Randomness and Game Design by Keith Burgun
Using that article as a springboard for this one, I've known since the 7th grade that random events are mathematically impossible. There's always parts to the equation. The more random something might seem, the more complex the equation might be. Of course all of this is relative and difficult to define. Some people believe in fate, some in willpower and determination.
I define random as an event that has the appearance of unpredictable. This is why Math.Random number functions work so well in programming - they're specifically designed to produce an unpredictable result. When we see the event enough times or we look into how the event breaks down, we find the pattern and therefor destroy its randomness.
When someone swings an axe at a tree numerous times, each swing is directed towards the same area and comes from the same direction. Likewise, when an arrow is shot at a target it follows the same rules as the axe. The equation for the result might include things like wind speed, air temperature, altitude, the person's strength, what materials the object is made of, how many times it has been used, if the person has done the action one time or one hundred times, is the person angry or calm or focused or distracted, etc. For our two examples: the axe hits with differing force at various angles and displaces a seemingly random amount of wood each time; the bow flexes a predictable amount, and the arrow's accuracy depends on the steadiness of the archer - the arrow may still land in seemingly random spots relative to the target's center. Even if we built machines to do these actions for us specifically to remove some of the unpredictability, there would still be some randomness left regardless. In math, the amount of randomness would be the standard deviation. Since the deviation is smaller with the machine, the random element can essentially be refined out to such a small amount that we would no longer detect it.