By The Numbers

Last night I sat down and realised that the setting I was coming up with wasn't working quite as planned. Basically, travel times between locations (potentially, I've not fleshed them out yet) would just be too short. You jump in your spaceship and even though something is just miles and miles away - you get there fairly quickly. I thought that a smooth 10m/s^2 acceleration (slightly higher than Earth-standard, but makes for easier calculation! Call it "metric gravity" maybe...) as a baseline would mean that it would still take days of travel for adventurers - not because I want things to be boring and tedious, but because I want some semblance of realism.

(I don't want Star Trek style space travel, where the ship moves at the speed of plot)

So what to do? I came to realise that, basically, the local area of space I was considering was just too small. So I scaled up. I started with a square that was about two light minutes across, and have now scaled up to a ten light minute square. For those who don't know: the Earth is approx eight light minutes out from the Sun; the region of space I'm setting this in is approximately 400,000 light minutes out from the Sun.

A ten light minute square might not be big enough, but I have to add the numbers etc to my tables and see what it does to travel times. My basic generation table starts off with a ten-by-ten Grid of single squares; roll two d10s for each square and any 1s indicate that there is a place of interest in the Grid - then refer to tables to generate those. Double 1s mean there is something alien there. Am considering tweaking it very slightly (possibly if any 2s are rolled these indicate something else about the square: a problem? A hazard?)

Enough maths for today! Two good things about progress with prep for all of this: first I have typed up a list of the traits for chargen, along with their effects. Chargen will have the option for three player selected traits or four random ones (should keep things interesting). Second, I've found the notes I had for chargen, so now I can type those up and hopefully streamline the process for players.

Next up, making weapon and armour selection simple!

(if anyone wants to see my maths for any of this, let me know, I'll see what I can do)

Generating Pugs

(this is a post written in haste and ignorance and contains thoughts that have not necessarily been taken to any kind of logical conclusion; so who knows if there is anything of value here, or anything that can be taken to a valuable conclusion. Perhaps you will take a chance?)

The other day I was thinking about generating large numbers of Pugs. Pugs are a goblin-y kind of creature that I wrote about when I was DMing the Somewhere North campaign earlier this year. They start as 2/3HD creatures (clerics and chiefs have more 4HD) and are found in various group sizes, from two person scout groups all the way up to 150 strong warbands. And you would not want to look in the old Dwarven Fortresses under the northern hills. Thousands and thousands of them in there.

So. You have two Pugs running from a party. Quickly you roll four d8s and there we go, you can get their HP and know what's what.

But: the Party is ambushed by a Medium group. (dice rolled as I write to illustrate point). They've been lying in wait and are prepared. (6+3d6 leads to 19 Pugs, 6 of them are 3HD, roll for 50% check and one is a 4HD Pug Warlord's Son) So the Medium group is comprised of a 4HD leader, six 3HD Pugs (two of which are Clerics) and twelve 2HD Pugs. That's a lot of dice to roll to stat them up. You can do it, but it seems like a little chore.

Thus: I started thinking, can a reasonable generator be made? Say, roll 2d20 and consult a table that will give Pug numbers, HP values, what they are armed with and so on. Of course, the original conception of the Pug is something that I have put together. There must be a million and one similarly created opponent humanoids.

Here's the interesting thing that was occuring to me as I was sat in Costa: there is something beautifully mathematical about all of this. You create a system to model some kind of objects. It's totally valid to create the objects and move from there too. But in some respects the model is quite complicated in some ways (i.e., if you want to generate a lot of Pugs at once). So can a different model be created (a different means of generating large numbers of opponents) that means fewer dice are rolled, but the result is representative of the larger model?

As I said at the start, none of this is thought through particularly well. I'm just curious.

(and say you had A.N. Other opponent that has 2HD and appears in large groups; if there was a 2d20 table, or something indexed with two d20s or something like it - the result from the d20 rolls in terms of HP would be valid as well potentially, i.e., a group of 2HD zombies might have other features but their HP values could be generated similarly)

(all of this floating around in my head, and partially prompted by Zak S's post about Elegance, which made a connection with the idea of mathematical beauty...)

