Exact approximation of average subword complexity of finite random words over finite alphabet

One of the ways to measure the random nature of a word is to evaluate the quantity of different subwords in it. Such a measure is called the subword complexity or complexity index. Direct interdependence between subword complexity and the state of chaos is intuitively obvious. In this article we develop an explicit formula suitable for approximation of the average subword complexity of the most chaotic–random–words.