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

So far, I don't think anyone has addressed a key point of your question: how do you come up with a good "quality value"? In AI, the quality value you refer to is usually called a "heuristic". Ideally, your heuristic would tell you exactly the minimum number of moves required to reach the finish, given the current position/velocity. In reality, we have to settle for something that's easier to compute.

One important guideline is that a good heuristic should be admissable; that is, it should never overestimate the cost of reaching the goal (in your case, the number of moves to reach the finish). The A* algorithm depends on having an admissable heuristic.

A common technique for coming up with an admissable heuristic is to relax the original problem. In games, you can often do this by changing the game so that it becomes easier (e.g. by dropping rules). In RaceTrack, for example, you could straighten out the track to make it an easier game. With a straight track, the best strategy is clearly to just continuously accelerate. Thus, an admissable heuristic is to compute the distance from the current position to the finish (i.e. the length of the straightened-out track) and then compute the number of moves required to travel that distance assuming constant acceleration.

You can come up with other heuristics by relaxing different rules, but there is often a trade-off between the accuracy of the heuristic and the amount of computation required.