Tables for testing randomness by means of length of runs

As one of the non-parametric tests, there is a test of randomness by means of runs, which is an application of combinatorial probability theory. Suppose that there are some elements of two kinds A, B. Let the numbers of A's and B's be m and n respectively. When these (m + n) elements are arranged in the order, the total numbers of Aand B-runs are denoted by r and s, and the numbers of A-runs of length 1, 2, • • , m and of B-runs of length 1, 2, •-• , n are denoted by r1, r2 • r„, and s1, s2, •-• , s„, respectively. Of course, the following equalities must hold,