Easily determining which urns are 'favorable'

The optimal sampling strategy for an urn, containing known numbers of plus and minus ones, can be simply described with the use of an empirically justified rule, based upon what appears to be a legitimate third-order asymptotic expansion of "the optimal stopping boundary" as the urn size goes to infinity performs exceedingly well. There is a known first-order asymptotic expansion due to Shepp. The reader is invited to try to justify a second-order asymptotic expansion of a type described by Chernoff and Petkau. The evidence presented in its support is very persuasive.