There are two basic approaches to generalize the propagation mechanism of the two-player Minimax search algorithm to multi-player (3 or more) games: the MaxN algorithm and the Paranoid algorithm. The main shortcoming of these approaches is that their strategy is fixed. In this paper we suggest a new approach (called MP-Mix) that dynamically changes the propagation strategy based on the players' relative strengths between MaxN, Paranoid and a newly presented offensive strategy. In addition, we introduce the Opponent Impact factor for multi-player games, which measures the players' ability to impact their opponents' score, and show its relation to the relative performance of our new MP-Mix strategy. Experimental results show that MP-Mix outperforms all other approaches under most circumstances.