combinatorics problem-number of game outcomes

Question

There are m concentric circles, and n straight lines through the center point, intersecting each concentric circle at 2n points. Let the outermost two adjacent intersections be A and B. Alice and Bob now want to play a game where starting from A and B. Rolling the dice for each round,player with bigger points takes one step and the other stays still. Whoever goes to the center first wins. You can take one step along a straight line or the same circle at a time. To make the game more interesting, it is stipulated that each person must walk at least k steps (k < n) along circle (may not be the same circle), and each intersection can only be walked once.Consider all possible game outcomes(even outcome with foolish strategy. Sort the outcomes by the form of the paths of Alice and Bob) with equal probability. Write a program to calculate the probability that Alice will win. note:we will consider, let's say Alice wins and terminate the game, not only when Alice reaches the central point, but also when Alice blocks Bob's all possible ways to the centre. If they block each other. We consider they break even and the game is also over.