Few cultural practices beyond language are as widespread as string figure games. Their global distribution and potential to yield insights into cultural transmission and cognition have long been noted. Yet, it remains unknown how or when this behavior originated and to what extent shared motifs are signals of repeated innovations or deep cultural transmission. Here, we combined a global cross-cultural inventory of string figures with a novel methodology based on knot theory, which enables the unequivocal numerical coding of string figures. We performed a computational analysis of a sample of 826 figures from 92 societies around the world. Across these societies, we found 83 recurring string figure designs, some of which are regionally restricted while others display a global distribution. The cognitively opaque nature of string figure designs and their clear geographic distribution reveals processes of cultural transmission, innovation, and convergent evolution. Most strikingly, the global distribution of some figures raises the possibility of shared ancient origins.