This paper considers the problem of designing efficient AI strategies for playing games at intermediate board states. While general heuristic-based methods are applicable for all boards states, the search required in an alpha-beta scheme depends heavily on the move ordering. Determining the best move ordering to be used in the search is particularly interesting and complex in an intermediate board state, compared to the situation where the game starts with an initial board state, as we do not assume the availability of “Opening book” moves. Furthermore, unlike the two-player scenario that is traditionally analyzed, we investigate the more complex scenario when the game is a multi-player game, like Chinese Checkers. One recent approach, the Best-Reply Search (BRS), resolves this by a process of grouping opponents, which although successful, incurs a very large branching factor. To address this, the authors of this work earlier proposed the Threat-ADS move ordering heuristic, by augmenting the BRS by invoking techniques from the field of Adaptive Data Structures (ADSs) to order the moves. Indeed, the Threat-ADS performs well under a variety of parameters when the game was analyzed at or near the game’s initial state. This work demonstrates that the Threat-ADS also serves as a solution to the unresolved question of finding a viable solution in the far-more variable, intermediate game states. Our present results confirm that the Threat-ADS performs well in these intermediate states for various games. Surprisingly, it, in fact, performs better in some cases, when compared to the start of the game.