The design and analysis of strategies for playing strategic board games, is a core area of Artificial Intelligence (AI) that has been studied extensively since the inception of the field. However, while two-player board games are very well known, comparatively little research has been done on Multi-Player games, where the number of self-interested, competing players is greater than two. Furthermore, known strategies for multi-player games have difficulties performing on a level of sophistication comparable to their two-player counterparts. The premise of this thesis is the hypothesis that game playing in general, and the problem of multi-player games in particular, can benefit from efficient ranking mechanisms, for moves, board positions, or even players, in the multi-player scenario. The research done in this work confirms the hypothesis. Indeed, we have discovered that this information can be applied to improve game tree pruning, and within other possibilities. In this thesis, we observe that the formerly-unrelated field of Adaptive Data Structures (ADSs), which provide mechanisms by which a data structure can reorganize itself internally in response to queries, can provide a natural ranking mechanism. The primary motivation of this thesis is to demonstrate that the low-cost ADS-based data structures can provide this ranking mechanism to game playing engines, and furthermore generate statistically significant improvements to their efficiency. In this work, we will conclusively prove that ADS-based techniques are able to enhance existing multi-player game playing strategies, and perform competitively with state-of-the-art two-player techniques, as well. We demonstrate, through two general-use, domain independent move ordering heuristics, the Threat-ADS heuristic for multi-player games, and the History-ADS heuristic for both two-player and multi-player games, that ADSs are, indeed, capable of achieving this improvement. We present an examination of their performance in a very wide range of game models and configurations. We thus conclusively demonstrate that ADSs are able to achieve strong performance, in game playing engines, in the vast majority of cases. Our work in this thesis provides not only these domain-independent, formal move ordering heuristics, but furthermore serves as a strong example for future investigation into combinations between the fields of ADSs and game playing.