A Chance of Snow

Every day in the frozen north brings a chance for snow. By leaving the relative safety of Rovaniemi and the surrounding villages behind, Külk and Joonas are taking a chance on the weather and the terrain. The wilds are not to be travelled without careful thought...

I had been fast and loose with the environment and weather up until now. I had always assumed that the PCs had some kind of provisions, and that they were wrapping up warm. I kept dropping hints that the weather was going to get worse though, and that heading north would lead to severe snowfall. Precautions must be taken etc.

However, I didn't want to railroad any blizzards or consequences. I wanted the weather to be unpredictable. So before the session on Tuesday I thrashed out a kind of probability-based "Fibonacci-like weather generator". A Fibonacci sequence is dependent on the numbers that came before. So the third number is dependent on the second and first numbers, the fourth number is dependent on the third and second and so on. I decided that a simple way to include this was to say that "today's weather is dependent on the previous two days, with some randomness."

Fighting Fantasy Maths

In a recent post I started to muse about the likelihood of surviving a Fighting Fantasy gamebook. Of course it is easy to say "the higher the SKILL and STAMINA, the more likely you are to survive." But therein lies a question for maths geeks like me. How much more likely?

Aside: The Maths of Fighting Fantasy

This blog, at least in name, talks about the maths of RPGs. Most of the time I actually just want to talk about RPGs, ideas and what happened the other night at the table, but I thought the following video was worth sharing, as it follows on a little from my post about Murderous Ghosts from last week, and also from the post that noisms made about us playing it at the weekend.

I'd recently been thinking about doing something similar to what this video does with Island of the Lizard King, which I found in a charity shop, but there is no way I could do it as much justice as this video does.

One follow-up question does occur: I wonder how much difference there is in the graph structure of the various Fighting Fantasy books?

And another interesting problem that might be do-able: what is the probability that a person actually makes it to section 400, given the skill/stamina that they start with?

There's some work in figuring that out, but it's essentially coming up with a general formula for calculating the odds of surviving an encounter, and figuring out the various general paths through the book (taking into account when you come across things like traps that you have to roll under skill or suffer penalties). To solve it you would build up a couple of general results, then plug in numbers. Not simple per se, but not hard... The actuarial tables of the Island of the Lizard King...

Turn To Stone!

noisms continues to negate the need for me to write any kind of actual play report of Yoon-Suin, by relating all the salient points. Suffice it to say that, as ever, a damn good time was had by all.

Even by me, when I was pecked by an evil magical peacock and turned to stone. Once the ongoing danger had been averted, and the rest of the party were safe, the question arose as to whether or not I could be moved. There is a monastery several days' journey away, and the monks there may be able to revert me back to flesh (or so the party thinks).

But since I am now literally stone, can I be moved? I was already a STR 16 Fighter in full plate mail, carrying about 300gp, a shield a big axe and a miscellany of adventuring gear. But now that my flesh is stone, could I be moved by five people, who already have to carry a man on a stretcher?

Gut instinct says no, but let's do the maths to check...

Games Night: A New Man in Yoon-Suin

Last night was another journey in Yoon-Suin, and my new character didn't disappoint. noisms has given a good account of the session, but states early on that I rolled "a ridiculously lucky set of stats" which, I guess, is probably accurate.

noisms method for rolling stats was to roll in order for STR, DEX, INT, WIS, CON and CHA, and he would allow one switch after they were all rolled (i.e., no re-rolling, but if I wanted to WIS and CON scores I could). Thankfully, the dice were extremely well-behaved last night!

STR 16
DEX 13
INT 11
WIS 13
CON 13
CHA 6

Well, OK, except for Charisma... I decided that these were pretty good stats for a Fighter, and early on decided that the only way to play someone with a Charisma of 6 is to act as someone who thinks they are very charming, and can't understand why others seem to screw their face up at him or roll their eyes. Poor Manjeet.

I don't have a clear picture in my head yet of what Manjeet actually looks like; I'm thinking tall, shaved head but with a few days of stubble coming in around his chin. His family are artisans (again, the luck of a random roll; after my previous success with stats and maximum hit points everyone was rooting for my personal history to reveal I was a eunuch) so I guess he would be fairly well turned out.

