Assume for simplicity that each letter in the n-letter string is i.i.d. i.e, that you see the letter A w.p p_A, B w.p p_B, ..., Z w.p p_Z, and sum of p_A to p_Z is equal to 1. Then as n grows large, you expect to see n*p_A occurences of A, etc. if it is truly random. Essentially you are checking to see if the sequence is one of a "typical set", which is defined as all sequences whose empirical entropy is within epsilon wiggle room of the true entropy. So in this case you could declare with high probability that the string of letters is random if its entropy is close to the entropy of the true distribution. You can extend this to non-i.i.d. sources.