The "From Dusk Till Dawn" Effect

(this could, I suppose, also be called the "Psycho" Effect)

(inevitably, spoiler alert)

When I was in my teens I watched From Dusk Till Dawn with my mum and dad. We put the video on reasonably late in the evening; by-and-by the film advanced as far as Clooney and Tarantino crossing the border and arriving at the Titty Twister. It was at this point, as it was late, that I went to bed. I hadn't seen the film before, but knew (roughly) what it was about.

What I did not know was that my parents knew nothing about the film. Nothing at all. My nan had cable TV and we did not, and she taped films indiscriminately, giving us a dozen films a month to watch (and then return, she liked to collect them). All my parents knew, at the point that I went to bed, was that Clooney and Tarantino were ruthless criminals, not averse to murder, kidnapping, robbery etc, and that they had arrived at a bar in the Mexican desert. They knew nothing of the plot that was to unfold from that point.

You can imagine their shock (and what they said to me the next day, as it had been my suggestion originally that we watch it).

I was musing on this today, and wondering about how this kind of shock might be put into a role-playing game. I'm not talking about a game of Cyberpunk where a bank job suddenly goes wrong: while you might have hoped that it would go well, it's not inconceivable that it would go wrong. I'm not talking about a game of D&D, where the sorcerer says, "I am your father."

My thought is about genuinely surprising players:

• vampires suddenly showing up in a bar, in a world which to all intents and purposes is completely normal;
• a player taking a shower, suddenly and brutally murdered, after successfully rolling persuade and evade so many times talking to cops and used-car salesmen, travelling across country with ill-gotten loot;
• a group of players suddenly discovering that one of their own has been the secret villain all along, a la Keyser Soze.

Being relatively new to the hobby, I don't know if there are any games that have similar mechanics; I don't know what would work well. I guess the key concerns - as a GM - would be knowing that your players could handle such a huge shift ("the game is no longer about hustling and stealing, it's about getting out of the city before the alien hunter killers find you"), and about setting up game mechanics - and player/character mechanics - that would realistically cover both genres seamlessly.

I have no idea if this would work - and having posted it online, I don't know if any future players might suspect I was going to do it if I got the chance to run a longer campaign. I just have this idea that if it was presented well it could provide a huge but satisfying narrative twist to a campaign.

Enough of me though: anyone out there got any thoughts/comments/ideas?

More Microscope

My friend P, from our gaming group, has put together a timeline of the space-time continuum that we built on Tuesday playing Microscope and posted it on his blog. Go and check it out, it's particularly cool I think, especially for paragraphs like this:

Karl-4 the Hyper-Neanderthal President of Humanity is persuaded to let Echelon VII lead the Ontological-Warhead strike by Stanislaw Brock the Grand Hierophant of Earth. Echelon VII will encode humanity in the Sun's Corona then seed Jupiter with self-creating nanoswarms that will transform the Jovian mass into a Hypermind that can re-constitute and recreate mankind. Sigmund Ross - Chief Warlock, and mutated psychic, and Augustus Schwarzkopf, 11-Star General of the United Military of Mankind, decide not to accept the offer and will stay and to fight to the death.

(yes, that really is how things played out; we took every single half-remembered hard sci-fi idea we had ever heard and spewed them out over the course of three hours)

Really looking forward to our first one-shot game in this shared universe now!

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

Games Night: Microscope

As we don't have a regular campaign/game running at the moment we decided to play Microscope last night. This was for two reasons:

1. It's a really great, engaging and fun game to play.
2. We're going to use the shared universe we created last night as the jumping off point for a series of one-shots and mini-campaigns that we're going to play over the coming months.

It was my third time playing, and again we started from scratch in our universe-building. It was the first time that we had played it as a whole group, but it didn't take too long before we settled in to the groove of establishing periods, then events and then launching into (often) crazy scenes. We were detailing a hard science, space opera, man reaches for the stars universe. For a flavour of things, this is what our "yes and no" lists looked like.

Yes

• Technological plagues
• FTL travel
• Geneered humans
• "Horrible costs for psychic powers"
• Mechs and powersuits
• F*cked up but explainable alien demons
• Artificial consciousness

No

• TNG humanoids ("no bumpy fore-headed aliens speaking English!")
• Terraforming
• Single biome planets ("welcome to desert world", "welcome to frozen world", "welcome to the land of hats!")
• Time travel (other than normal relativistic effects)

This was quite a departure from previous shared-world-building with Microscope, as previously we had always gone for more fantasy-style settings. It worked though, just as it had in the past. We had a really rich and varied timeline building up, with concentrations of interest around the first near-collapse of humanity (centring around very small, personal moments) and an incursion into our reality by Schwarm-Laden beings from beyond normal space-time. Imagine being on the bridge of the only starship, when a wave of 5 times 10^15 ships from beyond ab-reality arrives, too many ships occupying the same space, computers and space marines going insane...

Really, really good fun (so much so that two of us were crying with laughter at one role-played scene), and will lead in to next week's first one-shot/mini-campaign, based around the game GHOST/ECHO.

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!

TNG Season 8/In A Wicked Age Mashup

I've been thinking about Oracles since I had so much fun with In A Wicked Age last week. I cannot be the first person to think about them as a great way, not only of setting up one-shot games, but of developing campaigns, quests and the like in much longer games.

I've also really been loving the Twitter account, @TNG_S8, which are the always humourous, always plausible synopses of the continuing Season 8 adventures of the Enterprise-D. It hit me this morning when P and D from my game group retweeted a few that @TNG_S8 - or something very much like it - would make for a great game, and something which could be set up and played very, very speedily using the mechanics of In A Wicked Age.

