1. Dakota Ewigman Jacob Zimmermann
Computer Chess
Dakota Ewigman Jacob Zimmermann

2. History of Computer Chess
1950: “Programming a computer for Playing Chess” – Claude Shannon.
1951: Alan Turing writes first chess playing program (on paper).
1958: First computer program that can play a complete chess game.
1981: Cray Blitz wins a tournament and achieves master rating.
1989: Deep Thought loses 0-2 against World Champion, Kasparov.
1996: Deep Blue wins one game against Kasparov, but loses match 2 – 4.
1997: Upgraded Deep Blue wins 3.5 – 2.5 against Kasparov.
2006: Deep Fritz beats World Champion Kramnik 4 – 2.

3. Chess
Chess is a game with a finite number of outcomes, and no outside input
“Game of Complete Information”
About possible outcomes
Endgame Tablebases:
All Endgames with 3-5 pieces have been determined already

4. Computer Chess: The Basics
Tree structure, nodes represent game states, and edges represent moves
Possible states d moves deep is around 40d
Position Evaluation
Evaluates Position at Leaf Nodes
Pruning
removing branches which are likely a bad move.
allow for deeper searches of the tree

5. Position Evaluation Many Factors Pieces Remaining Weighted
Piece Location
King Safety
Pawn Structure
Checkmate
Mobility

6. Minimax
Assume Both players will play best moves, Maximize the computer’s score.
Perform depth first search, selecting highest values for computer’s moves and lowest values for opponents moves

7. Minimax
>=2 2
Computer
Opponent
<=2 2
<=1 1
Computer 2 7 1 8

8. Horizon Effect The inability of the computer to see past the “horizon”
Horizon is how deep the computer looks into the tree
Computer cannot see that plays are dangerous if the danger happens past the horizon
ex. being forced into losing a piece or missing out on a guaranteed capture

9. Progressive Deepening
b: branching factor
d: depth of tree
s: states to evaluate
s=O(bd)
If all states are evaluated:
s=(bd+1-1)/(b-1) = O(bd)
Helps re-order for Alpha-Beta pruning efficiency

10. Alpha-Beta Pruning Builds on the Minimax algorithm
Prunes branches that lead to lower quality board states
Alpha and Beta are the bounds that determine the lowest and highest value board states to consider

11. Alpha-Beta Pruning >=2 2 Computer Opponent <=2 2 <=1 Computer7 1

12. Alpha-Beta Complexity
Before: s=O(bd)
After:
Best case: s=O(2bd/2)
Average(Experimentally): s=O(2bd/2)
Worst Case: s=O(bd)

13. Negamax Similar to Alpha-Beta
Takes the maximum of the negatives in place of the minimum
Removes the need for a min function

14. Negamax 2
Computer
Opponent
>=-2 -2 2
>=-1 1
Computer -2 -7 -1

15. Aspiration Search Addition to the Alpha-Beta algorithm
In this search, Alpha and Beta are preset to a narrow window based on the results of the previous iteration
Advantage: it can remove more paths
Disadvantage: May have to run multiple times if no path is found within the window

16. Quiescence Search Only evaluates states that are relatively “quiet”
Allows for deeper searches in “noisy” paths to see if the outcome is better.