this is an exact value). At 4d6, this probability becomes 84%, and at 5d6 it is 97%. If we suppose that +8 is about right for a 1st level fighter, then we need to construct our system so that a first level fighter presents a target DC of about 19 if we want a 1st level fighter to hit a 1st level fighter about 50% of the time. A few other points:

  • If you think of bonuses as shifting a PC along the curve for a given dice pool, then a +1 bonus will tend to have a smaller effect as the dice pool increases in size. A +1 increase in the bonus will essentially improve a PCs chances of success by about 12% for a 3d6 dice pool, by 7% for a 4d6 pool, and by about 3% for a 5d6 dice pool
  • On the other hand, increasing the dice pool by 1 has a large effect on success probability. It increases the probability of success for any given DC by between 20 and 30%
  • Furthermore, the largest effect is in the first additional die. For example, the chance of beating a DC of 20 is 37.5% for a 3d6 pool, 76% for a 4d6 pool, and 94% for a 5d6 pool. So the first additional die doubles the chance of success, while the second one increases it by only another 20%.
  •  In terms of odds, the odds ratio for success is 5.3 times higher going from 3d6 to 4d6, and 5 times higher again going from 4d6 to 5d6. For a shift from a bonus of 8 to a bonus of 9, the odds ratio is 1.7.
  • This effect of dice pools is huge for small bonuses – the odds of success in going from 3d6 to 4d6 is 10 times greater for a PC with only a +4
  • Thus, additional dice are a powerful circumstantial modifier, and should be balanced carefully against bonuses

This makes a dice pool mechanism very successful, but I think Clayton might have been thinking to use the dice pool changes more than bonus adjustments to reflect circumstances. My suggestion would be that those additional dice be reserved for extreme circumstances (opponent is stunned, backstabbed, etc.) and smaller bonuses for things like magic weapons.

A Few Thoughts on Dice Pools and Target Number Mechanisms

The main benefit of Dice Pools as far as I can tell is that they give you a normally distributed random variate. Changing the number of dice will significantly increase the chance of success against the same DC, but also makes the random variate more normally distributed. Alternative mechanisms – like changing the dice type – will affect the parameters (mean and variance) describing the approximate normality of the random variate, but they’re in principle no different. So when you compare a dice pool result to a target number you’re not varying, fundamentally, from the method of 3rd edition D&D, all you’re doing is changing the relative balance of outliers and central values. I moved to 2d10 in 3rd Edition D&D to reduce the chance of criticals (and then dropped the second critical resolution roll), but you can do this without changing any of the bonuses and modifiers. Adding flexibility to the dice pool size gives the advantage of large steps in probability of success, but also gives the GM almost infinite flexibility to break the encounter by throwing in an excessive dice pool modification (as Figure 2 shows). In my opinion, D&D 3rd Edition was fundamentally flawed in using d20s, but otherwise the roll-and-beat-the-target mechanism is simple and useful. Changing dice pool sizes simply adds flexibility to the probability distribution underlying this mechanism.

Unless your game system is mainly story-telling, the probability structure of the underlying task resolution mechanism is going to be a strong defining aspect of the mechanics of play. Hopefully if anyone is designing their own system with a dice pool/target mechanism, the material I’ve put here (or the spreadsheet itself) will help them in establishing the parameters of their task resolution mechanism, and avoiding accidental game-breaking mechanics.

Calculation Methods

The formula for the probability of any outcome of a given number of dice is not pretty, but it can be obtained from this website, which gives an analytic solution from The Theory of Gambling and Statistical Logic by Richard A. Epstein, formula 5-14. This is relatively easy to implement in Excel using a visual basic function, or at least it would be if visual basic included a combinatorial function (how useless can a programming language be?) Once I’d figured out the details of that, it was fairly easy to implement the formula in a basic spreadsheet, which anyone who is interested in is welcome to ask me for. The formula can be extended to other dice pools (e.g. d10s, d8s), though my spreadsheet isn’t that flexible (I would have to change a few details of the function, which I’m willing to do if a reader needs it). Just leave a comment here if you want me to send it to you – but note I’ll only send it on one condition: that you have a RPG-related blog. Otherwise, perhaps one day some pesky university student will trick me into handing them the solution to their class assignment.

