Motivated by a real-life situation, we put forward a model and then derive an optimal strategy that maximizes the expected real-estate selling price when one of the only two remaining buyers has already made an offer but the other one is yet to make. Since the seller is not sure whether the other buyer would make a lower or higher offer, and given no recall, the seller needs a strategy to decide whether to accept or reject the first-come offer. The herein derived optimal seller's strategy,

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... maximizes the expected selling price, is illustrated under several scenarios, such as independent and dependent offers by the two buyers, and for several parametric price distributions.