## Basics of dice probabilities

26 May, 2009 at 7:32 pm (game design, linkedin, mathematics) (, , )

I’ll write a post or a few about probabilities that involve rolling dice. Those who know mathematics might be more interested in probability theory.

I will assume that all probability distributions are discrete and integer-valued. Trying to apply what I say here to continuous distributions will cause problems or require thinking.

# Probability

Probability measures, or indicates, how certain it is that some event will happen (or has happened, in case of imperfect knowledge). Probability of 1 means that something is certain, while 0 means impossibility. Probability 1/2, or $\frac{1}{2}$, or 50%, or 0.5 or in Finnish notation 0,5 means that something happens half the time (if the event is repeated).

I very much prefer working with fractions as they are exact and, in my opinion, more intuitive, but many people like percents. To convert a fraction into percents simply multiply it by hundred and add the %-sign.

An important axiom of probability is that something always happens. The sum of probabilities of all the specific outcomes is 1. By this I mean that if, say, a die is rolled than it gives one and exactly one result. It doesn’t land sideways. It is not hit by a meteor or eaten by a dog.

## Symmetry

Especially when playing around with dice symmetry plays an important role. Symmetric events have the same probability.

I will assume that all dice are fair; in practice they are not and it doesn’t matter. An n-sided die has n symmetric results. All of them hence have the same probability. Something must always happen, so the sum of the probabilities is 1. It follows that for an n-sided die the probability of getting any result from the set $\{ 1 , 2 , \ldots , n-1 , n \}$ is 1/n, while the probability of getting any other integer is zero.

## Notation

Since writing probability all the time gets boring, I’ll use a shorthand: $P( \text{event} ) = p$, which means the probability that event happens is p. For example: $P(\text{d}8=7 ) = 1/8$ and $P(\text{d}8=-4 ) = 0$.

## or, and, not

Some rules for performing calculations with probabilities are in order. First, a definition: Events are independent when knowing something about one of them gives no knowledge about the others. Dice rolls are, as far as this post is concerned, independent: I roll a d12 and get a 1. This tells me nothing about what the next result will be when I roll that d12.

Take two independent events A and B. Now $P(A \text{ and } B ) = P(A)P(B)$. For example: The probability of rolling 1, 2, 3, 4 or 5 (that is: not 6) with a six-sider is 5/6. If we roll two d6s, what is probability of both of them giving a result less than six? Since separate rolls are independent events, this probability is 5/6 times 5/6, which equals 25/36. This rule applies to any finite number of rolls. As long as they are independent, and means multiplication. The independence is not there for show only: Suppose I roll a singe d4. What is the probability of that die giving result of both 1 and 4 at the same time? Obviously, since a given die only gives one result per roll, the event is impossible and hence has probability zero. Careless use of the “and is multiplication”-rule would give 1/4 times 1/4 equals 1/16, which would be wrong.

Multiplying fractions, in case it is not clear: Supposing a, b, c and d are real numbers, b and d are not zero, then $\frac{a}{b}\text{ times } \frac{c}{d} = \frac{ac}{bd}$.

Take any event. Now $P( \text{not event} ) = 1 - P( \text{event} )$. This is a direct consequence of something always happening. Example: The probability of rolling 6 with a d6 is 1/6, from which it follows that the probability of not rolling a 6, which is the probability of rolling something else than 6, is $1 - 1/6 = 5/6$. Now we have the tools for solving one problems with some history: Roll 4d6. Should you bet on rolling at least one 6? The goal here is to determine $P( \text{at least one is 6})$. Using the law of not this problem is the same as determining the probability of none of the dice showing 6, which is same as all of them giving a result from the set $\{ 1 , 2 , 3, 4, 5 \}$. We already know this probability for a single die: It is 5/6. Since separate rolls are made, the events are independent, and hence by the law of and we can simply multiply 5/6 four times, which means raising it to the fourth power: $(5/6)^4 = (5^4)/(6^4) = 625/1296$, which is slightly less than half. By the principle of not we get that the probability of getting at least one 6 is slightly more than half and should be betted on. By symbols the calculation goes as follows: $P(\text{at least one die gives a six}) = 1-P(\text{none of the dice give a six} =$ $1-P(\text{first die is not six and } \dots \text{ and fourth die is not a six}) =$ $1- (P(\text{first die is not a six}) \times \dots \times P(\text{fourth die is not a six}))$ $= 1 - 625/1296 = 1296/1296 - 625/1296 = (1296-625)/ 1296 =$ $671/1296$, which is greater than 648/1296 = 1/2.

Take two events A and B. The probability of at least one of them happening, by which I mean P(A or B), equals the sum of their probabilities minus the probability of A and B both happening; otherwise  the “and” would be counted twice. So, for any events A and B, $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. An important special case: A single d12 is rolled. What is $P(\text{d}12=7 \text{ or } 9 )$?. Since rolling 7 and 9 are clearly distinct events, the probability of both happening with single die roll is 0 (since they never happen at the same time). Hence $P(\text{d}12=7 \text{ or } 9 ) = P(\text{d}12=7) + P(\text{d}12=9) - 0 = 1/6.$ Another useful application: Roll 2d6. What is the probability that at least one of them shows a 6? This can be formulated in another way: What is the probability of first die showing a 6 or the second die showing a 6? Here the events are independent since two dice are cast. Hence, $P(\text{at least one 6}) = P(\text{first d}6=6 \text{ or second d}6=6) =$ $P(\text{first d}6=6) + P(\text{second d}6=6) - P(\text{first and second d}6=6) =$ $1/6 + 1/6 - P(\text{d}6=6)P(\text{d}6=6) = 2/6 - 1/36 = 11/36$.