When I first met Marich (David) and Anil (Patrick) in the forest they gave great short descriptions of themselves. Patrick said, "You see a short, squat, bald man." David: "You see Prince Harry in a wizard's robe."

A high point of the session for me was being the one to deliver the killing blow to Manesh, the Bandit Chief who we battled against last time. I think we were really well coordinated, and Patrick's idea to hire retainers and to kit them out properly worked well. Not only did they hold their own quite well in delaying large numbers of attackers, but because we bothered to armour them up they didn't just die as soon as an opponent looked at them.

noisms claims I was ridiculously lucky; a quick bit of calculation and it turns out he is probably right: there's approximately a 1 in 6.8 million chance of me being that "lucky". And that's before you factor in the max HP roll as well. I just see it as the dice rewarding me for the spectacular fails in the last session. I wonder if I will be so lucky next Tuesday. When you have a Charisma of 6 you really have to make your own luck I guess...

Getting My Maths On

Watch this space; I've been struck by inspiration somehow today, and so am finally getting maths thoughts out of my head where they have been stewing for ages. I've been writing for a work-type project (I do skills training with PhD students and research staff) and need a different kind of outlet. I thought that was going to be figuring out whether or not to use Apocalypse World, GHOST/ECHO or Cyberpunk as the basis for a small campaign that I want to GM, but it turns out that I've had this growing thought about finally figuring out the In A Wicked Age dice-rolling probabilities that has been bugging me. I don't know the answer now, but I SEE the connections.

In maths, when you have enough pieces, sometimes you can just run them together and get an answer spit back out. Building proofs from the conceptual machinery of algebra is dizzying. You can go so far so quickly.

Of course, there are probably resources out there that have looked at this. On an internet with this many connected souls, the chances are quite high that that's true. However, there is something great about sitting down, spending the time and doing some maths for the sake of it. So that's what I'm doing.

Watch this space: soon we'll have the final word on rolling dice for In A Wicked Age!*

*because, you know, that's what everyone has been waiting for in RPGS...

A quick note on Ammo Maths

Some time ago I wrote about a curious little thought that I had had when writing out an ammo mechanic for the zombie game that I will get around to one of these days. I duly set about working on some all powerful equation that would calculate everything. This is what (some) mathematicians do, I did it quite often during my PhD: you reach to try and prove everything, building up from small cases until you have it all.
Except that that doesn't happen all too often in my experience. Instead, you find that the particular case you are looking in to has no easy way of stating it, and in particular, no nice way of explaining it to someone. You can talk in generalities, but often you are glossing over details. You don't find the "beauty" that you are looking for.

That's what happened to me while I was looking for my formula for the "Ammo Maths" problem. It dawned on me during one of those times I have been working on the problem that I was going about it all the wrong way. Sure, the formula(s), when complete, would have some novelty value or interest. But they, in themselves, weren't the interesting thing. In the first case, it would be great to know the answers to the two questions I asked originally.

But more importantly, it would be better to have a meaningful answer to the general case. There is no point in presenting a formula really. Who would use it? Instead, I'm working on typesetting the tables that (may) accompany the mechanic. They could be useful to GMs or players so that they have some idea about just how many shots they might get off. Having a narrative mechanic is a way of avoiding counting bullets and shells, but it would still be good for people to have some idea of just how high up the food chain they are.

So that's what I'm checking at the moment, what the numbers say and tell us, and then I will typeset it (which takes a little time as my HTML for tables is hopeless; I'll be copying and pasting over from word processor instead).

Games Night: LotFP/Isle of the Unknown

I've missed talking about our regular Lamentations of the Flame Princess game for a couple of weeks. Last time on the Isle of the Unknown, Patrick was DMing us through a dungeon underneath an old keep. We had killed some Cthulu-worshippers, some giant bats and avoided some traps along the way. All was well with the world, and I was enjoying playing my new cleric, Priam, servant of the powerful god Venn. Charley/Henry Shortbread, the specialist, had disappeared into the undergrowth, and Priam had just happened to walk along and find the party as they were on their way to the keep.

