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?
The great thing about maths (or one of them, at least) is that results are cumulative. Pythagoras (or someone he didn't attribute) only had to prove his most famous theorem about right-angled triangles once, and then the result stands forever. The re-proving in classrooms now is merely to try and introduce people to mathematical thinking. The theorem is a brick and when combined with lots of other bricks you can build incredible structures...
Back to Fighting Fantasy. Before you can build a structure that shows the likelihood of surviving a book, you have to think about the likelihood of your character surviving a fight. Before you can do that you have to think about the probability of winning a single round of combat.
This is where I am headed at the moment; in a future post I'll write some maths out clearly and scan it in, rather than try and typeset things here. Results I have: probabilities of winning a single round of combat; a formula which calculates the probability of surviving a fight (and killing your foe). I found out some interesting things along the way too.
However... As ever there are caveats. Pythagoras' Theorem only works with right-angled triangles. And these results only work if you discount the influence of LUCK in a fight. And these results don't tell you what STAMINA your character will be on when you finish a fight - that's a separate question altogether.
It may be, actually, that that is the question which needs an answer, more than the questions I'm currently trying to answer. With problem-solving in general, not just in maths, it's often not until you start trying to find a solution that you realise you're answering the wrong question.
NB: Of course, I have no idea if anyone else out there has done this important work* before. If they have, I'm still thinking that I might find something new and interesting.
*I am under no illusions that this line of enquiry lacks any kind of point. The maths is just interesting to me.