Hi 2+2=5,
You wrote:
Spew away
Weeeeeeeell ok then, this information may be old hat to you and I apologize in advance. If you asked a mathematician, scientist, engineer or man child (me) about randomicity and stochastic systems, the first question they should ask is: What is the probability distribution of the outcomes, which reduces to the problem of the probability that a particular event will occur.
For example say you have a fair six sided die. What is the probability of getting the number four?
Well that's sort of obvious, its 1 chance in a possibility of 6 outcomes or to put in simple mathematical terms: P=1/6 (16.667%)
What if you added a second die? Well you can get at minimum the number 2 (two ones) and the maximum of the number 12 (two sixes). So the probability of a particular outcome is 1 in 11. Right? Well actually no. The moment you have multiple events which are summed, the probability is different for each possible outcome.
How does this work?
To get a two, you need a 1 and a 1.
To get a three you need to throw a 1 and a 2 or you could throw a 2 and a 1.
To get a four you could throw a 1 and a 3, a 3 and a 1, or a 2 and a 2.
So there are 36 possible combinations that you can throw with a set of 2 dice, which affects the probability as follows:
So with a pair of dice, you're most lightly to throw the number 7 at 17% probability and the lowest is 2 or 12 at 3%. The more dice you add, the more the Probability distribution will start looking like a bell curve. This is famously the normal or Gaussian distribution, which can be discrete or continuous:
Sooooo... what if you had a set of 5 dice, with 45 sides each and you threw them all together and viewed the outcome as a summed event (as was done with the set of 2 dice)?
Continue?