AI algorithm for “RaceTrack” game

Question

does anyone know (or can suggest) a good algorithm for an AI for the RaceTrack pencil-paper game?

since you have 9 possible choices in each step and you need to look

Answer 1

I'd propose that you start by reversing the problem. Use retrograde analysis (like they do in chess endgames http://en.wikipedia.org/wiki/Retrograde_analysis) to calculate backwards from the end, assuming you are the only player, to see how many steps are needed to cross the finish line, given a position and velocity. If my thinking is correct, the time to calculate this should be linear in number of positions. Should be very quick.

It will not be the absolute truth, since you have competitors disturbing your path, but it will give you a very good heuristic for your search algorithm.