# More to come?

If someone finds this useful, please say so. I do not know how good I am at expository text like this and I really don’t know the skill level of my audience, if any. A topic I might handle in the future, if anyone is interested, is how to calculate the distribution of a sum of two arbitrary distributions.

I managed to land a quite demanding job, so frequent updates are somewhat unlikely, at least for some time. I’ll need to do some adjusting.

18 May, 2009 at 4:54 pm (meta) ()

I’m on Facebook. The user interface is very, very bad. Few questions:

Can I add my shared Google reader entries to my profile? What about my blog posts, their titles or something similar? Stumbled things?

Also, if I happen to know you, feel free to add me as a friend. If we have had a discussions via blogs or other means it is quite sufficient for me adding you as a friend.

## Why WordPress?

17 May, 2009 at 2:15 pm (meta) (, , , , , , , , , )

Before starting this blog I investigated the different options there are. Particularly the big three: Blogspot, Livejournal and WordPress. Which one I came to prefer should be obvious. Here’s some reasons, as I know that a few rpg bloggers read my site every now and then. Actually, here are the reasons why I do not use LJ or blogger/blogspot, and consequently the option I ended with was WordPress.

## Livejournal

Livejournal is a huge mess. It  lacks an RSS feed for comments. Hence, it is very difficult to follow discussions. Further, the comment threads tend to collapse due to nested comments and hence become difficult to read; always necessary to expand that or this comment and hope you expanded the right one.

I would not want any readers I might get to experience that nightmare. Hence, no LJ.

## Blogspot and blogger

Google does offer comment feeds (though they tend to be well hidden), which is good. On some themes the comments are separated to a separate comment page, which is frankly idiotic as it separates the discussion. Likewise the necessity of opening a new page to write a comment; not smart. There is also the annoyance of not being able to use blockquotes when commenting, but I don’t think I was aware of that when starting blogging.

In addition there’s the CAPTCHA, which means the distorted texts that one is supposed to understand when posting. They have the problem of being terribly annoying. The problem is further aggravated by the fact that when using OpenID I must suffer through the trouble twice, as the first time I enter the CAPTCHA it is not accepted. Very annoying. This, again, was not a problem when I first started blogging.

Why not simply use Google account when commenting? The primarily problem is that those comments are difficult to trace back to my blog. I’d have to write some signature, which looks and feels spammy, or hope people check out my Google profile and deduce my blog from it. More importantly, I want to know the blogs or website of any who comment on my website.

In summary: Commenting on Blogspot/Blogger is very inconvenient and finding out where the comments come from is also slow, as opposed to automatic on WordPress blogs, where you just click the link that is the commenter’s handle. It can be to a blog or static website or whatever else.

# Truncated feeds

Now that I’m ranting…

I’m not certain of the correct term here, but I mean those feeds that don’t show entire posts, only the first sentence or two or a hand-crafted summary. They are a pain. They force me to open a new tab and read that. Further, I must either wait for the page to load or read other stuff while waiting (which I prefer). Problem: I must keep the article unread in the case of it being of good quality so that I would want to share or star it (in Google reader). Or sometimes I won’t bother, but will rather just read on and forget sharing the truncated stuff. So: Truncated feed is not user-friendly and further might cost you a reader or two. When it is time to prune feeds, those that truncate their content are high on the list of candidates.

By the way: If my blog has truncated feeds, now is exactly the right moment to share the information. I’ll fix it. The feed is supposed to contain entire posts.

I am not exactly sure why people do use truncated feeds. A perversive desire to annoy people? Not likely. Maybe they want people to enter their website? That seems more likely. Maybe there are ads there? Personally, Adblock takes care of those. If I like you and your site, I might turn Adblock off there, but there’s little hope of that as long as I must open pointless tabs to read the posts of yours. Sorry. Want me to read more posts of yours? You might sometimes succeed, but links to former posts are at least as effective a tool and they don’t cause frustration.

If you want me to read your website and whatever goodies are there, here’s an excellent way of accomplishing it: Write a post that I will want to respond to. Also write a post that I will want to link to; that way, the three readers I have are likely to check out what you have there. More importantly, I or my readers will arrive to your website with curiosity or interest, not annoyance.

## Roleplaying in society

11 May, 2009 at 7:13 am (rpg theory)

In this post I’ll argue for three ways in which roleplaying can change society or elements of it. I don’t include crazy fundamentalist Christians or other similar attacks as one of these forces.

To start I need to define roleplaying in the context of this post. Actually, I won’t be doing that; rather, I’m going to say what qualities I require an activity or hobby to have so thay my argument works. Roleplaying fills these criteria, as do other activities. (This is the axiomatic approach used in modern mathematics: Take some phenomenon, gather relevant bits of it as axioms and work with the axioms, hence creating results that are more broadly applicable and often easier to work with.)

