1. Computer Chess Deep Thought(s) Remembered April 13, 2004
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Computer Chess Deep Thought(s) Remembered April 13, 2004
Topics
Chip-Test, Deep Thought, Wean Hall Rm8308
Computer Chess Basics
Representing the chess board
Game search
Evaluation function
Transposition Table
Tricks
Chess_211.ppt
S’04

2. Computer Chess at CMU Hans Berliner
World postal chess champion (1968)
CS Faculty in AI
Backgammon Computer Program Beats World Champion
Patsoc, a DEC-10 (mainframe) chess program
Hitech
Vs. a bunch of CS graduate students
Feng H. Hsu (Crazy Bird)
Thomas Anantharaman
Murray Campbell
Mike Browne
Yours truly

3. Chiptest, Deep Thought Timeline
A VLSI design class project evolves into F.H.Hsu move-generator chip
A productive CS-TG results in ChipTest, about 6 weeks before the ACM computer chess championship
Chiptest participates and plays interesting (illegal) moves
Chiptest-M wins ACM CCC
Redesign becomes DT
DT participates in human chess championships (in addition to CCC)
DT wins second Fredkin Prize ($10K)
DT is wiped out by Kasparov
Story continues
@ IBM

4. Opinions: Is Computer Chess AI?
From Hans Moravec’s Book “Robot”

5. Books to Read
“Chess Skill in Man and Machine”, ‘84, ISBN: Slate and Atkins describe Chess 4.5
F.H.Hsu’s book:

6. Chess Data Structures The chess board: Need some other stuff:
Castle status
En passant status
Repetition detection
50 Move rule
#define EMPTY 0
#define EMPTY2 8
#define PAWN 1
#define KNIGHT 2
#define BISHOP 3
#define ROOK 4
#define QUEEN 5
#define KING 6
#define WPAWN 1
#define WP 1
#define WKNIGHT 2
#define WN 2
#define WBISHOP 3
#define WB 3
#define WROOK 4
#define WR 4
#define WQUEEN 5
#define WQ 5
#define WKING 6
#define WK 6
#define BPAWN 9
#define BP 9
#define BKNIGHT 10
...
unsigned char board[8][8];

7. Fun with Bitvectors
Bit-board representation of chess position (see Crafty, Hyatt):
unsigned long long blk_king, wht_king, wht_rook_mv2,…; 8 7 6 5 4 3 2 1 1 2
wht_king = 0x ull;
blk_king = 0x ull;
wht_rook_mv2 = 0x10ef ull;
... /*
* Is black king under attach from
* white rook ? */
if (blk_king & wht_rook_mv2)
printf(”Yes\n”); 61 62 63
a b c d e f g h

8. Legal Move Generation
Chess programs spend a lot of time computing the legal moves for a given position
Observation: limited number of moves (~5000)
Complication: Move order matters
Capture moves first
Highest valued target first
Lowest valued piece first
Pieces under attack
Other heuristics
Deterministic order? Yes: can encode move by its sequence number
About 36 moves in midgame

9. Min-Max Tree search Limited depth, depth first search
Number of Nodes visited ~ (Branching-factor)Depth

10. Alpha Beta Search Works better at depth
Branching factor now ~6 (depends on even/oddness)

11. Iterative Deepening Improve move ordering via shallow searches
Need to search the same part of the tree multiple times but improved move ordering more than makes up for this redundancy
Difficulty:
Time control: each iteration needs about 6x more time
What to do when time runs out?

12. Limited Depth Search Problems
Horizon effect: push bad news over the search depth
Quiescence search: can’t simply stop in the middle of an exchange

13. Evaluation Function Guesses the outcome of an incomplete search
Eval(Position) = i wi * fi(Position)
Weights wi may depend on the phase of the game
Features fi:
#of Pawns (material terms)
Centrality
Square control
Mobility
Pawn structure
Many more …

