<P> 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 ) . </P>
<P> 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 ) . </P>
in reference to the quality of a sample the law of large numbers ( a huge sample ) guarantees
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
stable long - term results for the averages of some random events