So, with that in mind, I say that the essential qualities of roleplaying are

1. That it is social; there are at least two people involved.
2. That it is creative (or artistic, to be more political); roleplaying involves creating and interpreting fictional content.
3. That it is ephemeral; roleplaying happens in the moment and recording and retellings are insufficient at communicating that moment.
4. That it is motivated by the activity itself; it is not presented to an audience distinct from the players; even if audience exists, the purpose of the play is not to entertain them, but rather to play and have good time doing it.

This is not a value statement: I am not trying to say that other things are not really roleplaying. Rather, I am saying that for the purpose of this post those other things are not interesting.

In the book Rules of play Salen and Zimmerman explain how games can be viewed from three different perspectives: As formal systems, as systems of interaction between players or as cultural systems. I am taking the third perspective, here.

# On personal level

Society is composed of people. Roleplaying affects people. Personally, roleplaying has motivated me to research various subjects on some level and had other positive effects that are harder to quantify. I’ve also read stories of people focusing on roleplaying and ignoring their school-going. The lesson to learn is that roleplaying as a hobby can have a profound effect on people. I’m inclined to think the effect is mostly positive, but that there is an effect is hard to disagree with.

(Claims that roleplayers are particularly intelligent or creative or whatever I am deeply suspicious towards.)

# Small groups

For some roleplaying is a family activity. I recall some old school blogger describing the game he (I think a he.) is running for his family. There are plenty of others playing with their kids. In this way roleplaying is as good an activity as any, I think.

Roleplaying games are typically played with friends, in a fairly constant group over long periods of time. If we accept the characterisation of roleplaying as an activity that creates memories of experiences we have not actually had, then by condition 1. (social) in the definition roleplaying creates shared fake experiences. Shared experiences are a significant factor in forming and strengthening friendships. Further, by condition 2. (creative) people express themselves when roleplaying. Hence, fellow players learn something of each other when playing.

It can be seen that roleplaying shares at least two qualities with friendship. A pertinent question is: Are these qualities equivalent to friendship, do they arise from friendship or does friendship arise from them? There are other possible models, like both friendship and these qualities being a consequence of something else, but let us not go there. (I feel this is a distinctly philosophical question. Maybe I’m finally learning how to think like a philosopher; to find questions without trivial answers.) The question regarding the nature of friendship is interesting, but a bit too much for this blog post. Also, I have no answer, expect to say that equivalence is not the case, if only because liking the other person is another quality of friendship and I don’t think shared experiences and knowing the other person necessarily imply liking the other person. So, roleplaying. I’d argue that roleplaying creates reciprocal knowledge about the participants (as opposed to, say, stalking or merely reading someone’s blog) and, well, shared experiences, fake or not, are reciprocal by definition. Reciprocality makes, I think, roleplaying a good supporting activity for friendship. This powerful context can also be misused.

In summary: Roleplaying fairly frequently brings together a group of people and gives them shared experiences, in-jokes (which may or may not involve grand pianos or squirrels) and generally ties them together. Strong small groups are, I think, relevant to the welfare of society as a whole.

# Potential for large-scale change

This is the political part of this post. I have an ideology, though I haven’t found a name for it yet. Hence, take everything I say with a, say, spoonful of salt. That should be enough.

I am talking about roleplaying games as a way of creating and experiencing entertainment, maybe even art, on a group’s own terms. This is distinctly separate from merely consuming what someone else has produced, which characterises such forms of culture and art as movies and music, even books. Particularly, one can’t buy the roleplaying experience, only play and create it oneself.

Of course, much of rpg culture is focused around playing a particular game and buying everything that comes out for that game. Collecting, one might call it. Further, there is the drooling over fancy toys like miniatures, character generation software, 3-d maps constructed from whatever. PDFs with embedded flash videos. (For perspective on these, Michael Brewer’s post is a good one.) To take even more radical stance, even character sheets are unnecessary for roleplaying. Dice, too, as much as it hurts to say so. My point is not that all of these extra toys are somehow bad or evil; they are not and I enjoy rolling dice as much as the next roleplayer. What they do is to hide the fundamentally creative and self-sufficient nature of roleplaying.

Another way in which roleplaying games are potentially powerful is that they give permission to play. In modern world the sheer joy of playing is restricted and seen as childish. Being drunk seems to be the necessary condition for having the permission to play. I am talking about playing with or near other people, here. Computer games are another subject entirely; there you are in a way always isolated from other people, even if playing multiplayer games. Sports is serious business, though spectators can play a bit. Roleplaying games create a fairly secure environment (a group of friends, say) where one can and is expected to play. Larping even more so. Pervasive games are strange, as they typically involve playing in the open but hiding it.

I’m not saying that there will be a roleplaying revolution after which everyone plays these games and sun shines and all is well. Rather, roleplaying might be one element of a more fundamental change. Whatever changes, barring an apocalypse of some sort, internet will play a so much larger role that comparing the two is not even relevant.

