Let L = (onsite + offsite) / onsite. Then, given a certain bet distribution D, whether an investor (or the house as a whole for that matter) is +EBG or -EBG is solely determined by L. Specifically, there will be an L* such that for all L < L* the investor is +EBG and for all L > L* the investor is -EBG. Whether the offsite is real or not has nothing to do with this. Furthermore, given the current structure of the bankroll on BaB, there exists a legal (ie in conformance with the rules/limits) bet distribution D such that a player using D will be at +EBG.