 

A slightly weird idea I know, but I was struck by it while sitting in a Japanese drinking restaurant (izakaya) attempting to read the fantastical labels on all their Sake bottles. I tried a variation on this theme a while back, when I suggested translations of Osaka place names as inspiration for adventure settings. While western wines tend to be named based on their location (e.g. Jacob’s Creek or Chateau de Whatever), Japanese sake[1] tends to be named after auspicious, fortunate, or bold concepts. Previously on this blog I introduced the infamous suigei, or drunken whale, which was inspiration for a lie but not for a spell; however, many of the names that festoon your average drinking restaurant’s wine shelf would probably pass muster as a spell, ability or card. So, here are a few, taken from the Rakuten sake market. I’ve included some basic D&D stats.

Sound of Snow (Yuki no Oto)

  Class: Druid

 Level: 3

Duration: 1 rd/lvl

Area of Effect: 20′ radius

                   Saving Throw: None

The caster and his or her allies become as silent as gently falling snow; +4 on all Move Silently Checks. This spell is ineffective in areas of strong wind or great heat.

The Wine: Incapable of being mass-produced, this wine retains the elegance and mellowness of handmade sake, combined with a rounded and refreshing taste. It goes well with sashimi, grilled white fish, and delicate-flavoured vegetables.

Region: Akita Prefecture, Northeast Japan.

Favorable Reply (iroyoi henji)

  Class: Cleric

Level: 1

Duration: 1 round

Area of Effect: Caster

Saving Throw: None

With this spell, the caster can ask a minor deity a single yes or no question concerning the action to be taken in the round immediately following the casting of the spell. The minor deity will tell the caster whether or not they are capable of success with the given action, but will give no information as to whether, for example, the caster is embarking on the correct actions necessary to secure this success. The action in question must be describable in terms of a single die roll (e.g. a single attack or skill check), not a general sequence of actions (such as, for example, avoiding the snapping pincers of the giant crabs in the pit while balancing on a narrow log, and grabbing a hanging gem). Mechanically, whether this spell is useful depends on whether the GM usually gives this kind of information away for free. Note also that the deity invoked is a minor deity and cannot answer questions of a difficulty beyond its ken.

The Wine: Made with a special Yamagata yeast that achieves an excellent balance of flavours, this is a wine that is able to be enjoyed with food.

Region: Yamagata

Honorable Blade of Fortune (ofuku masamune)

Class: Paladin

Level: 4

Duration: 1 rd/level

Area of Effect: Caster/sight

Saving Throw: None

The caster summons a holy sword that grants him or her both good fortune and power for the duration of its use. The sword grants its wielder +1 to hit and damage, and is capable of damaging monsters that can only be hit by magic weapons up to +3. Furthermore, when the spell is cast the caster rolls 2d10+wisdom bonus. While the caster is wielding the sword, a single d20 roll can be replaced with the result of this casting roll every round. The caster or any ally can replace their roll with the result of this roll. At the very least, this spell will protect one member of the party per round from a critical fumble; note that if the caster rolls a natural 20, this does not grant critical successes (but it can be used on rolls to determine whether a natural 20 results in critical damage).

The Wine: Brewed from rice cultivated for more than 40 years by the famous Takeuchi family of brewers, in terraced rice paddies on the Sea of Japan coast of Niigata, this wine is a masterpiece imbued with the spirit of the brewer.

Region: Niigata

Hawk’s Courage (takayu)

 Class: Wizard

Level: 2

Duration: 1 rd/lvl

Area of Effect: One person

Saving Throw: None

This spell grants its target both great courage and fine vision. For the duration of the spell the target gains a +2 morale bonus to saving throws vs. fear, becomes immune to fear of heights, and gains a +2 bonus on spot, listen and search checks. Rumour has it that the spell was developed by wizards in the service of certain ancient clans of pirates who ply the skyways over the most forbidding mountain peaks of the realm.

The Wine: The flavour of this wine is a rare and exquisite thing of beauty. Anyone who receives this wine as a gift will surely be profoundly pleased.

