Dogs in the Vineyard, Session 2

Last week we left things with Sister Basemuth (Patrick), Brother Caleb (David) and Brother Paul (Steve) at the farm; they've tracked down Newton's kidnappers, Cornelius and Nate, but they're too late - Newton has been strangled to death...

...or has he?! The slight trace of breath is in him, and so they perform ceremonies to call him back, to tell him that his time has not come - and it works. They save the boy.

Dogs in the Vineyard, Session 1

Last night was the first outing for Dogs in the Vineyard in our group, and I was GMing. It was the first time any of us had played it, but I think that despite a couple of head-scratching moments with the mechanics (more on those later) it was a good evening.

We started out with character gen; it took a little while because of thinking about potential with relation to the setting (it's late August, 1851), but after a bit of thinking we arrived at:

• Patrick, playing Sister Basemath Armstrong, a fearless and funny Dog with a Strong Community background. During her initiation she corresponded with a geologist and was able to satisfy both him and the public that dinosaur bones had been left behind in Noah's Flood.
• David, playing Brother Caleb Romney (a distant relation perhaps), a Well-Rounded Dog who is able to employ a coldly logical perspective, track people and he's also pretty handy with a gun. During his initiation time he unfortunately failed to capture a criminal, but this has now spurred him on.
• Steve, playing Brother Paul Usher, a Dog with a Complicated History - not raised in the Faith, but a part of it now. He's rugged, stubborn and has all the traits that you might expect from a western gunslinger. During his initiation he saved a child from a burning building.

After initiations and descriptions of their coats they were given their commission by Brother Emmanuel from the Dog's Temple: go out on a long journey to the southern-most valley where the Faithful live. It's a long time since Dogs have been through that part of the world; give the Stewards letters, help the communities as you see fit and do whatever you have to do to keep the Faith strong in the towns.

We join the Dogs as they come up to a farm outside of the town of King's Bridge.

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.

Ready For Battle

Whatever comes my characters' way, they can handle it! Aside from the orange d20, the other dice have been collected over the last few months, just a few per week. The local games cafe usually has a good selection in colourful dice, and it's been good fun to build them up bit by bit. I could do with maybe getting  a few more d20s, and then I'll have a neat little gang to play with.

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.

Tracking Ammo

I've been throwing ideas around for a zombie game for ages, ever since I heard of All Flesh Must Be Eaten but was too cheap to buy it.

I circle around hacking games that I already know about - Risus, In A Wicked Age, Apocalypse World - and would want to use Liverpool as a setting because (a) that's where I live, and (b) I think it would be neat to have big city centre maps that get updated over time to show what has happened where - where there are road blocks, where other survivors might be etc. I'm still testing ideas out on paper with different systems, and aim to share these as time goes on.

Anyway, that's all preamble. The thing that I want to share is an ammo tracking mechanism. I thought it might be a nice halfway house between the "infinite ammo until you really fail a roll" that I have experienced in Apocalypse World and the "track every single bullet you fire" of Cyberpunk.

(not that there is anything wrong with either of these, of course)

Ammo is by default very rare. A gun has a rating from 0 to 6. After each time a character fires their gun (by whatever in-game mechanism that has) they roll a d6:

• If they roll higher than or equal to their current rating, they reduce their rating by 1.
• If they roll less than their current rating they stay on that rating.

So, if a person starts with a 6 their clip/magazine etc is effectively full. As time goes on, after every roll they make, the chances are that they are going to have less and less ammo in their gun. When the rating gets down to 1 they know that the very next time they shoot the gun it will be out of ammo.

I think that this mirrors the way that hit points and damage were presented to me in the past: when you have only lost one hit point, that's like a scratch or a graze; when you're down to less than a quarter you could be in serious trouble. In the same way with ammo, on a 4 you have let some shots off but you're alright; if you're in a pitched battle and your shotgun has a 2 rating you had best find a way out of the danger zone.

Anyway, I'm sharing this for a reason: what do you think? Any thoughts? Any tweaks?

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!

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.