Qubic

Abstract: This thesis describes a program which was written for the TX-0 computer to play the game of Qubic. The game is a three dimensional form of Tic-Tac-Toe with four squares on each side. The game is finite but at present unsolvable, as about 1025 different games are shown to exist.

The program uses rather standard lookahead and evaluation techniques, but employs a forcing lookahead to a depth of 12 to detect winning positions. This strategy is a major factor in the program's success.

A system of "opponent analysis" is also used in which the program is able to distinguish between different human players. The program will drastically modify its line of play in each game by consulting a record of the results of previous games against this opponent. Over a hundred games were recorded with the machine winning over 80%.

Appendices include: a discussion of symmetry and a derivation of all symmetries of the game; a calculation of the total number of possible positions and possible games; a mathematical description of the game as employed in the program; a discussion of forcing win situations and a description of all "three in a place" possibilities; and a move by move analysis of several actual games.