Qubic

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This article is about the board game. For the cosmological experiment, see Qubic experiment.

Qubic is the brand name of a four-in-a-row game played in a 4×4×4 matrix sold by Parker Brothers starting in 1953.[1] The original box, and the 1972 reissue, described the game as "Parker Brothers 3D Tic Tac Toe Game". Players take turn placing pieces to get four in a row horizontally or diagonally on a single board—or vertically in a column or diagonal line across four boards.

The four boards were made of clear plastic (in a simple square design in the original release and in a funkier design for the 1972 reissue) with circular playing pieces that resembled small poker chips in red, blue, and yellow; each player used a single color. Markers could be placed in any unoccupied position, rather than stacked in a pile on a square as in Score Four. The game is no longer manufactured.

Either two or three players could participate in a game. In two-person play, the first player will win if there are two optimal players. There are 76 winning lines. The 16 positions lying at the 4 space diagonals (8 corners and 8 internal positions) are equivalent and each involved in 7 winning lines; the other 48 positions (24 face positions and 24 edge positions) are also equivalent, each being involved in four winning lines. (The equivalence of a corner and an internal position is via an inversion; likewise for a face and an edge position.) The game was weakly solved by Eugene Mahalko in 1976, Oren Patashnik in 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 four stacked trapezoids. It was later ported to the HP 2647 demo tape with a graphical interface, using a simple mathematical transform to solve for 3D input position. It also was included in the Microsoft Windows Entertainment Pack in the 1990s as part of TicTactics.

Fool's Mate strategy

The cube structure makes the 8 corner-points and 8 centre-points extremely important; each of these is a member of 6 planes (flat, 2×vertical, 2×diagonal-vertical, 1×cross-vertical) of 16 points. O places his first peg A on one of the 16 powerpoints provided that X does not place his peg at a powerpoint then the second B on one of the 5 available powerpoints; the third peg C goes on one of the three available planes, which include A and B. X cannot block all these options. Once A, B and C are placed there is a forced win after a further 5 pegs.

.A...x3....3....B .1....5.....2....w x1...x2....4..... .C........x4....w

See also

  • Tic Tac Toe
  • Score Four
  • 3-D Tic-Tac-Toe (Atari 2600)

Notes

  1. ↑ United States Patent and Trademark Office

References

  • Eugene D. Mahalko, A Possible Win Strategy for the Game of Qubic, Computer Science Master's Thesis, Brigham Young University, 1976
  • Oren Patashnik, Qubic: 4 x 4 x 4 Tic-Tac-Toe, Mathematics Magazine 53 (1980) 202–216
  • 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.

External links

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