Scoring a board configuration for a territory board game is often not straightforward and yet there is a desire to determine such scores quickly and accurately. For example, in the game of GO, determining the score at the end of the game involves assessing whether stones on the board are alive or dead which is a difficult judgment. Given a board configuration, the game is played by a scoring system to obtain a terminal board configuration. This is repeated to obtain a plurality of terminal board configurations from which an assessment can be made as to how likely each board position is to be won by a particular player at the end of the game. The scoring system obtains the terminal board configurations by playing random moves or by making a biased sampling of moves. The biased sampling is made using an evaluation function or in any suitable way. In the game of GO, seki positions are quickly and easily identified. An automated game playing system uses the output of the scoring system to assess when to offer to end a game. The output of the scoring system can also be used to provide hints to players during a game.