If I remember correctly from my college AI days, thinking about upcoming turns and minimizing your opponent's gains is called minimax: http://en.wikipedia.org/wiki/Minimax

I'm surprised that there was only one AI in the competition that did this. We were all expected to use this strategy in my class. Once everybody's figured this out, it becomes a game of:

- Who can think ahead the most turns? - Who has the best "am I winning?" heuristic function? (For Mancala this function is fairly obvious, but for many games it's not.)