14. Deep Thought’s Evaluation Function
File: dbf_all game: 0 (drawn) move-#: 5 side-to-move: W move: o-o ( 1/1 )
8 R N B Q K B - R
7 P P P - * - P P
6 - * - * P N - *
5 * - * P * P * -
4 - * - p - * - *
3 * - * - * n p Ex =-6
2 p p p * p p b p E0 =29
1 r n b q * r k E =
a b c d e f g h
BadBishop * 0= KingShelter *-256= 4 PPCentral * 0= RookOpenTrop * 0=
Backward * 0= KingShelter * 256= 26 PPCentral * 0= RookSemi * 0=
Backward * 0= KnightCentrality * 0= PawnPlaceA *-102= -5 RookSemi * 0=
BishopBlock * 0= KnightCentrality * 0= PawnPlaceC * 0= RookSemiTrop * 0=
BishopDefense * 0= KnightCentrality * 0= PawnPlaceCA *-102= 5 RookSemiTrop * 0=
BishopDefense * 0= KnightDefense * 0= PawnPlaceK * 0= RookValue K! 0=
BishopPlacement * 768= 7 KnightDefense * 0= PawnPlaceM * 0= SingleIsoClosed * 0=
BishopPlacement * 768= 1 KnightInCorner * 0= PawnPlaceMA *-102= 4 SingleIsoClosed * 0=
BishopPlacement * 768= 0 KnightInCorner K5* 0= PawnPlaceMC * 0= SingleIsoOpen * 0=
BishopValue K5! 0= KnightTropism * 0= PawnPlaceMCA *-102= -17 SingleIsoOpen * 0=
BlockedKingShelter0 -27* 0= KnightTropism * 0= PawnValue K2! 0= TripleClosed K3* 0=
BlockedKingShelter1 21* 0= KnightValue K3! 0= PawnValue * 0= TripleClosed * 0=
DoubleClosed * 0= NoBishopPawn * 0= QueenCentrality * 0= TripleIsoClosed0 2K0* 0=
DoubleClosed * 0= NoBishopPawn * 0= QueenCentrality * 0= TripleIsoClosed1 -1K0* 0=
DoubleIsoClosed * 0= NoKnightPawn * 0= QueenCentrality * 0= TripleIsoOpen K0* 0=
DoubleIsoClosed * 0= NoKnightPawn * 0= QueenTropism * 0= TripleIsoOpen * 0=
DoubleIsoOpen * 0= NoRookPawn * 0= QueenTropism * 0= TripleOpen K3* 0=
DoubleIsoOpen * 0= NoRookPawn * 0= QueenValue K! 0= TripleOpen * 0=
DoubleOpen * 0= OneBishop * 0= RookOnSeventh * 0= TwoBishop * 0=
DoubleOpen * 0= OneBishop * 0= RookOnSeventh * 0= TwoBishop * 0=
KingCentrality *-512= -8 PPAdvance * 0= RookOpen * 0=
KingCentrality *-512= 6 PPAdvance * 0= RookOpen * 0=
KingCentrality *-512= 7 PPAdvance * 0= RookOpenTrop * 0=

15. Deep Thought’s Evaluation Function
Implemented in Xilinx FPGA’s, heavy use of look-up tables (Piece placement table, etc…)
Material weighting to adapt to game phases
Notable deficiencies:
No Mobility term
No Square control term
Made up by speed!

16. Deep Blue’s Eval function
Over 10,000 Features
How do you determine the proper weights???

17. Evaluation Function Tuning
Given data base of Grand-Master games: goal tune the weights such that DT chooses the move made by the GM
Idea: Symbolic evaluation of differences between Positions (see )

18. Transposition Table
Chess isn’t really a tree:

19. Transposition Table Maintenance
Compute hash function incrementally via piece position table full of “random” numbers:
Remove pawn from a4:
Add pawn to a5:
Transposition table content:
Actual position (optional)
Depth
Value
Other flags
Pos_hash ^= rnd_tab[pawn][a4];
Pos_hash ^= rnd_tab[pawn][a5];

20. Useful Real Life Application
Memory Model checker /*
* Basic loop test */
Processor 0:
(0) st #1,[a]
Processor 1:
(1) st #0,[a]
(2) loop: ld [a],%r
(3) cmp #1,%r
bne loop
(4) st #2,[a]
Program execution flow:
0i0 < 0p0
1i0 < 1p0 < 2.0 < 3.0 < 4i2 < 4p2 ^
2.1 < 3.1 < 4i1 < 4p1
2.2 < 3.2 < 4i0 < 4p0
Possible values under all memory models:
1:r a example sequence of events
i0 0i p p loop via P2:loop
i0 0i p p i0 4p0

21. Tricks
Many tricks and heuristics have been added to chess program, including this tiny subset:
Opening Books
Avoiding mistakes from earlier games
Endgame databases (Ken Thompson)
Singular Extensions
Think ahead
Narrow window searches
Contempt factor
Strategic time control