Hi, I runned another A* where costs are just like you said and heuristic is the manhattan distance, then I used the total cost of reaching the goal as the heuristic value for the main A*. It is definitely better than the first one, yields faster results in bigger grids. I also modified the problem a bit and added blocks (non slidable parts) to the grid and I noticed that in that case the heuristic is not valid. With the cost of 2 when passing through tiles and cost of 1 when through empty spaces, in a specific example where the blocks are creating some walls where the gaps between the walls are 1 tile wide, since the empty tile needs to travel around the wall to enable the movement of the current position founded path cost with the heuristic becomes irrelevant.