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We consider opportunistic spectrum access (OSA) strategies for a transmitter in a multichannel wireless system, where a channel may or may not be available and the transmitter must sense/probe the channel to find out before transmission. Applications for this work include joint probing and transmission for a secondary user in a cognitive radio network. Limited by resources, e.g., energy and time, the transmitter must decide on a subset of a potentially very large number of channels to probe and can only use for transmission those that have been found to be available. In contrast to previous works, we do not assume the user has a priori knowledge regarding the statistics of channel states. The main goal of this work is to design robust strategies that decide, based only on knowledge of the channel bandwidths/data rates, which channels to probe. We derive optimal strategies that maximize the total expected bandwidth/data rate in the worst-case, via a performance measure in the form of a competitive regret (ratio) between the average performance of a strategy and a genie (or omniscient observer). This formulation can also be viewed as a two-player zero-sum game between the user and an adversary which chooses the channel state that minimizes the useriquests gain. We show that our results correspond to a Nash equilibrium (in the form of a mixed strategy) in this game. We examine the performance of the optimal strategies under a wide range of system parameters and practical channel models via numerical studies.