Abstract: The invention is directed to a system and a method for generating game pieces and movement sequences. The game pieces are used in a game of chance having a predetermined number of winners with respect to the movement sequences. By way of moves determined by randomly selected movement sequences, a player's marker is directed from a start position to an end position on a game piece. The method involves selecting the vertical difference (number of grid sections) between the start and end positions on the game piece, dividing the game pieces into parts and preferably randomly generating a series of marker moves for each part of the game piece. The series of marker moves, when applied to a game piece, results in a player's marker traveling from the start position to the end position. The system includes a computer arranged to generate and store the series of marker moves which, when applied to a game piece, causes the player's marker to travel from the start position to the end position.