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

Others recommend A*, which is probably the way to go, but there is a problem with that approach. Let me first say that the 'cost' of going from one node to another is always 1, as you want to minimize the number of steps, there simply is not other cost involved.

But the important point I want to make is that a location (x,y) is not a unique node in the search graph of A*! The node is characterized by x and y, but also by the x and y coordinates of the node the car is coming from(or by the velocity components vx and vy if you will). So you cannot just traverse the A* algorithm over a 2 dimensional grid; it should actually be 4-dimensional. That said, A* is probably still the way to go.

As for the heuristic, you could get really creative about that one, but I suggest something like distance to finish minus current velocity, where the distance is precalculated for each point in the regular 2D grid(use a Dijkstra algorithm for that). This makes the A* algorithm search first towards the finishline and preferably as fast as possible. I believe such an algorithm would do very well to calculate the entire route immediately.

One problem though, is that A* will always yield the optimal route, so an AI using such an algorithm wouldn't be fun to play against, as it would always win(assuming the startingpositions are fair).