In the resource-rich grid computing environment, there are plenty of idle resources that compete for similar tasks. In order to make resources gained the maximum benefit, a guarantee of victorious probability algorithm (GVP) based on game theory is presented in this paper. This algorithm predicts the action of adversaries based on historical information, and determines its own action based on the forecast. We use GridSim toolkit to implement a resource-rich environment and verify our algorithm through experiments. The experimental results show that the resources using GVP algorithm can be close to their expectation of victorious probability comparing with the other resources using the random algorithms. The two-player game and multi-player game are discussed and a more in-depth analysis is made. Finally the Nash equilibrium of game among resources is also discussed.