  Clearly, the property of large numbers is a necessary condition for randomness of a sequence. It is not sufficient, however. Consider the sequence 10101010…. This sequence is not biased. But it is clearly not random either, as it develops in a completely regular and predictable fashion. So we need to impose additional constraints. Each of these constraints will be another property of stochasticity we should expect of a random sequence, including all other such limit properties of ‘unbiasedness’.