As a final word and something of a conclusion, I don’t know where this line of thinking will lead to, but it feels important. Following it seems important.

## My rpg history

7 May, 2009 at 3:41 pm (roleplaying)

Secret and very informal Finnish rpg blogger history carnival. Well, actually, Sami just emailed a bunch of us to write about our roleplaying history.

# Early years

Before roleplaying I was a huge fan of fantasy literature; I started with Tarzan and Jurassic Park, moving on to such classics as Eddings and Dragonlance books and basically everything that resided in the regrettably small fantasy shelf of my the library of Ylöjärvi. Occasionally I even read a scifi book or two.

This guy called Niku introduced me to roleplaying when I was 12, +/- 2, years old. For context, I was born in 1987. He had already been playing with his friends. I had the joy of running one session of Miekka ja magia (translation: Sword and sorcery), a Finnish dungeoncrawling rpg of unremarkable quality, pretty near the start of my roleplaying career.

I had this intricately (given my age an experience) designed cavern, which had a bunch of challenges and specific ways of passing them. There was also a dragon in there, in a sulfurous cave, of course. So, the brave party of adventurers enters the nameless dungeon. There was this stone block acting as a door to somewhere; the players spent a good deal of time trying to open it but eventually managed to push it, hence opening their way. Talk about pixelbitching on my part. The next obstacle was some sort of slime or ooze or mass of tentacles; there was also some burning metal-like substance in trenches that kept it away. Players, of course, cast some slay monster-style spell instead of jumping through whatever hoops I had designed and started immediataly experimenting with the burning substance. That was fun. I don’t really remember anything else about the game. Lesson learned: Don’t bother planning as the plan will not hold anyway. Especially don’t bother trying to guess what the players will do.

Around that time we observed how bad the rules of Miekka ja magia were. Naturally we made our own. We had character classes and attributes, later also races. Fighters were immune to fear, I think. Different races and classes rolled attributes in different ways. There was also hit points and maybe magic points, too. I may have a character sheet or two from that age still in my archives. From that game on certain computer games were a huge influence on our design work; later it was mostly my design work. To name the most influential: ADOM (a roguelike). I also loaned all roleplaying games in the library of Ylöjärvi and later of Tampere; there was Cyberpunk, Rolemaster and MERP, Elhendi, Ultima Thule (the local librarian asked if I was certain I wanted to loan it, as it was classified in some section of the library related to ancient Finnish history or customs or something similar), THOGS, Stormbringer, Amber diceless, Paranoia, Over the Edge, Ars Magica, Warhammer frpg, some World of Darkness stuff and maybe others. We played some of them but never stuck with them for long. My own game designs had two major branches: Dungeoncrawling games and “proper” roleplaying games, the latter of which usually included lots of statistics. Characters had 13 stats at some point. I’ve got plenty of those character sheets remaining. We also played freeformish cyberpunk with magic (we did not know of Shadowrun). I was an avid reader of Johnn Four’s rpg newsletter.

Overall, gaming of that age was mostly character generation: We built characters, played for a session or two of arbitrary encounters and maybe sometimes storming a location, and then moved on to new shiny characters. My game mastering style was refined: Throw something, possibly orcs, at the characters, see how they are decimated, desperately scrape until you can figure out something else that happens, possibly roll dice (high is good, low bad) to get inspiration and so on. Sometimes there were strange shrines and other stuff; having players interact with them was fun, as it still is.

Somewhere along the way we had Gastogh try roleplaying; the game was Paranoia, session utterly sucked, but he was hooked regardless.

# Internet, the Forge, Dragongame, D&D

So, at some point near one of my first visits to Ropecon, the very best roleplaying con there is that everyone should attend, I figured out that the new edition of D&D was not AD&D (which sucked, though I have no idea how we knew that; AD&D was not real roleplaying, but mere hacking and slashing; so were our games, but we did not know that) but rather some thing called third edition. Around then I also started participating in the official D&D forums. Just so you know, undead are not inherently evil, railroading is inherently evil, assassins and poison use are not inherently evil, +2 intelligence or whatever else is not inherently unbalancing, there should be paladins of all alignments, alignments in general suck, and various other facts I learned and fiercely defended therein. I was Gilean back there and had dragon of some sort in my avatar. For all I know the account is still alive.

So, we bought D&D and various books, including Savage Species and Draconomicon, for it. We played some D&D, playing style much as before. It was not significantly better or worse than previous games, I think. My homebrewing went on as before, though maybe a bit more refined due to age and having read Over the Edge (freeform traits!).

I discovered many an interesting new things in the Internet. Namely: Beyond role and play which started me on the paths of rpg theory and to some degree philosophy (I learned semiotics from BRaP, later encountering them in a philosophy book), RPG.net wherein discussions where much more useful than on WotC’s forums, and finally the Forge. Year was at least 2004, seeing the release date of BRaP. I soaked all the rpg theory I could find, learning GNS and big model stuff and seeing that my games were not actually fun, but rather incoherent/simulationism messes.

