You should look at the basics of AI and various search algorithms.
The first priority would be to quickly pick up the vocabulary: what is a state, what is a utility function and so on.
I recently took a class on AI and we used the (rather popular) Artificial Intelligence: A Modern Approach by Russell and Norvig [1]. I didn't actually read the book, but I've heard good things about it so it's definitely worth a look.
All the lectures for the course are available online as well[2]. The professor my semester (Dan Klein) was a brilliant lecturer, so the lectures are worth watching if you have the time. The lecture notes[3] are also online.
Of course, if you want to participate in this game, you are doubtless in a hurry. So you might want to skim through lectures 2, 3, 6, 7, 10, 11 in roughly that order--they seem to be the most pertinent.
Combinatorial game theory would be the wrong tool for this, I believe, since this isn't a strictly finite turn-based combinatorial game. (And in my opinion combinatorial game theory is more useful for analysis and proof techniques than for creating AI algorithms, but I've only had one class on it.) The blog mentioned "fruitwalk-ab" uses minimax (with the alpha-beta optimization of course), which is the bread-and-butter algorithm for these kinds of games and I expected it to be in 1st place. Sure enough, it is at the moment. (Edit2: No longer.)
In an intro machine learning course you'd learn about minimax and others, but skip paying any money and just read the basic algorithms here and look up the wiki pages for even more examples: http://www.stanford.edu/~msirota/soco/blind.html (The introduction has some term definitions.)
Thanks for the info, interesting stuff. I've got more first-gen minimax going right now, sorta works but gets stuck in a repeating move pattern. Interesting stuff to work on though, i really appreciate the pointers. Hopefully this weekend i can work out a better heuristic valuation of a game state, for a first run i'm just counting my objects vs theirs(very simple), but i need to somehow weight it such that it prefers picking objects up sooner than later. And of course it would better match if it also took into account groupings, but thats for after i get basic board-clearing working.
