CPE/CSC 480 Lab Exercise 6

This lab exercise is about games. We will use a variation of the n-in-a-row game, where you need to align pieces in horizontal or vertical connected areas. Two players take turns placing their pieces on a grid, and the first one to have n in a row wins. This is similar to the Connect Four game, but a few differences differences: Pieces aligned diagonally do not count, the playing field is infinite (no boundaries), and gravity does not play a role here. It is derived from a game called "Simple" described by Dennis Shasha, a computer science professor at New York University, and the author of the "Puzzling Adventures" column in Scientific American.

N-in-a-Row Questions

• Give an example of an evaluation function for the board positions in this game, and explain why it reflects the most important aspects of the current state of the game (i.e., who is at an advantage, and how significant is the advantage).
  
  

• For this game, is it possible to reduce the branching factor of the search tree by eliminating board positions that are permutations?

Three-in-a-Row

The objective in this version is to place three pieces in a row vertically or horizontally.

Questions

• Is it possible for the first player to force a win? Explain your answer!





• Construct the tree for this game based on the mini-max method. Indicate places where alpha-beta pruning can be used to eliminate branches that will not be taken by a rational player.

Four-in-a-Row

The objective in this version is to place four pieces in a row vertically or horizontally.

Questions

• Is it possible for the first player to force a win? Explain your answer!





• Construct a partial tree for this game based on the mini-max method. Indicate places where alpha-beta pruning can be used to eliminate branches that will not be taken by a rational player. Your tree should explore eight plies (levels) with the most significant moves by each player.