How to clamp a value from 0 to infinite to a value from 0 to 1?

Question

I have a program in Java that generates a float value aggressiveness that can be from 0 to infinite. What I need to do is that the higher this float is, the higher there are chances the program fires a function attackPawn().

I already found out that I need the function Math.random(), which gives a random value between 0 and 1. If Math.random() is lower than aggressiveness transformed into a float between 0 and 1, I call the function attackPawn().

But now I am stuck, I can't figure out how I can transform aggressiveness from 0 to infinite to a float which is from 0 to 1, 1 meaning "infinite" aggressiveness and 0 meaning absence of anger.

Any ideas or math equation?

Answer 1

You want a monotonic function that maps [0...infinity] to [0..1]. There are many options:

    y=Math.atan(x)/(Math.PI/2);
    y=x/(1+x);
    y=1-Math.exp(-x);

There are more. And each of those functions can be scaled arbitrarily, given a positive constant k>0:

    y=Math.atan(k*x)/(Math.PI/2);
    y=x/(k+x);
    y=1-Math.exp(-k*x);

There is an infinite number of options. Just pick one that suits your needs.