Patrick has a nice house rule when it comes to magic; as with many D&D type games, you have your spell slots, but you can also try to cast any spell appropriate to your level, so long as you roll for success. Success is determined according to the Apocalypse World success rules: 2d6 plus or minus any modifier, a 10+ gives you what you want (the successful spell), a 7-9 gives you success plus a roll on a "something bad happens" table and a 6 or less just gives you the roll on the "something bad happens" table.

The Bless cleric spell/prayer in LotFP, as understood by me, means that you get d6+level points to spend/declare for future rolls. So having points like that means I can spend points to attack, to evade, for WIS checks - or even, to try and get future spells using Patrick's magic house rule. So if I get a good Bless result early on, then I have points in reserve for the night. I just needed to make that first AW-style roll.

It worked last week. It didn't last night.

I roll a 9, so get my blessing, but immediately have to spend the points to get favour from Venn again in order to cast cure light wounds on myself. Why? Displeased with my constant requests, Venn placed a small dog in my abdomenal cavity. Yes, that's right: A SMALL DOG. Not warts or boils on my face, or a limp, or blindness. A SMALL DOG. Luckily I was able to perform a caesarean on myself and have enough HP to then invoke cure light wounds (using many of the bless points that I just got).

Phew. I was up on the deal I guess. The dog was out, I had more HP than I had had before, I had some bless points left, and a dog that (rolls for loyalty)... hates me.

Lesson learned: don't try to game your deity.

Despite having the highest wisdom in the group I failed four rolls in a row - which is improbable enough - but then for the first three rolls I rolled a 16 each time. A one in eight thousand chance.

The small dog, Priestly, was eaten by a giant moth, we had our first big toe-to-toe battle with some giant Amber Scarabs (was touch and go), escaped from a crazy trap, got suspicious about the Bandit/Cleric who put us up to the job in the first place and the younglings were shouting at each other so much at one point that I passed Patrick the encounter die and said "You may as well just roll."

I can't make it for a couple of weeks, so have asked Patrick if my character can try to slip out of the dungeon (so that he isn't killed in the background when the others do something incredibly reckless). We'll see what happens. I'm enjoying playing a cleric much more than playing a specialist, so am hoping that I'll be able to get him back into play at some point soon.

In Which I Fail To Blog

Time pressure, work, maths not working, not making time, yadda yadda yadda.

• The maths has come together for my ammo maths question (or at least partly), so I'll be typesetting that over the next few days and putting it up - along with some thoughts on why this is interesting in general.
• noisms is really knocking it out of the park with his latest blog posts; two in particular have been really good. I really liked his thoughts on Hanafuda cards, and the discussion underneath really seems to have sparked something (in me and in other readers) thinking about using cards in play generally.
• The other post was a bit of AP from the LotFP game that we are both involved with. My nephew and his friend joined us, and last week brought along another two friends. This has really added something to the game, and noisms makes some really interesting observations about differences in play styles.

As I noted in the comments there, I don't think that age is the biggest contribution to the difference so much as the profound difference in culture that exists. If I was my 18 year old self playing D&D with my nephew there would still be a profound difference, because we have lived through such different times - in fact, it feels right to call them different eras.

noisms does make some good points that there might be a broader question here connected with styles of DMing and what they might be used to as well; I can't really comment on that: I've only played under the GMing of noisms and Patrick and I know them both to be fair but lethal, so I know what to expect.

Anyway, more soon. I promise. (and you know what that leads to, right?)

Simulating a dX

I've been thinking for a few months about how to best simulate rolling a dX, which is the same as indexing X entries randomly. It takes time to sort ideas and thoughts out; this is a starting point for collecting things together.

There are six standard polyhedral dice: d4, d6, d8, d10, d12 and d20. When using these we assume that the dice are fair - each side is equally likely to come up. If we were to create or simulate a die with X sides it would be best if it were fair. We cannot simulate a d11 using 2d6 directly - we get a range of 11 possible values, but there are different probabilities for each value. The simulated die would not be fair.

We can simulate a few dice with the six standard polyhedral dice through either re-rolling on the high value, or by "halving the die". It is not too difficult to introduce simple notation to account for both of these actions.

d6/2 gives a d3. We let d6r stand for the situation where we reroll the 6. We only want values 1-5 so d6r results in a fair d5. However, d10/2 also gives d5, and without the reroll. From the standard polyhedral dice we can simulate the following dice easily:

d2 = d4/2, d6/3, etc. d3 = d6/2, d12/4. d5 = d10/2, d20/4. d7 = d8r.

d9 = d10r. d11 = d12r. d19 = d20r.