Namely, the one game we had going is nowadays called Dragongame, wherein players played dragons. It started as 3rd edition D&D but we later changed to a homebrew system of my design, which Gastogh also started tweaking. The rules were somewhat broken and my game mastering style had not greatly developed from “encounter strange things, interact, occasionally there is a fight, continue”; it was eminently not suited to the game I wanted to run and the game my players wanted to play. Dragongame eventually died. Gaming was again fleeting bits of games and character generation.

The Forge. I became a Forge zealot of the worst kind: Spouting off and spreading theories I hardly understood. I was also a jerk on the internet at that time (and possibly earlier and occasionally still). I literally flamed myself off the D&D forums (they just could not understand GNS even though I pointed them the links and repeated what I thought they said so many times!) and participated in several rpg.net “debates”. Thanuir was my handle at that time, as it still tends to be.

Eventually I calmed down and realised that yeah, maybe GNS was not all that I thought it were and maybe I had been a jerk and a troll. My gaming situation did not improve much; I still lacked the techniques to run games in style but the one mentioned before and I found that style unsatisfying. Actually, there were a few pretty good games, too, now that I think of it. Homebrewing happened as before, though now I had some idea what I was doing; consequently, the designs moved closer to minimal in terms of rules material. Niku, know that most of the designs were made with your style in mind, though the level of success was not very good.

# Burning Wheel, army, Jyväskylä

I discovered Burning Wheel and bought it from Arkkikivi/Arkenstone after having read a few reviews and some rpg.net threads. It opened my eyes to an entirely new way of roleplaying; or, more likely, finished the process of figuring it out that had been going on for a while. We tried playing some BW, but it just did not work that well due to various reasons. Gastogh hated it because, umm, I have no idea, really.

So, I moved to Jyväskylä to study mathematics. I discovered the local roleplaying game club, Ropeapina, and participated in sessions. I GM’d one short game whose idea I had stolen from the BW demo scenario “The sword” and played in some games; this was the first time in long while that I actually got to play roleplaying games, as opposed to running them. It did not work very well.

Half a year of army with no roleplaying, though I did read a bit about them on the ‘net.

After the army my roleplaying life, and other life, too, suddenly took on a much better quality. My self-confidence was boosted by seeing what people of my age were like in the Finnish Defense Forces (I’ve never been a huge fan of my own generation) and by noticing that hey, I’m actually pretty good at this mathematics stuff. That was a year and a half ago, I think. I also started this blog. Since then I have had two roleplaying groups: The weekly university group where I GM roughly 2/3 of the time or so (there are three games going on at any one time there) and a group of friends where I’ve been the only GM for some time now. I’ve GM’d Burning Wheel successfully. I’ve played various games, traditional and indie alike. 4e and old school D&D I still want to play. I’ve run a bunch of games, still mostly homebrewed. I’ve been following blogs and letting forumers reside in their own land, not well suited for sharing elaborate ideas. I still occasionally come off as hostile on the ‘net.

## D&D my way

4 May, 2009 at 5:16 pm (game design, generic fantasy setting) (, )

Starting today I’ll be running my version of D&D in the university/Kortepohja gaming evening/club, assuming, of course, that there are interested people. I am too cheap to buy anything and too lazy to print excessive materials, so I’ll homebrew/design my own version. As such, the rules presented herein are in flux and draft stage. Before the rules, a bit more detail on the game I’ll be running.

# Setting and some situation

The world is my very own homebrewed generic fantasy world. As such, it is not of much interest to outsiders (I keep assuming). I’ver written about it before and ran games in it before. All of the related material should be in the generic fantasy setting category (which I might rename some day if I bother naming the setting; naming is difficult business).

This game happens a number of years, such as ten or nine, after Tirae, the capital of the only credible human kingdom, experienced rebelling and fires as a result of the actions of a heretical cult of dragon-worshippers. The area claimed by the kingdom of Tirae is very light on wood (hence, fairly constant warfare with the elves who inhabit the northern forest of Thaleth(ia); I told, generic fantasy setting). It is bordered by the aforementioned elven forest, ocean, and some tribes of dissenting, semi-hostile barbarians who are much like the Tiraeans themselves, except they are living in blissful freedom/without the benefits of civilisation. In the north there is a formidable range of mountains. Previously there has been one garrisoned entry through the mountains (in the eastern part of the range, yet still firmly in Tirae’s grasp); the three lizardfolk that are born annually in place of humans have been thrown off the garrison; literally, after the serpent cult and related chaos. They are not killed and the lands beyond the garrison are not settled due to a prophecy, or a curse, involving the dragons coming back. Just a few months ago another entrance through the mountains was discovered near the western ocean. Behind it lies a vast forest, but also untold dangers; many a treasure-seeker has perished there. Regardless there is plenty of wealth to be found there and even a small, but growing, village to support more adventurers. The wealth can be acquired by cutting and selling wood (a task somewhat boring to play through), by protecting people and keeping peace, or by exploring the occasionally mysterious locations found within the woods.

Unfortunately, the forest strikes back (in a way similar to, but distinct from, the one outlined in that article) and is closely connected to the Dreaming so that some of those strikes are formidable; in particular, nasty monsters might appear now and then. In addition, there are natives already inhabiting the forest: A tribe of lizardfolk and some wild elves. To add further excitement, the scum of Tirae is flooding to the newly established village. In particular, there are rumours about certain heretical and dangerous cults, like the serpent cult that people in power had, to their knowledge, already rooted from Tirae. As the game starts the village is ruled by a certain somewhat wealth ruffian, whose position is fairly perilous.

