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The recently-proposed channel-adaptive multiple-input multiple-output (CA-MIMO) detection significantly reduces the average complexity of MIMO detection. Aiming at the just-acceptable error rate (JAER), the detection methods are switched according to the channel condition. In this letter, we formulate the switching of detection methods as a multiple-choice knapsack problem (MCKP). Then, based on the linear relaxation MCKP, the lower and upper bounds of the potential complexity saving of CA-MIMO are derived, where the former comes from our proposed switching strategy. The simulations show that the lower and upper bounds are tightly matched, demonstrating our two contributions: the evaluation of the optimal performance of the CA-MIMO detection without solving the NP-hard MCKP, and the design of an efficient and practical switching strategy.