1. Algorithms & Data Structures for Games
Minor Games Programming
Algorithms & Data Structures for Games
Lecture 5

2. Algorithms and Data Structures
Feedback previous lectures
Theory:
Boards Game Algorithms
Jan Verhoeven

3. Theory: Some Board Game Algorithms
Static Evaluation function
Alpha-beta pruning
Move ordering
Iterative deepening
Killer heuristic
Transposition table
Zobrist hashing

4. Static Evaluation function
Not done at leave nodes! But what is a stable situation? Horizon effect?

5. Alpha-beta pruning
Greatest effect when the moves are ordered! Best move first ….  Move ordering

6. Move ordering Best moves first (more pruning!):
Defend against direct winning opponent’s moves (“mate”-moves)
Capture moves
Killer moves (see later)

7. Iterative deepening -1-
Iterative deepening means repeatedly calling a fixed depth search routine with increasing depth until a time limit is exceeded or maximum search depth has been reached.
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8. Iterative deepening -2-
The advantage of doing this is that you do not have to choose a search depth in advance; you can always use the result of the last completed search.

9. Iterative deepening -3-
Also because many position evaluations and best moves are stored in the transposition table, the deeper search trees can have a much better move ordering than when starting immediately searching at a deep level.

10. Killer heuristic
The killer heuristic is used to improve the move ordering. The idea is that a good move in one branch of the tree is also good at another branch at the same depth. For this purpose at each ply we maintain one or two killer moves that are searched before other moves are searched. A successful cutoff by a non-killer move overwrites one of the killer moves for that ply.

11. Transposition table
The transposition table is a hashing scheme to detect positions in different branches of the search tree that are identical.

12. Zobrist hashing
A smart way to construct hash keys for a transposition table, depending on the board position.

13. Transposition Tables Presentation
See and study blackboard:
Transposition Tables.ppt
And if you are really interested:

14. Exercise: -give the transposition table (size=8) - randoms are in octal1
0123
0456 2
0172
0263 3
0314
0557 4
0662
0527 5
0116
0374 6
0252
0153 7
0771
0722 8
0742
0275 9
0337
0142
Situation 1: Situation 2:

15. Extra Presentation, please read and don’t study …
On blackboard: Game programming workshop Japan By prof.dr. Jaap van den Herik

16. Homework This Chapter 10.5.2 Articles, Presentations and the Internet
Homework, study/read:
This
Chapter
Articles, Presentations and the Internet

17. Practice (next THURSDAY !!!)
Practice, be prepared for:
Implement a Transposition Table class using Zobrist hashing for a given board game.
Make a test program to demonstrate this class.