Random Number Distribution

Chart Type: 3D
In probability theory, the law of
large numbers (LLN) is a theorem
that describes the result of performing
the same experiment a large number of times.
According to the law, the average
of the results obtained from a large
number of trials should be close
to the expected value, and will
tend to become closer as more
trials are performed.
        
The LLN is important because it "guarantees"
stable long-term results for the averages
of some random events. For example, while
a casino may lose money in a single spin
of the roulette wheel, its earnings will tend
towards a predictable percentage over a large
number of spins.
Any winning streak by a player will eventually
be overcome by the parameters of the game.
It is important to remember that the LLN only
applies (as the name indicates) when a
large number of observations is considered.
There is no principle that a small number of
observations will coincide with the expected
value or that a streak of one value will
immediately be "balanced" by the others.
Source: Wikipedia
Random Distribution (interactive + google charts)
