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).