Considered was combinatorial actions' winners determination problem (WDP) with computational complexity.  Bidding strategies of VCG mechanism were studied.  Two types of essential probabilities is presented to indicate bidders' belief in WDP algorithm and the effects on his/her value on the allocation efficiency.  Some deterministic relationships among the two probabilities, ex-post winning utility, ump bidding increment and bidding strategies in the VCG were explained by using the models and corresponding propositions.