Region: Tottori

There are many, many more wines on the Rakuten marketplace – a whole spell book’s worth if you have the skills. And then there is the shochu … want to give it a try?

fn1: which is called nihonshu in Japanese, btw – literally, “Japanese alcohol”

When I played AD&D I think one of the first aspects of its magic system I dropped was the material components. It’s a shame, but they just represented too much of a constraint on what was already a hideously underpowered class (especially at first level). Some of the material components even for first level spells are quite challenging to provide, and they’re consumed in the casting of the spell. Consider, for example, the following spells:

  • Alarm: A tiny bell and a very fine piece of silver wire
  • Armor: A piece of finely cured leather that has been blessed by a priest
  • Color Spray: A pinch each of powder or sand colored red, blue and yellow
  • Dancing Lights: A bit of phosphorus or wychwood, or a glowworm
  • Friends: Chalk, lampblack and vermillion
  • Identify: A pearl worth 100gp and an owl feather soaked in wine
  • Light: A firefly or a piece of phsophorescent moss
  • Protection from Evil: Powdered silver

and so on.  The spells Burning Hands, Detect Magic, Charm Person and Magic Missile require no material components of any kind. These material components are very cool and really add to the romance and style of wizards, but they’re an enormous burden, especially on low level wizards. A first level wizard starts with 20-50 gps, so will not be able to cast Identify and probably can’t afford the ingredients for Protection from Evil, Dancing Lights or Color Spray in most medieval settings. That’s without considering the difficulty of carrying phosphorus, glow-worms and phosphorescent moss. Some of these spells also can’t be cast in the casting time given in their description, because the ingredients need to be steeped, smeared or scattered in a circle. Find Familiar, much more powerful than its 3rd Edition version, requires 1000Gps of herbs and incense. Even Sleep is probably beyond the reach of a lot of wizards, requiring as it does a pinch of sand – sand would have been a rare sight in 12th Century Glastonbury, I’m willing to bet. So here you have a first level wizard with 40 GPs, and before he goes adventuring he needs to gather together a piece of silver wire, several portions of powdered silver, a collection of tiny bells, some phosphorescent moss, some sand and a drop of bitumen (!! for Spider Climb).

One can imagine what happens if the party kills a gnome, who has a small admantite file in his toolkit. The file is worth 50gps and everyone else just wants to sell it, but the Wizard recognizes here an opportunity to make himself self-sufficient in powdered minerals, and snaffles it up. A libertarian party would probably charge him 200gps premium for it[1]. And at higher levels it gets ridiculous, of course:

  • Invisibility: An eyelash encased in gum arabic[2]
  • Melf’s Minute Meteors: nitrite[3], sulphur, pine tar and a (reusable) fine tube of gold worth 1000gps
  • Evard’s Black Tentacles: a piece of tentacle from a giant octopus or squid
  • Feeblemind: a handful of clay, crystal, glass or mineral spheres
  • Chain Lightning: A piece of fur, an amber, glass, or crystal rod, and a small silver pin for each experience level of the wizard

Some of these material components are very very difficult to get hold of. I doubt I could get most of them easily, even living in Tokyo. If one were to rigorously adhere to the spell components rules, every wizard would need the regular services of an alchemist, silversmith, blacksmith, and a couple of other extremely talented craftspeople; the wizard would also need to be very assiduous about cutting up and preserving any roadkill or adventure-kill he or she came across. There’s no doubt that this sort of thing makes these PCs much more interesting, but it also makes them virtually unplayable, because it essentially restricts the number of spells the PC knows in any one day, as well as the number they can cast – effectively it puts a bunch of spells beyond the PC’s reach at any time, while maintaining daily limits on those that the player does have the ability to use. A good example is Identify: a wizard at first level can’t use it, but by second level may be able to afford a pearl of suitable value. They can then cast the spell; but they can only cast it once, on one object, and they can’t cast it in the dungeon because they only know two spells a day and they need Shield and Magic Missile in the dungeon. So the party stumbles upon a ring that may be of great use right there and then, but the wizard can’t cast the spell even though it was a week’s work to find the owl feather and the pearl. So then they have to wait till they leave the dungeon, at which point they have a second item to identify but they can’t do so because they don’t have enough ingredients. Alternatively suppose that the wizard has spent all their treasure on pearls and owl feathers; they can still only cast the spell once today, because they couldn’t memorize more than two spells; but the party is pressed, and has found a magic sword and armour that they really need to use now, in the dungeon. Even though the wizard has spent his last money on two pearls and two owl feathers, he can only identify one item today.

