This paper establishes a resource-rich environment of the grid computing at first, and then put forward a new type of grid resource competition algorithm in the environment. There are plenty of idle resources that can complete the similar task in the resources-rich grid computing environment, hence how these resources can gain the maximum benefits are discussed here. This paper presents a Guarantee of Victorious Probability algorithm (GVP), which can predict the action of an adversary through historical information, and determine its action based on the forecast. This is the essence of the game theory and this algorithm. The results of experiments show that the resource using GVP can be close to their expectations of victorious probability compare with the other resource using the random algorithm. The game of two resources using GVP is also discussed and the final victorious probability remain at 0.5. In this paper, a more in-depth analysis of the phenomenon is made, and the Nash Equilibrium of two-resource game is also discussed.