Modern digitally-augmented boardgames have, with few exceptions, relied primarily on mobile devices rather than taking advantage of other components such as microcontrollers, sensors, and actuators. What alternative shapes might such games take? And what types of player experiences might such games support? To begin to map out answers to these questions, we collected information about how 31 hobbyist boardgame players envision interacting with technology in future analogue-digital hybrid games, using a rapid idea generation activity. We employed a qualitative content analysis approach to identify their envisioned game components, player interactions with these components, and game effects triggered by these interactions. From this analysis, we constructed a taxonomy of analogue-digital hybrid board games as envisioned by players. This paper uses the taxonomy to organise a detailed discussion of players' imagined interactions. This work thus contributes a player-centric exploration of the design space of hybrid digital-analogue games, with the aim of inspiring new, alternative approaches to boardgame design. Based on the taxonomy, we have additionally released a free and open-source ideation card deck to support new avenues into the design of future hybrid games.