Due to the inevitable defect of information and the limited rationality of human, grey number becomes a very important and useful tool to describe the pay-off matrix of game. Corresponding, the comparison of grey numbers without additional information becomes the key way to search the equilibrium of grey game. From the thinking and decision-making habit, and from the initial idea of grey potential degree, the conception system of Grey Potential Degrees, including Grey Superiority Potential Degree, Grey Inferior Potential Degree and Grey Total Potential Degree of two grey numbers is built up in this paper. The Judgment Rules of Grey Total Potential Degree are presented and the totally ordered Characteristic of set of Grey Total Potential Degree is proved. Furthermore their distribution and implications are discussed, and the relationships of grey numbers are presented in figures respectively. It is concluded that Grey Potential Degree, which is put forward based on the key factors of grey number, can be used to general grey number which has two basic features, interval center and length. Grey Total Potential Degrees are good reflection of the relative positional relationship between the two grey numbers and the conception and model of Grey Total Potential Degree are reasonable and scientific. Finally, the paper finds out the Optimal Pure Strategy of Grey Potential Pure Strategy of Static Grey Game by the way of Grey Total Potential Degree. Example presents the application of Grey Total Potential Degree. It is found that Grey Total Potential Degree is a useful tool to solve grey game.
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