There are six dice pools in In A Wicked Age, and I think that only a few of them would have to be renamed, if, for example, the player characters were restricted slightly to play Starfleet personnel. The mechanics would work exactly the same, rolling when in conflict, each character carrying a different strength. Data and Picard might be a bit too powerful for player characters (special strengths, Android and Captain respectively). Riker, Troi, Crusher and Geordi should all be fine, Worf too.

I'm not sure if this would be the most serious game in the world - but it would make for some interesting plots I think. And it could be interesting as well to play a game that was formatted a little like a genre TV show. noisms has told me about a game before which was a little like this - it was maybe called Primetime Adventures? I might have to check it out.

All in all, perhaps something worth tinkering with! I have other ideas running in the background about Oracle based games. There are so many settings which it could work well with; and I'm convinced that in terms of providing background events for a long running game it could be really, really useful. More thoughts on that another time perhaps.

Someone I Was

Chaplain was my Gunlugger in Apocalypse World. In other games he might almost be a Solo, or a Warrior. I think that in Apocalypse World's messed up future he might even be close to a Paladin (if you really, really squint). Maybe I am only seeing what I want to see. He was a damage sponge, things just didn't connect properly. He always tried to do the right thing, but according to his own rules of what was right.

Chaplain was the first character I ever created in a tabletop RPG (I leave aside a Mutants and Masterminds game noisms and I tried to play over Facebook messages). His first action in play was to draw a gun on someone who was beating up someone else in the street. It felt right, the more that I went on, that he was just trying to do the right thing - not necessarily for himself (to profit by things) but to ultimately keep other people safe. And most of the time, him being a Gunlugger, that meant having to do something violent. When he came into contact with a Hive parasite he argued his way out of being killed, put on a pair of gloves to avoid touching others, and then worked to see how long he could survive. Along the way he developed a small amount of psychic talent (via a Brainer move upgrade), which was explained away in-game as a gift of the Hive parasite.

I hadn't read the Apocalypse World manual when I realised something very clear: moves snowball (which is pretty much the exact term in the playbook). It wasn't obvious to me when I first started playing RPGs. There was a hangover from things like Final Fantasy X and the like, that you as a player have wiggle-room, but ultimately you're moving at the MC's pace. But of course, this isn't true - and I can't imagine playing an RPG now where it was the norm that you were forced to do X at location A, and then attempt Y at location B (proceed straight to set piece C).

Chaplain was someone I was. He didn't die at the end of the chapter actually, although for a time it looked like none of the characters would survive. He came out of it worse for wear, nowhere to live, no great possessions to speak of, but he was alive, the parasite was dead, and even his friends pretty much didn't like him (although I would like to think they realised just how useful he was). I'm not sure I would take him up as a character if/when we return to Apocalypse World, but I know he'll always be there, hiding in the background, waiting to walk back on-camera and go aggro.

Different Dice

I've been thinking about notation. A quick Google shows me that there are lots of people out there who are interested in probability questions with dice - and by extension with RPGs. Or perhaps that flows the other way, they are interested in games, and then start to get interested in how probabilities come from dice mechanics.

In either case, there are people out there who are interested in these areas. It's not my interest largely (when it comes to maths and RPGs) but it is definitely a good place to start, and one that throws up interesting points. Dice have different contexts. Rolling 2d6 in Apocalypse World, when you want to know the sum, gives you a value from 2 to 12, and those 11 values are distributed unevenly. In this case, you don't really care what either of the dice actually gives. You care about the total.

Rolling two d6s when you care about the values of each dice gives you a different proposition. Picture having a red d6 and a blue d6. Rolling 2 on red and 5 on blue results in something different from 5 on red and 2 on blue. Rather than have 11 values given by the sum of the faces, we have 36 possibilities, each with the same probability of occuring.

For future posts then we can consider 2d6 in the normal way and, to be clear, two d6 for the situation when we care about each individual result on the two d6s. Or three d8s. 3d10 is different from three d10s. A numeral in front of a die size will indicate that we want to sum them, a number in words will indicate that we want to use each result from the dice.

All sound fine? It might be a basic sort of thing to write about, but this is the foundations: important in games (of all kinds) and maths. On foundations we can extend outwards, upwards and in as many ways as can be supported.

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!

Roll 2d6

There's a lot more to tabletop role-playing games than dice-rolling. A lot more. Role-playing is about inhabiting a character, thinking the way they might do, telling a story with others, playing a game.
Oh yeah, and hopefully having a good time while doing it.

I started playing tabletop role-playing games in autumn 2011. In the last six months or so I've played Apocalypse World, Cyberpunk, D&D, Microscope and In A Wicked Age. It was while playing AW that I started thinking about the maths associated with some of the mechanics in games.

AW has you roll 2d6 for actions. Depending on what stat you are rolling with you have a modifier (generally) from -2 to +3. It dawned on me at one point that my character - a Gunlugger - would have to roll a 2 or a 3 in order to outright fail at an aggressive action.

With that being the case, questions come my way: should I steer my Gunlugger towards violence, as he'll succeed? Should I steer him away from violence to make things more interesting? What do other people think?

As a mathematician I know that maths is everywhere. Including tabletop role-playing games. And not just in terms of the statistics of dice rolling. And so the idea for this blog came about. I don't know exactly what I'll write about, although I have some ideas. I'll talk about some maths, some actual play, some setting ideas and some game mechanic/rule ideas.

I hope you find something interesting here!