This thesis discusses a formula to reconstruct the P-position of three-pile Fraenkel game by using mex operator. P-position is a dynamic position where a gamer can decide his victory. The result shows that P-position of three-pile Fraenkel game is a series (An;j ,Bn;j ,Cn;j), with the value of An;j is the smallest positive integer which does not exist in (Ai;j ,Bi;j ,Ci;j) with 0 ≤ i < n, whi…