Archerfish are well known for their specialized hunting technique of spitting water at prey located above the water line. This unique ability has made them a popular focus of study as researchers try to understand the mechanisms involved in targeting and spitting. In more recent years, archerfish have also become an increasingly popular model for studying visual discrimination and learning in general. Until now, only the alternative forced-choice (AFC) task has been used with archerfish, however, they may be capable of learning other classical discrimination tasks. As well as providing alternative, and potentially more efficient, means for testing their visual capabilities, these other tasks may also provide deeper insight into the extent to which an organism with no cortex can grasp the concepts underlying these tasks. In this paper, we consider both the matched-to-sample (MTS) and the odd-one-out (OOO) tasks as they require the subject to learn relatively sophisticated concepts rather than a straight, stimulus-reward relationship, of the kind underlying AFC tasks. A variety of line drawings displayed on a monitor were used as stimuli. We first determined if archerfish could complete the MTS and OOO test and then evaluated their ability to be retrained to new stimuli using a 4-AFC test. We found that archerfish were unable to learn the MTS and had only a limited capacity for learning the OOO task. We conclude that the MTS and OOO are impractical as paradigms for behavioral experiments with archerfish. However, the archerfish could rapidly learn to complete an AFC test and select the conditioned stimulus with a high degree of accuracy when faced with four stimuli, making this a powerful test for behavioral studies testing visual discrimination. In addition, the fish were able to learn the concept of oddity under particular training circumstances. This paper adds to the growing evidence that animals without a cortex are capable of learning some higher order concepts.