Score Four
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Score Four is an abstract strategy game that is basically a 3-D version of Connect Four. The object of Score Four is to position four beads of the same color in a straight line on any level or any angle. Beginners will often overlook a simple threat to score four; it is therefore important to always check all vertical, horizontal and diagonal possibilities before making a move.
In a score four game in progress, one aims at forcing a win by making two threats simultaneously; conversely, one should prevent the opponent from doing so. As a general rule, discs played in the center columns are more valuable than border columns, because they participate in more potential four-ball lines (and accordingly limit the opponent's score four opportunities and his chances of winning).
Among good players trying to score four, the short term goal is to connect three balls, thereby preventing the opponent from playing in a certain column. Towards the end, the game then often turns into a complex counting match: both players try to score four by forcing the other to play a certain column. In these situations, it is useful to realize that, if it's your move, then after filling an even number of places, it's still your move. Every column has an even number of places.
The first player will win if there are two optimal players. There are 76 winning lines. It was weakly solved by Oren Patashnik (1980) and then solved again by Victor Allis using proof-number search. A plotter based 3D computer game was written by Arthur Hu and Carl Hu in 1975 on a HP 9830 in Lindbergh High School . It used 4 stacked trapezoids. It was later ported to the HP 2640 HP 2647 demo tape with a graphical interface, using a simple mathematical transform to solve for 3D input position. It also was included in a Microsoft Windows Game Pack in the 1990s.
[edit] See also
- Unit cubic
- Connect Four
- Tic Tac Toe
- Solved game
- Qubic
[edit] References
- Oren Patashnik, Qubic: 4 x 4 x 4 Tic-Tac-Toe, Mathematical Magazine 53 (1980) 202216
- L.V. Allis, P.N.A. Schoo, Qubic solved again, in: H.J. van den Herik, L.V. Allis (Eds.), Heuristic Programming in Artificial Intelligence 3: The Third Computer Olympiad. Ellis Horwood, Chichester, 1992, pp. 192-204.
