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Classical planning aims to find a sequence of actions, a plan, that maps a starting state into one of the goal states. If a trajectory appears to be leading to the goal, should we prioritise exploring it? Seminal work in goal recognition (GR) has defined GR in terms of a classical planning problem, adopting classical solvers and heuristics to recognise plans. We come full circle, and study the adoption and properties of GR-derived heuristics for seeking solutions to classical planning problems. We propose a new framework for assessing goal intention, which informs a new class of efficiently-computable heuristics. As a proof of concept, we derive two such heuristics, and show that they can already yield improvements for top-scoring classical planners. Our work provides foundational knowledge for understanding and deriving probabilistic intention-based heuristics for planning.