So we see the law of large numbers applies as the mean of a fairly accurate sample moves towards the mean of the population (in this case the overall customers) very slowly. The law of large numbers is the foundation of such business enterprises like gambling casinos and insurance companies.The winnings (or losses) of a gambler on a few plays are uncertain - that's why gambling is exciting. If you take 100 gamblers and make 100 observations the mean of the sample is not very close to mean of the population, it is only in the very long run that the mean outcome is predictable. The house plays tens of thousands of times so the the house unlike individual gamblers can count on the long run-regularity described by the law of large numbers. Hence the average winnings the house on tens of thousands of plays will be very close to the mean of the distribution of winnings which translates effectively to say that the mean guarantees the house a profit and that's why gambling like insurance is usually a profitable business. At the end of the day the odds are always stacked up against the consumer.

Thoughts,

Sam Kurien