# Characters to play and generating them

There are Tiraeans, barbarians, very lucky Thalethians, wild elves and daring lizardfolk to play. If people create characters clearly in conflict with each other they must also be okay with inter-character conflict leading potentially to death. This is D&D and I’m going to assume there is a party that can, at least in theory, stay together. It is recommended that players do not come to table with elaborate character concepts, as dice will be rolled. There’s no point buy here.

Character generation, then. First select the character’s species: Human, lizardfolk or elf. Next, roll attributes. There are six of them and they might be familiar: Strength (voima), constitution (kestävyys), dexterity (ketteryys), intelligence (älykkyys), wisdom (viisaus) and charisma (karisma, since I can’t be bothered to actually properly translate it, at least now). Humans roll everything with 3d6 in order. Lizardfolk roll strength with 4d6, drop lowest and con with 5d, drop two lowest. Elves roll everything with 5d, drop 2 lowest. Everything includes constitution. Elves are powerful (a quick estimation gives them an average score between 13 and 14, but I can’t be bothered to actually confirm that). Attribute levels 3 and 4 indicate a -3 malus; 6 and 5 map to -2, 8 and 7 to -1, 9 to 12 grant 0, 13 and 14 +1, 15 and 16 +2, 17 and 18 +3.  The trend continues upwards and downwards. Attribute of 0 is bad news. It should be noted that elves are harmed by prolonged contact with iron and that lizardfolk have natural armour equal to their constitution modifier. Elves can see well in all but utter darkness, while lizardfolk “see” heat.

Next step is selecting a class. Physically competent characters are encouraged to be warriors, while too smart ones can try the difficult path of summoner/diviner/sage and the particularly charismatic ones can develop themselves in apprenticeship to shamans/wise women or men/mages/witches/sorcerers/wizards. Elves have one additional path they can tread: That of woodshaping. At this point, players of human and lizardfolk characters should write the past pursuits of their characters in one word, like “soldier”, “hunter”, “pickpocket” or “healer”. Elves are live eternally; even starting characters are somewhat aged and I don’t want to read that novel. More background info can freely emerge in play.

Warriors are skilled at the following activities (hence gaining their level as a bonus): attacking, defending, fortitude and reflex saves, potential maximum hit points. Further, they can use any and all commonly available and even rare weapons.

Summoners are extremely sharp folk; in game terms, intelligence bonus is required to make most use of the class. The most feared ones can contact power entities living elsewhere. Their profession requires strict self-control; many are ascetic and wear simple robes (if that). Summoners are skilled at will and fortitude saves. In addition, they can cast divinations as detailed below.

Shamans have strong personalities (cha 13+ recommended) and can bend others, living or merely animate, to their will. The powers of shamans are often used unwittingly by untrained or weak-willed (wisdom bonus or at least lack of penalty also recommended) shamans. Shamans are skilled at will saves and can cast spells as detailed below. Elven shamans do their magic by singing.

Elven woodshapers can create various items from living wood by focusing on it. Their craft requires significant patience and attunement to achieve (wisdom bonus would be nice). Shapers are skilled at will saves and moderately skilled (half level, round down) at fortitude saves, attacking, defending and shamanism (as shamans of half their level). In addition they can shape wood as explained later. All elves can shape wood as shapers of half their level.

Characters also need to be equipped. They start with suitable fairly basic equipment; no rich ones. A weapon or two, some leather armour, clothes, camping equipment, maybe something little implied by their background. A shield or two, mayhaps.

All characters can speak and understand Tiraean or some language of northern barbarians (they are dialects of the same language and which one the character knows does not affect communication very much, though social position of characters who are not fluent in Tirae’s main dialect may be bad). Lizardfolk also can speak Draconic, lizardfolk dialect. All elves speak their native brand of elven (all elven languages are dialects of each other, too, and enable mutual communication). Characters can learn one additional language per point of intelligence bonus, if any. Alternatively it can be used to learn a written version of some language. Draconic and the elven dialects have written forms. Human languages do not. A certain archaic dialect of elven is the dominating language among human scholars. Anyone with relevant background can communicate in that dialect at fair level, though reading it is far more rare a skill.

## Derived values

Some basic arithmetic, such as deriving attack bonuses, is unfortunately necessary. Attack score: Strenǵth modifier plus any from level, -4 if unskilled with the weapon in use. Ranged attacks use dexterity modifier instead. Defense score is influenced by dexterity: First, take all negative modifiers (such as negative dexterity modifier) and add them to 10 (or substract, since adding a negative number is the same as substracting a positive one). Next, add highest positive modifier to what has been established before. Next, sum all other modifiers and halve this result; it, too, is a bonus on defense. In summary: All negative modifiers apply, highest positive modifier applies, as do half of the others (round correctly). Leather armour gives +1, chain or breastplate gives +3 and shield gives an extra +2 (as well as splintering occasionally). Fortitude save is constitution modifier (plus suitable levels), reflex save comes from dexterity modifier, will save from wisdom modifier.

