Social play involves a dynamic combination of competition and cooperation, yet few studies have systematically evaluated the cooperative side of play. We studied dyadic play in domestic dogs to investigate factors influencing variation in cooperative play strategies like self-handicapping and role reversal. Dyadic play bouts were videotaped and coded for asymmetric behaviours. We predicted that variation in play style would reflect salient aspects of the canine social system, including dominance relationships and age and size differences, but not sex differences. Our results refute the 50:50 rule proposed by some researchers, which asserts that participants must equalize their behaviour to maintain a playful atmosphere. We observed divergence from 50:50 symmetry to varying degrees across dyads. This variability was especially linked to dominance and age advantages, such that higher-ranking and/or older dogs generally showed higher proportions of attacks and pursuits and lower proportions of self-handicapping than their disadvantaged play partners. These results contradict the notion that more advantaged individuals consistently relinquish their advantage to facilitate play. Role reversals did occur, but certain social conventions apparently dictated which behaviours could be used during role reversals. For example, role reversals occurred during chases and tackles, but never during mounts, muzzle bites or muzzle licks, suggesting that these latter behaviours may be invariant indicators of formal dominance during play in domestic dogs. Play signalling was linked to self-handicapping behaviour but not to attack/pursuit behaviour, indicating that perhaps self-handicapping and play signalling work together to communicate playful intent and reinforce existing roles.