We played this game at school. It was popular in many places of the
former USSR and was called something like football on squared
paper. I called the computer version "gridball". Alternative
names are welcome.
Computer doesn't think too far, in fact it counts only 2 moves ahead. So it's quite possible to win (if you know how to play, ha ha).
Latest updates:
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There exist a number of versions of the rules. The program supports the simplest version described above.