A board game of the type which combines the use of a game board having a playing surface divided into large numbers of subunits with one or more playing pieces which are movable over the playing surface from subunit to subunit during the course of a game in order to achieve a particular objective. The game includes a random movement piece movable periodically in an unpredictable manner during the course of the game and one or more counters for each player which are also movable periodically during the course of the game. The object of the game is for a player to move his counters so as to interact with the random movement piece in a specified manner and to then move the counters to an exit position on the game board, and the first player that moves all of his counters to the exit position wins the game.