Human economic transactions are based on complex forms of reciprocity, which involve the capacities to share and to keep track of what was given and received over time. Animals too engage in reciprocal interactions, but mechanisms such as calculated reciprocity have only been shown experimentally in few species. Various forms of cooperation, for example food and information sharing, are frequently observed in corvids, and they can engage in exchange interactions with human experimenters and accept delayed rewards. Here, we tested whether crows and common ravens would reciprocally exchange tokens with a conspecific in an exchange task. Birds received a set of three different types of tokens, some valuable for themselves, that is, they could exchange them for a food reward with a human experimenter, some valuable for their partner and some without value. The valuable tokens differed between the birds, which means that each bird could obtain more self‐value tokens from their partner's compartment. We did not observe any active transfers, that is one individual giving a token to the experimental partner by placing it in its beak. We only observed 6 indirect transfers, that is one individual transferring a token into the compartment of the partner (3 no‐value, 1 partner‐value and 2 self‐value tokens) and 67 “passive” transfers, that is one subject taking the token lying in reach in the compartment of the partner. Individuals took significantly more self‐value tokens compared with no‐value and partner‐value tokens. This indicates a preference for tokens valuable to focal individuals. Significantly more no‐value tokens compared with partner‐value tokens were taken, likely to be caused by experimental partners exchanging self‐value tokens with the human experimenter, and therefore, more no‐value tokens being available in the compartment. Our results presently do not provide empirical support for reciprocity in crows and ravens, most likely caused by them not understanding the potential roles of receiver and donor. We therefore suggest further empirical tests of calculated reciprocity to be necessary in corvids.