Permutations w in Sn for which the (type-A) Schubert variety Ωw is smooth are characterized by avoidance of the patterns 3412 and 4231. The smaller family of codominant permutations, those avoiding the pattern 312, seems to explain a lot about character evaluations at Kazhdan-Lusztig basis elements C'w(q) of the (type-A) Hecke algebra. In particular, for every Hecke algebra character χ, and every 3412-, 4231-avoiding permutation w, there exists a codominant permutation v such that χ(C'w(q)) = χ(C'v(q)). Moreover, these character evaluations can be computed by playing simple games with unit interval orders P = P(v) corresponding to the codominant permutations. We generalize these facts to the hyperoctahedral group Bn using signed pattern avoidance and an appropriate analog of unit interval orders.