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Face image synthesis has progressed beyond the point at which humans can effectively distinguish authentic faces from synthetically-generated ones. Recently developed synthetic face image detectors boast ``better-than-human'' discriminative ability, especially those guided by human perceptual intelligence during the model's training process. In this paper, we investigate whether these human-guided synthetic face detectors can assist non-expert human operators in the task of synthetic image detection when compared to models trained without human-guidance. We conducted a large-scale experiment with more than 1,560 subjects classifying whether an image shows an authentic or synthetically-generated face, and annotating regions supporting their decisions. In total, 56,015 annotations across 3,780 unique face images were collected. All subjects first examined samples without any AI support, followed by samples given (a) the AI's decision (``synthetic'' or ``authentic''), (b) class activation maps illustrating where the model deems salient for its decision, or (c) both the AI's decision and AI's saliency map. Synthetic faces were generated with six modern Generative Adversarial Networks. Interesting observations from this experiment include: (1) models trained with human-guidance, which are also more accurate in our experiments, offer better support to human examination of face images when compared to models trained traditionally using cross-entropy loss, (2) binary decisions presented to humans results in their better performance than when saliency maps are presented, (3) understanding the AI's accuracy helps humans to increase trust in a given model and thus increase their overall accuracy. This work demonstrates that although humans supported by machines achieve better-than-random accuracy of synthetic face detection, the approaches of supplying humans with AI support and of building trust are key factors determining high effectiveness of the human-AI tandem.