The one-parameter logistic model with ability-based guessing (1PL-AG) has been recently developed to account for effect of ability on guessing behavior in multiple-choice items. In this study, the authors developed algorithms for computerized classification testing under the 1PL-AG and conducted a series of simulations to evaluate their performances. Four item selection methods (the Fisher information, the Fisher information with a posterior distribution, the progressive method, and the adjusted progressive method) and two termination criteria (the ability confidence interval [ACI] method and the sequential probability ratio test [SPRT]) were developed. In addition, the Sympson–Hetter online method with freeze (SHOF) was implemented for item exposure control. Major results include the following: (a) when no item exposure control was made, all the four item selection methods yielded very similar correct classification rates, but the Fisher information method had the worst item bank usage and the highest item exposure rate; (b) SHOF can successfully maintain the item exposure rate at a prespecified level, without compromising substantial accuracy and efficiency in classification; (c) once SHOF was implemented, all the four methods performed almost identically; (d) ACI appeared to be slightly more efficient than SPRT; and (e) in general, a higher weight of ability in guessing led to a slightly higher accuracy and efficiency, and a lower forced classification rate.