By the balancedness of the 3-spinner considered, it suffices to give two of the three numbers written on the spinner to uniquely identify the spinner. However, the same spinner has different names in this way, like (3,-2) and (-1,3) and (3,-1) would all refer to the same 3-spinner with the numbers 3, -1, -2 written on it. To get uniqueness, we apply the convention to write the numbers of a spinner in nondecreasing order, and omit the third one. Therefore, the name of the 3-spinner mentioned above would be (-2,-1).
Assume each player brings five balanced 3-spinner to the game: (-4,-1), (-2,-2), (-1,0), (-3,1), and (0,0). Each player selects one of these five spinners simultaneously. The question is, which sppinner should be selected?
Solution: Take 1/3 of (-2,-2), 1/6 of (-1,0), and 1/2 of (-3,1).