Chess engine presentation
- 2. Guided By Dr Nishant Shrivastava Head of Department Presented By Tanushree Sharma (8818103001) Amit Verma (8818103004)
- 3. CONTENT 3 Objective Scope Building Blocks of Chess Engine Introduction Flow Charts Tools and Techniques Home Page Board Representation Move Generation Implementation AI Algorithms Integration of AI Algorithms Future Enhancement
- 4. The objective is to checkmate the opponent’s king by placing it under an unavoidable threat of capture. 4
- 5. The scope of our project is limited for two players to play chess as real in computer. And a player also able to play with computer according to the intelligence we gave it. 5
- 6. Building Blocks of Chess Chess Board Possible Moves Move Choose Animate Move Update
- 7. 7 Chess is a game played between two opponents on opposite sides of a board containing 64 squares of alternating colors. Each player has 16 pieces: 2 rooks, 1 king, 1 queen, 2 bishops, 2 knights and 8 pawns.
- 8. Tools & Techniques 8 Python 3 It is a General-purpose dynamic programming language which provides the high-level readability and it is interpreted. In our project we use python for calculate the players's move. Pygame Pygame is a Python framework for game programming. We use pygame in our project for creating, updating and handling GUI.
- 10. 10 Start User's Move Move is Legal Move Generator Move Evaluation Best Move Stale/Chec k mate End Playing Steps (AI) True End True False Stale/Chec k mate True Fals e False
- 11. Home Page 11 The user may play against a friend or the computer.
- 12. Representation of Chess Board 12
- 13. Move Generation 13 After representation of board we shift to the move generator. Each piece in chess has its own list of moves, therefore for each piece is necessary to write a specific function to generate the moves. Here are snapshots of chess piece's move from are code.
- 14. Pawn's Move 14
- 15. Knight's Move 15
- 16. Bishop's Move 16
- 17. Queen's Move 17
- 18. King's Move 18
- 19. Rook's Move 19
- 20. we should introduce two things to computer for making the game Intelligent which will make the game to do optimal moves A technique to choose the move to make amongest all legal possibilities, so that it can choose a move instead of being forced to pick one at random. A way to compare moves and positions, so that it makes intelligent choices. 20
- 21. AI Algorithms 21
- 22. Mini-Max Algorithm 22 The Mini-max algorithm is a way to find an optimal move in a two player game. Mini-max algorithm is a recursive or backtracking algorithm which is used in decision- making and game theory. It provides an optimal move for the player assuming that opponent is also playing optimally. The minimax algorithm performs a depth-first search algorithm for the exploration of the complete game tree. The minimax algorithm proceeds all the way down to the terminal node of the tree, then backtrack the tree as the recursion
- 23. Properties of Mini-Max algorithm: 23 Complete- Min-Max algorithm is Complete. It will definitely find a solution (if exist), in the finite search tree. Optimal- Min-Max algorithm is optimal if both opponents are playing optimally. Time complexity- As it performs DFS for the game-tree, so the time complexity of Min-Max algorithm is O(bm), where b is branching factor of the game-tree, and m is the maximum depth of the tree. Space Complexity- Space complexity of Mini-max algorithm is also similar to DFS which is O(bm).
- 24. Working of Mini-max 24 Minimax: Assume that both White and Black plays the best moves. We maximizes White’s score Perform a depth-first search and evaluate the leaf nodes Choose child node with highest value if it is White to move Choose child node with lowest value if it is Black to move Branching factor is 40 in a typical chess position
- 25. Mini – max Algorithm Graph 25
- 26. Pseudocode 26 function minimax(node, depth, maximizingPlayer) is if depth = 0 or node is a terminal node then return the heuristic value of node if maximizingPlayer then value := −∞ for each child of node do value := max(value, minimax(child, depth − 1, FALSE)) return value else (* minimizing player *) value := +∞ for each child of node do value := min(value, minimax(child, depth − 1, TRUE)) return value
- 27. Pruning Techniques 27 The complexity of mini-max algorithm for d ply ahead is O(b*b*…*b) = O(b^d). With a branching factor (b) of 40 it is crucial to be able to prune the search tree.
- 28. Alpha-Beta Pruning 28 Alpha-Beta Pruning is a way of finding the minimum solution. Alpha-beta pruning is a modified version of the minimax algorithm. It is an optimization technique for the minimax algorithm. Alpha-beta pruning can be applied at any depth of a tree, and sometimes it not only prune the tree leaves but also entire sub-tree. parameter can be defined as: Alpha : The best (highest-value) choice we have found so far at any point along the path of Maximizer. The initial value of alpha is -∞. Beta: The best (lowest-value) choice we have found so far at any point along the path of Minimizer. The initial value of beta is +∞.
- 29. Alpha-Beta Pruning 29 The Alpha-beta pruning to a standard minimax algorithm returns the same move as the standard algorithm does, but it removes all the nodes which are not really affecting the final decision but making algorithm slow. Hence by pruning these nodes, it makes the algorithm fast. If Beta is less than Alpha, then the position will never occur assuming best play If search tree is evaluated left to right, then we can skip the greyed- out sub trees
- 30. Mini-max with Alpha Beta Pruning Graph 30
- 31. Pseudocode 31 function alphabeta(node, depth, α, β, maximizingPlayer) is if depth = 0 or node is a terminal node then return the heuristic value of node if maximizingPlayer then value := −∞ for each child of node do value := max(value, alphabeta(child, depth − 1, α, β, FALSE)) α := max(α, value) if α ≥ β then break (* β cutoff *) return value else value := +∞ for each child of node do value := min(value, alphabeta(child, depth − 1, α, β, TRUE)) β := min(β, value) if β ≤ α then break (* α cutoff *) return value
- 33. Thank You