A system for determining the skill of a player eliminates the element of chance by comparing players who have the same initial position. In the case of cards, the initial position is the hand dealt to the player and in tile games, it is the initial distribution and arrangement of tiles. A player with a less than advantageous initial position may win a game over an opponent having a better initial position. It cannot conclusively be said whether this win is due to the good play of the winner or the bad play of the loser. However, it can clearly be said that the winning player has a higher skill level than the losing player.