Example - piece heuristic wherein the piece count is obtained from a mask on the state. In many (most?) games the set of moves that can set/reset a particular base prop from this masked set will be a fixed set of moves, and furthermore these moves will ALWAYS set/reset these props if they are played (e.g. - move queen e1 e2 will always clear the queen-at-e1 prop and set the queen-at-e2 prop, as well as ALWAYS clearing the anything-else-at-e2 props). In such cases it is possible to construct an action heuristic from the state heuristic.
The motivation is that application of an action-based heuristic is much cheaper since you do not need to calculate the next state for the action in order to assess its heuristic value. In particular this makes the heuristic applicable to use within rollouts. Breakthrough is probably a good test game.
Example - piece heuristic wherein the piece count is obtained from a mask on the state. In many (most?) games the set of moves that can set/reset a particular base prop from this masked set will be a fixed set of moves, and furthermore these moves will ALWAYS set/reset these props if they are played (e.g. - move queen e1 e2 will always clear the queen-at-e1 prop and set the queen-at-e2 prop, as well as ALWAYS clearing the anything-else-at-e2 props). In such cases it is possible to construct an action heuristic from the state heuristic.
The motivation is that application of an action-based heuristic is much cheaper since you do not need to calculate the next state for the action in order to assess its heuristic value. In particular this makes the heuristic applicable to use within rollouts. Breakthrough is probably a good test game.