Minimax Homework

The purpose of this homework is to have you play with alpha-beta pruning.
  1. Make up two player game with at least two turns for each player.  On the first two turns, there must be at least three possible actions.  Suppose that player 1 goes first.
  2. Find the minimax value for the game for player 1.
  3. Either by writing a computer program or by computing the solution on paper, show how many nodes need not be visited to find player 1's minimax value when you use alpha-beta pruning.
  4. Switch the order that you expand nodes and repeat the previous problem.  (For example, on the online minimax notes the algorithm expands u1 first and then u2; if I switch the order that I expand nodes then I would expand first u2 and then u1.) Show how many nodes need not be visited when alpha-beta pruning is used.
Since I won't be able to see all of your code (if you chose to program), make sure that your discussion justifies your answer.  Pretend that you are writing an essay on an exam and that you must convince me that not only can you generate an answer but also that your answer is right.