In several fish species with paternal care, females prefer males guarding many eggs in their nest. This preference might be advantageous because the presence of many other eggs dilutes the risk of newly laid eggs being eaten by the father. To evaluate this hypothesis quantitatively, we constructed a simulation model that mimics the breeding biology of the blenny Aidablennius sphynx. In contrast to earlier verbal models, the costs of choice are explicitly taken into account. We systematically varied factors such as the stringency of choosiness and the level and nature of the costs of choice. For realistic parameter values female choosiness mali result in a fitness advantage of more than 50%. The optimal choice strategy created a distribution of eggs over the nests which resembles that found in the field for A. sphynx. Our model shows that the relative fitness of a choice strategy is not constant but frequency dependent in a complicated way. If most females are choosy a bimodal distribution of eggs over the nests results, with many nests containing few and some nests containing many eggs. In such a situation choosiness is profitable, since randomly laying females will often lay their eggs in nests with few eggs, producing a high mortality per egg due to filial cannibalism. If, on the other hand, only few choosers are present, their influence on the egg distribution is limited. A unimodal distribution results which is profitable for nonchoosers, since the average egg mortality is low and nonchoosers do not bear the costs of choice. The positive relation between chooser frequency and chooser fitness makes it easy to understand why choosiness is evolutionarily stable. However, it is not obvious how the trait is established by selection in the first place.