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Real-time heuristic search is a challenging type of agent-centered search because the agent's planning time per action is bounded by a constant independent of problem size. A common problem that imposes such restrictions is pathfinding in modern computer games where a large number of units must plan their paths simultaneously over large maps. Common search algorithms (e.g., A*, IDA*, D*, ARA*, AD*) are inherently not real-time and may lose completeness when a constant bound is imposed on per-action planning time. Real-time search algorithms retain completeness but frequently produce unacceptably suboptimal solutions. In this paper, we extend classic and modern real-time search algorithms with an automated mechanism for dynamic depth and subgoal selection. The new algorithms remain real-time and complete. On large computer game maps, they find paths within 7% of optimal while on average expanding roughly a single state per action. This is nearly a three-fold improvement in suboptimality over the existing state-of-the-art algorithms and, at the same time, a 15-fold improvement in the amount of planning per action.