A tire (100) rolls on a surface (105). A method (600) for providing maximum traction coefficient between the tire (100) and the surface (105) include steps for detecting a momentary slip of the tire (100) on the surface (105); detecting a momentary traction coefficient; forming a tuple (410, 510) from the slip and the current traction coefficient; choosing a characteristic curve (205, 305) from a number of predetermined characteristic curves (205, 305) on the basis of the tuple (410, 510), whereby each characteristic curve (205, 305) describes a traction behavior of the tire (100) or a corresponding characteristic pitch; determining the maximum traction coefficient on the basis of the selected characteristic curves (205, 305); and thus providing the maximum traction coefficient.