Abstract: Embodiments of the present invention include an almost limitless number of board games, based on the familiar children's game Tic Tac Toe, that include dice or other random-play-generation means used by players to partly and/or completely select plays, and also include the game environments on which the game embodiments are played Players alternate in employing the random-play generator to select a next move, placing a labeled token, inscription, or other indication on a region of the game board when the selected move involves occupying a game-board region. A game embodiment of the present invention can be played by a single player against one or more imaginary, or virtual opponents, and can be played by two or more players, each player employing tokens or inscriptions that uniquely identify the player. Play continues until a winning player's tokens occupy a defined set of board regions, such as a set of laterally, vertically, or diagonally adjacent board regions that together span the game board.