We could also simulate a fair d9 by rolling two d3s; these act as indexing nine entries in a table. We could denote this with d3 x d3 or (d3)^2.

d3 x d3	1	2	3
1	1	2	3
2	4	5	6
3	7	8	9

These various actions - re-rolling, halving and dividing across tables - allow us to build up a greater number of simulated fair dice. I'll go into more detail in future posts, and see if I can start to make sense about how we might simulate a dX for any positive integer X.

Posts I Keep Meaning To Write

I have lots of ideas for things that I want to write on here. And I most definitely want to get back to connecting maths with RPGs. Here are some things that I've got in development:

• simulating dice rolls, and how that is the same (homomorphic!) as random generation for a large number of entries.
• breaking down random generation sensibly, possibly using a schema of books, pages, tables, rows, columns, entries.
• building proofs. How amazing it is that you can show something once and know that it is true, and can be applied in other places. And also that proofs can be combined to produce even bigger results!
• more on the zombie game that I want to play, and which proof-like I am putting together.
• Oracle games in general - looking for innovation out there, and seeing what I can contribute.
• dice probabilities; thinking towards a resource for different ways that dice rolls can be combined, to then help myself (and others?) who are looking for mechanisms that work for them.
• more Wicked Wednesday posts with "strengths" for NPCs in In A Wicked Age.

Anything else that I should be thinking about?

Ammo Maths

Almost as soon as I posted Tracking Ammo it dawned on me that an obvious series of questions arises:

• If I find a handgun with a 5 rating, what's the likelihood that I will get at least ten shots from it?
• If I have a shotgun with a rating of 3, how many shots am I likely to get from it?

More generally:

• If I have a gun with a rating of X, what is the probability, p,  that I get N shots from it?
• If I have a gun with a rating of Y, how many shots, Z, am I likely to get from it?

These questions are all inter-related, so a bit of thought on one or the other will start to get some answers. I'll have a think and get back to you over the coming days.

Tuesday Night's Stats Lesson

GHOST/ECHO was pretty amazing on Tuesday night, another great example of a wonderfully complex story being built up from simple pieces collaboratively. That was one of two amazing things that happened on Tuesday.

The second was when someone (I feel like I should protect his identity) rolled three d6s and said, "Wow, look at that!" He had rolled three 6s. Which is quite amazing - but more amazing was the comment that followed next from him: "There's only a 1 in 18 chance of that."

My head snapped around like Linda Blair. "Whaaaaaat?!" I cried. "1 in 18? 1 in 18?!!!"

"What? What's wrong?"

Sigh. What do they teach people these days?

If two (or more) events are independent - meaning that one has no bearing at all on the other (and vice versa) - then we can take the probabilities of these two events and simply multiply them together. So if we had a coin and a d6, and wanted to know the probability that upon flipping and rolling them we got a Head and a 5, we would take the two probabilities (1/2 and 1/6 respectively) and multiply them together to give us 1/12. Job done.

The same holds true in this case for our three 6s. For all intents and purposes we can assume that they do not affect each other. So rolling three 6s is (1/6) times (1/6) times (1/6) or 1/216 in total. If you're a percentage kind of person that means there's slightly less than a 0.05% chance of rolling three 6s. 1 in 18 is around 5.5%.

Dice and Tables

I have been thinking again about the problem of indexing up to 400 elements in some kind of random table. In a previous post I mentioned that this was all possible using various computer methods. The main motivation here is thinking about how to do this at the table with just a bag of dice, and for the method to be unbiased, so that every entry has the same chance of being selected by the dice as any other.

Ideally, we want to:

1. use the standard polyhedral dice: d4, d6, d8, d10, d12, d20;
2. minimise re-rolling dice as much as possible;
3. not have any more dice involved than necessary.

All of this, mathematically, leads to thoughts of "best" algorithms, and "best" processes. In any mathematical investigation, we very rarely are able to jump from ideals and assumptions to the final answer. This time is no different, but there is hope I think that something can be done which is both easy to use and simple to understand (mathematically).

