Balancing play can be important for engaging people in games since it allows players with different skills and abilities to play together and still feel challenged. Balancing play in exertion games has mainly been explored by challenging the physical effort. To further our understanding of how to design for more balanced experiences, we extend this prior work by studying the affect on player’s score by a score handicap. This gives the less skilled player an initial score advantage. A performance handicap was also studied by asking the most skilled player to play with the non-dominant hand. We studied digital and non-digital table tennis games, which provide different game interactions, as examples of non-parallel, competitive games. Our results show that these different game interactions influenced the impact the different handicaps had on player’s scores. Therefore, we suggest the game interaction is a key element to understand the suitability of score and performance balancing methods.