Whether to forgive is a key decision supporting cooperation. Like many other evolutionarily recurrent decisions, it is made under uncertainty and requires the trade-off of costs and benefits. This decision can be conceptualized as a signal detection or error management task: Forgiving is adaptive if a relationship with the "harmdoer" will be fitness enhancing and not adaptive if the relationship will be fitness reducing, and the decision should be biased toward lowering the likelihood of the more costly error, which depending on the context may be either erroneously not forgiving or forgiving. Building on such conceptualization, we developed two cognitive models and examined how well they described participants' forgiveness decisions in hypothetical scenarios and predicted their decisions in recalled real-life incidents. We found that the models performed similarly and generally well around 80% in describing and 70% in prediction. Moreover, this modeling approach allowed us to estimate the decision bias of each participant; we found that the biases were generally consistent with the prescriptions of signal detection theory and were directed at reducing the more costly error. In addition to testing mechanistic models of the forgiveness decision, our study also contributes to forgiveness research by applying a novel experimental method that studied both hypothetical and real-life decisions in tandem. These models and experimental methods could be used to study other evolutionarily recurrent problems, advancing understanding of how they are solved in the mind.