The following programs apply Findler's version of polynomial learning (with aggression) and a modified version of Findler's generalization learning to the game of Score-Four.
Score-Four is similar to tic-tac-toe except that it is three-dimensional, with a win achieved by gaining for-in-a-row in a single plane.
Findler's generalization technique built up a table of all possible board positions and respective moves.
Move selection then, consisted of table lookup and thus did not use an Alpha-Beta look-ahead procedure.
Even though the table was reduced by removing board positions that were symmetrically equivalent, table size was still excessive.
Even though Findler's generalization technique does not rely on skilled opponents to achieve significant learning, it does depened on polynomial learning to achieve significant results.
These programs, on the other hand, only store board positions that directly lead to wins.
This reduction in table size is great enough to allow table lookup to be employed by the Alpha-Beta look-ahead heuristic.
The result is a generalization technique that does not rely on skilled opponents to achive significant learning, and does not use polynomial learning to achieve significant results.
A statistical analysis is applied to the results to determine the relative merits of polynomial learning (with and without aggresion) and generalization (with and without polynomial).
Utilities:
Play two games with Alpha and Beta alternating the first move.
Apply the learning algorithm to different sets of coefficients.
Play a game of Score Four against a human.
Determine the symmetry of trap patterns.
Measure time for Polynomial and Generalized learning heuristics.
Measure time for Score Four moves.
1.4.5