Feller gives the PMF for the number of runs, but not the mean and variance, if that helps. Let M be the number of +s and N be the number of -s. Let (M)C(N) = M!/N!(M-N)!. Then for integer v,

P(2v) = 2.(M-1)C(v-1).(N-1)C(v-1)/(M+N)C(M).

P(2v+1) = {(M-1)C(v).(N-1)C(v-1)+(M-1)C(v-1).(N-1)C(v)}/(M+N)C(M).