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 law 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 (see the gambler 's fallacy).
in reference to the quality of a sample the law of large numbers (a huge sample) guarantees
stable long - term results for the averages of some random events