The law of large numbers is a statistical principle that states as the number of trials or observations increases, the average of the results will get closer to the expected value. This means that if you flip a fair coin many times, the proportion of heads and tails will approach 50% as the number of flips grows. This law is important in fields like probability theory and statistics, as it helps predict outcomes in various scenarios. For example, in gambling, understanding this law can inform players about the long-term results of their bets, emphasizing that short-term results can be misleading.