SYS611A HW1

(c) 2 pts Using words, explain the logic that determines whether a Tic-Tac-Toe model state contains a tie. (d) 2 pts Implement the Tic-Tac-Toe is tie derived state function in a modeling tool (e.g. Python or Excel). Inspect the model state and display a boolean True or False . 1.3 Modeling a Board Game as a Simulation [12 points] Chess is a very old board game described as 1 : a two-player, abstract strategy board game that represents medieval warfare on an 8x8 board with alternating light and dark squares. Opposing pieces, tradi- tionally designated White and Black, are initially lined up on either side. Each type of piece has a unique form of movement and capturing occurs when a piece, via its movement, occupies the square of an opposing piece. Players take turns moving one of their pieces in an attempt to capture, attack, defend, or develop their positions. Chess games can end in checkmate, resignation, or one of several types of draws. (a) 3 pts What is the elementary model state for chess? Describe it in su ffi cient detail to allow someone to create a mathematical (symbolic) model. ( hint: what information is required to “save” a game and later recreate it? It may help to reference an image. ) (b) 4 pts Using words, explain the logic that determines the following derived state func- tions for chess in terms of the elementary state in (a): (i) get num pieces which counts the number of remaining pieces owned by a player. (ii) get valid moves rook which lists cells to which a particular rook could move. (iii) is check which determines if the current player is in “check” (king under attack). (iv) is checkmate which determines if the current player has lost. (c) 3 pts Using words, describe how following state changes modify the elementary state in terms of variables in (a): (i) capture piece : Captures one of the opponent’s pieces (ii) move piece : Moves one’s own piece to a new cell (iii) promote pawn : Promote a pawn that has reached the last row (you may need to research this rule) (d) 2 pts Draw an activity diagram to show the chess game progression from start to end with the following simplified set of actions: choose valid move , capture piece , move piece , next player turn and derived state variables: is move capture (checks if a move results in a capture), is checkmate 1 https://boardgamegeek.com/boardgame/171/chess Copyright c 2022 Paul T. Grogan 2 Creative Commons BY-NC 4.0 License