In probability, the law of large numbers means that 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. Â This law 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 law of large numbers that will bring the net gains and losses back to an average.