MDP discussion 4

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Southern New Hampshire University *

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370

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Computer Science

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Feb 20, 2024

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 Design a set of states, rewards, and rules for an intelligent agent playing a simple board game. You may choose any board game that you are familiar with. In your design, be sure to consider the following: o States, including starting and ending states, and possible actions o Rewards or penalties for reaching a state o Rules for navigating from one state to another  Compare your approach to the Markov Decision Process (MDP) that you learned about in this module. What similarities and differences do you see between your approach and the MDP? Hello class, A simple board game I have chosen to design for an intelligent agent is a board game I like to play is the game of chess. The game of chess is a board made up of an 8 X 8 grid, 64 alternating-colored squares of black and white with 16 chess pieces having six different functions within the game. The goal of chess is to checkmate your opponent or have the opponent surrender. The starting state of chess is the complete configuration of board pieces of black and white. Possible actions are how the intelligent agents control the chess pieces. Each chess piece has its own designed function as pawns can move only forward. On the first turn they can move two spaces forward or one, but on every turn after the first turn they can only move one space. Rooks can move only horizontally and vertically anywhere if they are not blocked, bishops can only move diagonally on their adjacent color, queens can move anywhere on the board, knights can jump over pieces while only moving two squares vertically and one square horizontally or vice versa, and kings can only move one space in any direction. The action of the game is to move a chess piece to a spot on the board and also take the opponent’s piece. The rewards of chess are when a player takes the opposing player’s piece and punishment is when the opponent takes a player’s piece. Each time a piece is moved, or a piece is removed from play a new state occurs for chess as they are different possibilities and outcome from the game from the different moves. The end state of a chess game is when either the player or opponent gets checkmate or surrenders as they are no more available moves. My approach is similar to Markov Decision Process (MDP) as the state is the configuration of the chess board and its pieces. Action is the possible move a player can make. Each move corresponds to a possible action in MDP. Transition Probabilities occurs as each action taken a new state occurs. Every time a player makes a move, that function defines the probability distribution over possible next states. It describes how the system transitions from one state to another based on the chosen action of the player. Rewards are similar as rewards can be based on the outcome of the game, winning or losing, and rewards within the game as goals are to capture chess pieces. Lastly, policy is based on a strategy or decision-making rule that maps states to actions. In chess, each player has their own strategy and decision making based on the set rules of chess.

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