I have a card game that I am analyzing with Maple. Actually, it's a series of card games, one for every parameter k, where k is a natural number (representing the number of ranks of cards used in the game). For small k, it is feasible to completely solve the game by reverse induction. I am trying to create an AI that will play optimally from this.
Given a winning position (and it being the computer's turn) the computer can answer easily with any move that takes the position to a losing one for the player. However, what to do with a losing position? Of course, picking a random move is a terrible strategy. Is there some way to make life very difficult for the human player? One idea I had was to make it choose a move that maximizes the length of the minimum path needed for the player to win the game. That would seem to avoid getting into all the psychology of what human weaknesses are in the game etc.
I am aware that this problem is completely general (does not depend on the game). However, I had difficulty finding good references. Does anyone have any references for someone interested in learning about AI in this setting?