Hit points are determined as follows: Take number of six-siders equal to level. Add number of dice equal to the absolute value of constitution modifier (e.g. 2 dice for +2 and -2). Roll them. Forget number of dice equal to constitution modifier; the highest ones if con mod is negative, the lowest ones if con mod is negative. In other words: Positive con modifier adds bonus dice and the highest results are kept, while negative modifier adds malus dice that are rolled and then lowest ones are kept. E.g. level 1, constitution 14: Roll 2 dice, keep the higher. Level 2, constitution 4 (modifier -3): Roll 5 dice, keep the two lowest ones. Hit points are capped above by constitution plus any fighter level. Someone with 5 constitution can never have more than 5 hit points unless he has fighter levels; a 2nd level fighter with 5 con can have up to 7 hit points (but good luck rolling that with two penalty dice). Damage characters deal is d6 for most one-handed weapons; 2d6 take higher for two-handed ones and bows; 2d6 take lower for light or improvised ones (dagger, unarmed, thrown rocks). An off-hand weapon in melee increases damage by one step.

# Gameplay and magic

The primary activity shall be adventuring, which includes exploring places, combat, interacting with creatures and finding lost treasures. As a GM, I’ll stick with arbitrating the world and offering hopefully interesting things to get involved in; the players ought to have motivated characters (greed is good motivation to start with; let more emerge in play) and either engage opportunities I provide or create their own goals and go for them.

The rules have fairly good coverage of combat. First everyone declares what their characters are attempting, then the activities are resolved in an order that makes sense; this means that quick actions happen before slow ones and ranged attacks happen before spear-thrusts which precede sword-strikes. Shamanistic magic is slow. In case of equal situations, roll d6 + dexterity modifier to determine initiative. Attacking characters roll d20 + attack and the attack hits if opponent’s defense is reached or exceeded. Damage roll tells how much damage the attack deals. Damage is reduced from opponent’s hit points (which are abstract and not pints of blood). Anyone reduced to 0 hp is safely unconscious; anyone reduced below it must make ortitude save, difficulty 10, to not bleed to death. Any character at negative hit points can be automatically killed by taking an action to achieve that.

Characters naturally heal 1 hit point per night of proper rest. Characters reduced to negative hit points require the services of a skilled healer or shaman.

Saving rolls and some magic involve rolling d20, adding relevant modifiers and hoping for a suitably high result.

General resolution works by the help of a six-sided die. As a GM I estimate chance of success for task at hand; for example, picking pockets might be 1/6 or 3/6 for someone with background as a thief. Next, a relevant attribute modifier is added to the aforementioned chance. For someone with +1 dexterity modifier, the chances would be 2/6 and 4/6, while a somewhat clumsy (-1 dex mod) would-be pickpocket would have chances of 0/6 or 2/6. Then roll a d6 and try to get under the chances. I declare the chances before you need to roll, assuming there does not a exist a specific reason for not disclosing them (the target is something preternatural in disguise, say).

Experience and advancement need a few rules, too. Human characters need current level times thousand xp to get a new level, lizardfolk characters 3/2 times that, elves double what humans require. Each gold piece is worth one experience point to whoever acquires it. Slaying monsters is worth 100 experience per hit die to those engaged in the killing. In addition, I’ll let players set up goals for their characters. Minor or boring goals are worth d1oo experience when completed, while major or interesting ones give ten times that. What is minor or major is entirely up to GM fiat. Level means rerolling hit points and gaining whatever benefits the level gives.

## Mysticism

Summoners know one first-level divination per point of intelligence bonus at the start of the game. They can prepare one divination per level per day so that they always prepare more divinations of lower levels than of higher levels (at first level, 1 level 1 divination; at second, two first level divinations; at third, two first level divination and one second level one). All divinations give information or do something else to the caster; this is intensely personal craft.

New divinations can be mastered only by hard studies or as a gift of dubious value from some powerful entity. Learning a divination takes number of days equal to the divination’s level squared and can happen through reading or being taught, with the latter being more common. Receiving a divination as a gift means that the entity has typically installed a backdoor of some sort so that whenever the divination is used the entity learns what is happening and can perhaps influence the events in some way. Consult proper summonings of the same level for guidance. Suitable D&D spells of same levels can be pretty freely added to the list.

The entities summoning is concerned with are always powerful ones and characters happen to know the true names of them, which grants a measure of power over them. Still, they are far beyond controlling.

