Problem solving in a materially rich environment requires interacting with chance. Sixty-four participants were invited to solve 5-letter anagrams presented as movable tiles in conditions that either allowed the participants to move the tiles as they wished or only allowed random shuffling (without rearranging the tiles post shuffling) thus contrasting pure luck with an interactive model. We hypothesised that shuffling would break unhelpful mental sets and introduce beneficial unplanned problem-solving trajectories. However, participants performed significantly worse when shuffling, which suggests luck (...) plays less of a role than has been previously suggested. Granular analysis of seven critical cases revealed arbitrary path dependency across both conditions and moments of missed luck. It also questions current models of non-agentic luck and the ability to separate agent and luck. This research has implications for fostering better problem solving in an uncertain and fluid world. (shrink)