The first insight which was really helped is the idea that indexing X elements in tables is the same as rolling a dX, where X is any positive integer. Imagine that you take X square pieces of paper, write the numbers from 1 up to X on them, and paste them to a board. Throw a dart blindly at the board and you randomly select a number - which, for all intents and purposes is the same as rolling a dX.

Take the numbers down off a board now and try to arrange them into a table, or into a series of tables. Here comes the IF:

If we can arrange the X squares into a series of good* tables, then we can index X elements easily.

A consequence of all of this is that those good tables could just as easily contain the numbers from 1 to X written on them. So rolling a dX and rolling to get one of those X elements add up to the same thing, more or less (in maths terms, I think we could safely say that the two things were homomorphic).

And this was my big thought on the topic so far (well, one of them at least): it makes as much sense to see how we can simulate a dX using the standard polyhedral dice as it does to think about organising X elements into tables.

In future posts, simulating dX with the standard polyhedral dice! And how this ties in to random tables.

*in the sense of the three criteria from earlier in the post

Random and Biased

Following on from my post "Different Dice" a few days ago, I think there is another important distinction to be made between the ideas of random and biased.

For example, if we roll a fair d6 - i.e., one which is not weighted in favour of any particular result - then whatever it lands on we know that it the result is both random and unbiased, because the die is fair. If we roll 2d6, paying attention to the sum as the result of this event, then while the result itself is still random it is biased. Because of the different ways that you can make a total of 7 from rolling two d6 dice, a 7 is six times more likely than getting a result of 2 or of 12 (both of which have only one way of being achieved).

I'm interested in this kind of bias a lot at the moment; I was tinkering/hacking together a zombie game* based a little on Risus and a little on Apocalypse World. Apocalypse World works well with its main dice mechanic because it is so straight forward: for around 60% of the time on a general (unmodified) roll your action carries - or at least you get some success. For less than 20% of the time the dice give you exactly what you want. This seems like a neat way to do it: the outcome is random, and there is a slight overall bias towards success.

But in the messed up post-apocalypse, maybe those are the kind of odds you need.

*more on that setting/game another time!

Getting Dice All Random

In my first post I mentioned that I had started to get interested in the maths of RPGs from the probabilities in Apocalypse World. There was something else that started me thinking, which is when one of the regulars in the gaming group I play with asked a question on his tabletop role-playing game blog, False Machine.

P was looking at randomly generating an island from a series of entries in a table. He had come up with a means to do that, but only on a computer, which meant while the island was randomly generated the setting would be determined ahead of his session. To him, the problem was, as he put it at the end of the post:

I need a dice method that can randomise 343 hexes

I've always had a strange little fascination with powers of numbers, so this jumped out at me as soon as I saw it. 343 is 7*7*7, which means that you could have seven tables, with seven rows and seven columns; you could then get any entry out of the 343 in your master list by rolling three d8s and re-rolling any 8s.

Problem solved! Until P realised later that there were actually 330 entries in the table for Isle of the Unknown. But this wasn't a problem either, if we imagined the entries arranged in ten tables, each with three columns and 11 rows. Roll a d10 for the table, a d3 (or d6/2 if you must be formal) and a d12 with re-rolls on the 12s. Again, problem solved!

Which got me thinking...

GMs who like to make things up through random tables could possibly have a large number of random encounters or random elements that they would like in tables. 330 or even 343 entries could be quite small. Is there, in general, a sensible schema that we can use for producing sets of random tables for game data, that we can index with dice? Let's assume d4, d6, d8, d10, d12 and d20s are available.

To put some bounds on this, let's assume, for now (although it may be easily extendable, who knows) that we want to consider for sets of random tables with up to 400 elements in total. I'm going to have a think about this and let you know what I think over the next week or so, as well as share a small random table of my own for In A Wicked Age.

Counting Stories

In yesterday's post I posed the following question:

How many stories are there in the manual for In A Wicked Age?

In A Wicked Age has four Oracles - Blood & Sex, God-kings of War, the Unquiet Past and a Nest of Vipers. To start a game the GM and players select one Oracle to draw elements from, and then pick 4 cards (let's assume randomly) from a standard 52 card deck of playing cards. These cards are then matched up to references within the tables for each Oracle.

