The ‘haplodiploidy hypothesis’ argues that haplodiploid inheritance in bees, wasps, and ants generates relatedness asymmetries that promote the evolution of altruism by females, who are less related to their offspring than to their sisters (‘supersister’ relatedness). However, a consensus holds that relatedness asymmetry can only drive the evolution of eusociality if workers can direct their help preferentially to sisters over brothers, either through sex-ratio biases or a pre-existing ability to discriminate sexes among the brood. We show via a kin selection model that a simple feature of insect biology can promote the origin of workers in haplodiploids without requiring either condition. In insects in which females must found and provision new nests, body quality may have a stronger influence on female fitness than on male fitness. If altruism boosts the quality of all larval siblings, sisters may therefore benefit more than brothers from receiving the same amount of help. Accordingly, benefits of altruism would fall disproportionately on supersisters in haplodiploids. Haplodiploid females should be more prone to altruism than diplodiploid females or males of either ploidy when altruism elevates female fitness especially, and even when altruists are blind to sibling sex.