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).

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?

Games Night Supplemental

Rather than edit my last post, I just wanted to add two points that were really good about the house rules last night IMO. These both came via Patrick who was GMing.

First was our equipment; I've mentioned before, and Patrick has too, this idea of using a certain number of syllables to generate your equipment. Last night he tied it into a person's Charisma stat, which seemed to work really well I think. My Charisma of 11 was enough to get me

• Long knife
• Blow gun
• Cloak
• Kit bag
• Specialist tools

I.e., whatever a person who was escaping from a sinking ship might actually have on them (their most valuable and useful possessions and nothing more).

Second was the rules for unmemorised magic that I did mention in the AP post. The magic user had their one Level 1 spell as normal, which they could use as and when they wished, but then had the option of trying to perform "unmemorised magic" - it may work, it may not, you might get the magic missile that you want or you might cause your hands to turn to cheese. Using 2d6 plus a person's Intelligence modifier gave a fast and useful way to keep the magic user pivotal, but not overpowered. With a modifier of +1, as my nephew had last night, the character has about a 28% chance of total success, and still has a pretty good chance of getting a lesser success (getting the desired outcome but also something unfortunate happens). Not too powerful, but powerful enough to really help turn the tide.

Patrick showed me these rules a few months ago, and I thought they were great at the time - especially with the section full of names for what a person is as a magic user - Magician, Wizard, Incantrix, etc.

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?