Let's assume (wrongly, but go with me on this) that the number of stories is the same as the number of sets of four elements that we can take. This being the case, our magic number can be found by multiplying

The Number of Oracles

times The Number of Ways One Can Draw 4 Cards from a 52 Card Deck

times The Number of Ways One Can Arrange 4 Cards

First and last things first: we have 4 Oracles - we've said that quite a few times! If you lay out four cards in an ordered row - any four, distinct cards - then you have 4 choices for what you put down first, 3 choices for what goes second, 2 choices for what you put in third place and only 1 choice for the last one (i.e., whatever card you have left in your hand).

The number of arrangements of 4 distinct objects is thus 4*3*2*1 = 24. In general we can use the notation n! to denote the arrangement of n objects (and we interpret this as "n factorial").

So, how many ways can we take 4 cards from a 52 card deck? Interpreting and explaining the notation is a matter of combinatorial maths, in particular combinations, and while it is not difficult it would take a bit of time to explain here. So if you're really interested, go and read it on Wikipedia!

In maths, if we want to count the number of ways of taking 4 distinct objects from 52 distinct objects then we can denote this as "52C4" which we could read as "52 choose 4". Again, looking at Wikipedia will tell you mathematically what that comes to.

But here we can now say that the number of set of elements from Oracles, and hence the number of stories in In A Wicked Age is:

4 Oracles times 270,725 card draws times 24 ways of arranging cards.

Which is 25,989,600 stories!!! AKA, lots!

While this makes for good maths fun times, I did state further up that there was an incorrect assumption with this process. The maths makes for interesting times, but the assumption that the number of sets of elements is the same as the number of stories is wrong. It has to be.

People interpret things differently. That's one underlying reason. Two days ago, when GMing, we had the element "the guardian of a tomb, a statue cast in silver with ruby eyes". I took that to be, and started coming up with ideas based around the statue BEING the guardian. One of my players, P, took it to be two provocations, that there was someone in the game who was a guardian, and that there was a silver statue with ruby eyes. Already, that's two ways of looking at things.

But:

• The statue could be like a golem, prowling the tomb.
• It could be that an eye is missing.
• It could be that the guardian is a man who pilots the statue like a mecha of some kind.
• The statue might not be humanoid (I definitely don't want to tick off a silver spider guardian).
• Or it might be really small, a foot high only.

There are all kinds of ways of taking these elements, these inspirations.

The maths of this is fun: in In A Wicked Age, the invention and creativity of making a story collaboratively is even more fun, both for GM and players.

Wicked Numbers

This week I played In A Wicked Age for the first time, and in doing so I GMed for the first time. I got my initial thoughts about the experience down on my tumblr account. TL;DR - I love the game, I loved my first time as a GM and can't wait for both again - possibly with me GMing In A Wicked Age.

One of the things that I think was really strong about the game was the use of Oracles for setting up the game. I'm really into creativity and creative thinking as a skills trainer, and so using random provocations is very familiar to me. Last night we seeded our game, and the characters who were in it, by taking inspiration from the Oracle for The Unquiet Past. The elements that we randomly took (using a deck of cards*) were:

• The guardian of a tomb, a statue cast in silver with ruby eyes
• The arrival of honored emissaries from a wealthy exotic land
• The son of a great tyrant, born crippled and denied his inheritance
• A new village built on the ruins of a forgotten people

From these, ideas for about a dozen characters or types of characters who might appear came really easily, and I think that we then had a lot of fun during the game taking these in all kinds of directions. At the start of the night I had no idea what might happen; at the start of the game I still had no idea where things might go. And that worked out really well.

There's something understated in some ways about the In A Wicked Age manual. I've not read hundreds of RPG manuals/sourcebooks, but those that I have generally have a couple of ideas for campaigns or stories. Some have clear and cool guidelines for setting up campaigns, scenes and settings. In A Wicked Age doesn't have any of those. It has something better. It has the Oracles.

It has millions and millions of stories in the manual. Millions and millions in a 37 page pdf.

How many millions? We'll get into that in the next post.

*playing cards from the Bellagio hotel in Las Vegas. That's how I roll!