A Scrabble Heuristic Based on Probability That Performs at Championship Level

Abstract

The game of Scrabble, in its competitive form (one vs. one), has been tackled mostly by using Monte Carlo simulation. Recently [1], Probability Theory (Bayes’ theorem) was used to gain knowledge about the opponents’ tiles; this proved to be a good approach to improve even more Computer Scrabble. We used   probability to evaluate Scrabble leaves (rack residues); then using this evaluation, a heuristic function that dictates a move can be constructed. To calculate these probabilities it is necessary to have a lexicon, in our case a Spanish lexicon. To make proper investigations in the domain of Scrabble it is important to have the same lexicon as the one used by humans in official tournaments. We did a huge amount of work to build this free lexicon. In this paper a heuristic function that involves leaves probabilities is given. We have now an engine, Heuri, that uses this heuristic, and we have been able to perform some experiments to test it. The tests include matches against highly expert players; the games played so far give us promising results. For instance, recently a match between the current World Scrabble Champion (in Spanish) and Heuri was played. Heuri defeated the World Champion 6-0 ! Heuri includes a move generator which, using a lot of memory, is faster than using DAWG [2] or GADDAG [3]. Another plan to build a stronger Heuri that combines heuristics using probabilities, opponent modeling and Monte Carlo simulation is also proposed.