Suppose then, that instead of using the standard approach to magic of AD&D, one introduced a simpler system in which a wizard can cast any spell they know as often as they like, provided they have the material components. This would mean that the wizard would usually have some spells (such as Burning Hands) on rotation, but I don’t see this as a bad thing. A first level wizard with Burning Hands once per round at will can do 1d3+2 hps damage per round on anyone within combat range (save for 1/2). It’s not a game changer; free use of Magic Missile makes a high level wizard pretty scary, doing 5-25 damage per round with no saving throw, but a few tweaks on minor spells (e.g. fixing magic missile at a maximum of two missiles) would easily solve that problem. Alternatively, you could give these spells simple material components: magic missile could require an arrow per missile, for example. Burning hands could require the wizard be carrying a lit flame source, that is extinguished by the spell. This would reduce the spell to the potency of WFRP 3rd Edition, where wizards have basically unlimited spell use but mostly have to use one every other round.

Even for high level spells with simple components, like the Bigby’s Hand spells, this method wouldn’t lead to infinite amounts of spell casting. Bigby’s Hand requires a glove; no one can realistically carry more than, say, 10 gloves in their equipment if they also have to carry: a small bag full of crystal spheres; a collection of test tubes carrying the components for Melf’s Minute Meteors and Invisibility; 8 or 10 small pouches of different powders, nitrites and the like; a sheath or case with several different rods; some vials of acids, pure water, tears, etc; additional pouches carrying fur, bits of leather, feathers and wings; a jar with a pickled piece of a giant octopus tentacle; a small cage of fireflies; a pestle and mortar to crush gems with; a couple of miniature platinum swords; and a collection of iron, silver, and bronze mirrors. Sure, this would make the task of spell-casting a little like a complex system of inventorying, but you could handle it, I’m sure, and if it’s hard for the player imagine how complex it is for the PC! You could also argue that if a Wizard is carrying components for more than, say, 5 spells on their person, they can’t cast a spell every round (they need a round to find the item[4]).

Furthermore, one could introduce different effects for more imaginative components. E.g. Invisibility lasts a round longer if the eyelash is from a thief (handy if you have a thief in the party); the component is never destroyed if the eyelash is from an Invisible Stalker. Water from another plane makes a spell that uses it more powerful, and the effect of spells like Identify is enhanced with more expensive pearls or more esoteric feathers (e.g. from a Sphinx). Expending a magic arrow adds one to the damage of a Magic Missile spell, and so on. You could also rule that every time a wizard is struck in combat one of their more fragile components is damaged or destroyed (randomly determined). It would also make wizards very eager to kill or capture each other, since they can loot their rivals’ components as well as their spell book.

Power limits could be obtained easily by dividing wizards into specialties, so that from first level they are limited only to conjuring or evocation, etc. Many RPGs do this, so that wizards have access to very few spells over their career. This would prevent a single wizard from being able to cast Burning Hands (alteration), Magic Missile (evocation), Charm Person (enchantment), and Chill Touch (Necromancy). I would make the conjuration, divination and abjuration specialties common to all wizards and then force them to choose one of the other four

fn1: libertarian parties probably last as long as the first Cure Light Wounds spell, and then decide socialism is the way to go.

fn2: According to Wikipedia, gum arabic was an extremely valuable export commodity and is an essential ingredient in soft drinks, and the Sudanese president recently implied he could bring down the western world through suspending its export

fn3: I find it hard to believe that nitrite was readily available in the medieval world but nitrates were as saltpeter, again not exactly your common or garden middle-ages corner store product

fn4: This could be a good rule for PCs with more than 5 magic items in general, I think.