Alright, I'm not one to complain too much, but I need to get this off my chest.
Woe is me.
Woe
Is
Me.
Okay so first off, I have to say I've never been good at maths. I hated that in highschool, and ended up with a college curriculum designed to avoid that topic as much as possible. Never saw any value in it when I was younger.
As I left college, and went on with my life, I found myself a passion for imagining how foreign and distant universes would look like. This is what drove me to Dwarf Fortress by a matter of fact. But it also drove me to find myself finding ways to design random universes and set of rules for tabletop rpg games, so as groups of players could play an original adventure each time without needing a GM. The universe would have to
• Make sense
• Be fair
• Be new each time
Among my researches on systems that has been proposed, I finally found one I liked that would fit my checklist. But after a couple of test runs, I discovered that the system was unbalanced. It would make sense and create new situations, but it wasn't fair so I decided to try and fix it.
Problem now : that involves maths. I banged my head repeatedly over the problem of the explosive dice the system was using. Basically when you roll a 6, you roll another dice and you add the new number to the 6. If you roll another 6, you roll another dice, potentially to infinity. How can I measure the average of a potentially infinite dice ? I needed that average, but it felt to the imbecile I was, totally impossible.
Yesterday however I learnt a property of convergeant functions. Convergent functions, it appears, have a finite value. 1/6^1+1/6^2+1/6^3+[...]1/6^n actually have a value.
So I calculated that value, and was left with a number. I tried to toy with it. I knew the answer was here. The average of the explosive dice was right here. Me, who suck at maths all my life, was finally given by fate an occasion to redeem my honor, to reconcile my passion with what I need to fullfill it. And it was just, right there, slightly out of reach.
I had all the pieces of the puzzle. x/2+1 is the average of the x sided dice. 2 is the result of my function. Now what do I do with that.
Tried to multiply, divide, substract, nothing worked to my satisfaction.
And today I was given the answer : 4.2
4.2 was the average I tried to achieve. How could I have been so wrong
I went back to my notes. Compared it with the demonstration. Everything fitted. I fucked up somewhere. Couldn't figure out where.
Then I tried to see the relations between 4.2 and x/2+1 (3.5 in this case). 4.2/3.5=1.2, so basically 3.5+(3.5*0.2) = that damned average.
Then I redid all my maths.
It appeared I read the wrong number on my calculator. 0.2 was the result of my convergeant function, not 2. I could have figured it out by myself. Yet I didn't.
Woe is me.