The law of large numbers in trading and investing for non-statisticians

The law of large numbers is a theorem that describes the result of performing the same experiment a large number of times. According to the law, 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. [Wikipedia]

This law in trading and investing can be applied two ways:

To derive the true (expected) value from some tested event, we should gather as much event and its outcome(s) samples...