Law of Large Numbers

There are many schemes and systems that people claim can make you a big winner at the casino. But what these people fail to see is the reason why casinos are lucrative money-makers; the odds are always on the casino's side, ensuring that the casino will come out ahead and always win (in the long run). What the casinos have come to depend on is something called the law of large numbers.

Before we figure out how the casinos always make themselves winners in the long run, we need to define several terms. The first is sample average, or sample mean. The sample mean is what everybody thinks of when they think of the average. You calculate the sample mean by adding up the results and dividing by the number of results. Let's say we flip a coin 10 times and it comes up heads 7 times. We calculate the sample mean, or the average number of heads per flip, like so:

Figure 9.1: Formula for sample mean

The sample average is typically denoted...