(I have seen this question but it is too complicated for my needs, and my math skills are not good enough to convert the answer.)
I am writing a game and I need a way to increase the armor of the character in a meaningful way: I want the increase in armor to mean a decrease in damage taken (meaning an increase in damage absorbed), approaching but never reaching 100% absorption. In other words, I need a simple, polynomial function f(x) so that $\lim\limits_{x \to \infty} f(x) = 1$ (x will never be less than zero.)
Of course, the question has trivial answers, like f(x) = 0.9; I need a non-trivial one, preferably one where f(x) grows faster at first and then "slows down".
[Edit] Removed the polynomial requirement... duh!
[Edit] I found something stupidly simple... $x / (x + 5)$ This is close enough to my requirements. Unfortunately, I have absolutely no idea how to allocate the "solution" checkmark, so I'll pick the responder with less points, and add a +1 to the other. I hope it won't create problems.