I have a little problem with understanding of the concept of independent identically distributed random variables. Random variable is a function that assigns some values to the all events from sample space. If I roll the dice then I have one random variable available, because there are numbers on the sides of if, so there is an assignment. No I understand that if i want to have another random variable then I should create another assignment ... so for example I can assign +2 to every wall. So I have two independent identically distributed random variables ... one which assigns values from 1 to 6 and second which assigns values between 3 and 8 ... right?
Then if I roll the dice five times in two series, and I use the same wall-value assignment can I treat every series as different random variable, so data from first series are independent identically distributed random variables from data from second series or should I treat it as one random variable? Can random variable be treated as series of data ?
I ask because central limit theorem says that distribution of the average of $n$ iid is close to normal distribution, so if I want to achieve this distribution I should always use different random variables, or simple different series of data with the same event-value assignment function ?