### Some first-level divinations

• Perfect memory: Perfectly recall one scene, including all perceptions related to it, for as long as concentration is unbroken. Analysing the scene can take minutes or hours, depending on the level of detail involved.
• Instance of time: Everything happens in bullet time; your actions are no more accelerated than anyone else’s, but you do have time to think and observe. Gives +3 (if d20 is used) or +1 (if d6 is used) in any situation that demands fast reaction and where thinking it through can help. Also, the player can take his time making the decision.
• Recognise: This divination can be cast up to wisdom bonus times; if the modifier is not positive, this divination can only be cast once and only works when the caster actively concentrates.  Each casting selects one person, whom the caster will thereafter instantly recognise, no matter the circumstances. The target can be hidden, disguised, shapeshifted, or dead but the caster will nevertheless recognise them. Moreover, the caster can be unconscious and will upon waking still know that the target was nearby. This spell is permanent; the caster can dismiss any recognition at any time by willing so. Recognise can be cast whenever in the presence of the to-be-target; this includes contact entity and similar summonings.
• Accurate [sense]: Each sense is a different divination. The relevant sense is greatly amplified, making the caster generally hard to surprise and very scary to be around. The effect lasts for as long as the character keeps concentrating on that one sense (so sniping would be possible with enhanced sight and eavesdropping an entire discussion with enhanced hearing likewise).
• Contact entity: Character contacts one entity whose real name is known; the entity learns what the character thinks is happening at that moment and can communicate its general pleasure or displeasure about the situation, as well as vague instructions. This divination is instantaneous.
• Detect auras: Diviner senses auras; that is, spells and entities of power; in some idiom suited to the caster. Sight is traditional. This spell lasts for as long as the caster concentrates. An aura can give vague sense of the power some entity wields. Careful observation can even tell something of the disposition and intentions or past deeds of some observed target.

### Few second level divinations

• Open window: Pronouncing the name of some powerful entity the character opens a window the thing can sense through. It can use some power roughly equivalent to first level shaman spells through the window, hence closing it. Alternatively it can reveal itself or communicate through the window. Unless the entity uses its powers the window closes at next dusk or dawn.
• Read languages: Character can read one particular written document, regardless of language it is written in. Lasts as long as the character focuses on that document.

## Shamanism

Shamans wield power to impose their will on their surroundings. They can cast one spell per level and more lower level spells than higher level ones, much as summoners do. In addition they can cast extra spells but at a cost. Shamans know one spell per level and an additional one per point of wisdom bonus. Shamans don’t have to prepare spells ahead of time. They can improvise spells but at even greater cost and risk.

When improvising spells or casting over one’s daily allotment the shaman’s player must roll a single d6. If result exceeds the spell level, nothing bad happens except that future similar rolls get +1 until the shaman has rested. In case of known spells the shaman gets to add wisdom bonus to the roll. Wisdom penalty hurts all of these rolls. When improvising a spell the player first tells what he is attempting and the GM then decides what level the spell is of.

Failing the roll above gives GM free reign to come up with nasty problems. In general, they should be in line with the level of the spell just being cast. The spell itself may or may not come to pass. Maybe I’ll write down a random chart or something.

The difficulty of saves is 10 + charisma modifier + shaman level, unless otherwise mentioned.

D&D spells of same level tend to be somewhat more powerful. Generally spells can be increased in level by doing one of the following, assuming suitable spell: Increase range on scale touch/personal -> presence -> sight -> far -> wherever, increase duration on scale short/concentration -> till next dawn or dusk -> till next full moon or other suitable lunar phase -> year and a day -> suitable number of years, like 81, 101, 49, 169, 666, 42 -> eternal, increase spell’s target along following scale: single person -> handful of people -> hundreds -> kingdom or species -> everything

### Spells of first level

• Pain: Touched target takes d6 damage per combat round, up to charisma bonus rounds. This spell never kills a target but is excellent at subduing them. Resisted with fortitude.
• Scare: Target within presence that fails will save must flee or take -4 on all actions.
• Courage: Target gets +2 on attacks and resisting mental effects as long as it keeps on fighting; resisted with will.
• Healing: Up to charisma bonus targets heals d6 hit points per night of sleep and rest.
• Sleep: Target becomes drowsy or, with failed save, falls asleep.
• Leaping flames: The flames in bonfire or similar suddenly flare, causing 1 damage to those nearby (and serving as a distraction and maybe blinding people; I’m sure there is more ways of using this spell). Avoided with reflex.
• Breeze: Sudden breeze may extinguish torches, scare, distract, or do whatever else breezes tend to do. It may also move feathers.
• Hold portal: Door or other closed means of physical entry or exit clasps shut and chooses to not open: Only those with strength at least equal to caster’s charisma may even attempt opening it. Duration is till next dusk or dawn.
• Charm: Resisted with will. Target treats everyone as basically trustworthy and good personality until evidence to the contrary presents itself. Duration is till next dawn or dusk.
• Command: Failed will indicates that target follows one simple command spoken out loud by the caster; the spell is instantaneous, so extended actions can’t be forced through this spell. Target must understand the command for the spell to be effective. Self-defenestrate is a bit complicated.

### Second level spells

• Instant healing: Immediately heals d6 hit points.
• Burst of fire: Any flammable object (like someone’s hair) bursts to flames, dealing d6 damage to anyone nearby and thereafter acting as a normal fire. Successful reflex reduces damage to 1.

## Woodshaping

All suitably experienced elves can do some woodshaping. Select one object per level: The elf can effortlessly create a near-perfect wooden version of the object, given suitable wood and some time (minute for a knife, hour for a spear, days for a house). In addition, woodshapers know one wondrous effect per point of wisdom bonus, but no more than one per level: Items as hard as iron, fireproof wooden items, reviving some random wooden thing (e.g. fence, door, spearshafts, firewood), growing thorns, so on.