C SC 483 Chess and AI: Computation and Cognition. Lecture 5 September 24th

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1 C SC 483 Chess and AI: Computation and Cognition Lecture 5 September 24th

2 Your Goal: by next time have the bitboard system up and running to show: e.g. click on a piece, highlight its possible moves (graphically) or equivalent Task 2

Rotated Bitboards Last time we discussed the rank and file attacks computed using a lookup table for the rank file case reduces to the rank case if we maintain 90 degree rotated

3 Rotated Bitboards Last time we discussed the rank and file attacks computed using a lookup table for the rank file case reduces to the rank case if we maintain 90 degree rotated bitboards Good Reference (from lecture 3, slide 34): att/bitmaps.html hex 14 hex rank returns msb hex 0 hex 1 byte 8 byte 1 lsb

4 Rotated Bitboards Sliding pieces: leading diagonal ( : queen: either diagonal bishop: either diagonal 4b4 3b5 2b7 2b2 b6 b3 b1 b0 Key idea: make diagonals consecutive bits in rotated bitboard 5b4 6b3 3b0 2b3 3b1 b7 2b4 b4 2b0 b2 b5 Worked example: Leading Diagonal bitboard is organized as shown 7b1 7b6 4b0 2b5 2b1 2b6 8b2 3b4 8b5 4b3 8b7 2b7 2b6 2b5 2b4 2b3 2b2 2b1 2b0 b7 b6 b5 b4 b3 b2 b1 b0

5 Rotated Bitboards Bitboards for the leading diagonal maintained in parallel with the other bitboards leading diagonal ( : 4b4 3b5 2b7 2b2 b6 b3 b1 b0 ldk leading diagonal white king ldk leading diagonal black king... ldb leading diagonal white bishop... ldp leading diagonal black pawns Computed Bitboards ldwhite = ( ldk ldq ldr ldb ldk ldp ) ldblack = ( ldk ldq ldr ldb ldk ldp ) 5b4 6b3 7b1 7b6 8b2 8b5 8b7 2b3 b7 2b4 b4 2b0 2b5 b2 b5 2b1 2b6 3b4 4b3

6 Rotated Bitboards Two arrays/tables needed: leading diagonal ( : Find your diagonal by right shifting the bitmap Mask with your diagonal (of varying length) 4b4 5b4 3b5 2b7 2b2 b6 2b3 b3 b7 b1 b4 b0 b2 Example: ldb = 0x ldq = 0x b3 7b1 2b4 2b0 2b5 b5 2b1 look up table: 7b6 2b6 given a bitmap, find its shift number 8b2 3b4 diagonal_shift(ldb) = 28 8b5 4b3 (ldwhite ldblack) >> 28 will give what s on the diagonal and more 8b7

7 Rotated Bitboards Two arrays/tables needed: Find your diagonal by right shifting the bitmap Mask with your diagonal (of varying length) Example: ldb = 0x ldq = 0x look up table: given a bitmap, find its mask diagonal_mask(ldb) = FF (8bits long) summary: diagonal(bb) = ((ldwhite ldblack) >> diagonal_shift(bb)) & diagonal_mask(bb) will give the diagonal leading diagonal ( : 4b4 3b5 2b7 2b2 b6 b3 5b4 2b3 b7 6b3 2b4 7b1 7b6 8b2 8b5 8b7 b1 b4 2b0 2b5 b0 b2 b5 2b1 2b6 3b4 4b3

8 Rotated Bitboards Access diagonal trailing diagonal ( : diagonal right shift (>>) mask 1 0 0x x x x0F x1F x3F x7F xFF x7F x3F x1F x0F x x x01

9 Rotated Bitboards Computed diagonal can be looked up using the existing rank attacks tables rank attacks lookup: rank returns diagonal(bb) = ((ldwhite ldblack) >> diagonal_shift(bb)) & diagonal_mask(bb) computes a single byte Note: if diagonal is shorter than 8 bits, fill in with 1 s for 8 bit lookup diagonal(bb) inv_mask(diagonal_mask(bb)) Examples: mask inv_mask 0xFF 0x00 0x0F 0xF0

Rotated Bitboards define compute diagonal attacks ld_moves(ldbb) = rank((( ldwhite ldblack) >> diagonal_shift(ldbb)) & diagonal_mask(ldbb)) inv_dmask(diagonal_mask(ldbb)), ldbb >>

10 Rotated Bitboards define compute diagonal attacks ld_moves(ldbb) = rank((( ldwhite ldblack) >> diagonal_shift(ldbb)) & diagonal_mask(ldbb)) inv_dmask(diagonal_mask(ldbb)), ldbb >> diagonal_shift(ldbb) & diagonal_mask(ldbb)) << diagonal_shift(ldbb) Worked example: white bishop ldwhite = ldb = 0x ldblack = ldq = 0x diagonal_shift(ldb) = 28 diagonal_mask(ldbb) = 0xFF rank((0x a >> 28) & 0xFF 0x00, (0x >> 28) & 0xFF) << 28) rank(0x0a,0x08) << 28 + mask out white pieces 0xF6 << 28 = 0x F (msb) (msb)

11 Rotated Bitboards Similar considerations for the trailing diagonal representation Functions (or arrays): diagonal_shift(bb) diagonal_mask(bb) (described earlier) can be reused on the understanding that they apply to the trailing diagonal representation trailing diagonal ( : (1,1) (8,1) b0 b1 b3 b6 2b2 2b7 b2 b4 b7 2b3 3b0 b5 2b0 2b4 2b1 2b5 2b6 (1,8) (8,8)

12 result: Rotated Bitboards

13 APPROXIMATE CHESS RANKINGS 1. Complete beginner ( Rating<300) 2. Beginner (Rating ) 3. Stronger beginner (Rating ) 4. Strong beginner (Rating ) 5. Intermediate player ( Rating ) 6. Class D player (Rating ) 7.Class C player (Rating ) 8.Class B player ( Rating ) 9. Class A player (Rating ) 10. Expert (Rating ) 11. Master (Rating 2200) 12. National Master ( Rating 2200 up to about 2300 ) 13. Senior Master (Rating of about 2300 to 2400 ) 13. FIDE Master ( International Rating of 2300 or higher after 24 games) 14. International Master ( International rating of 2400> and 3 Norms completed ) 15. Grandmaster ( International rating of 2500> and 3 Norms completed ) 16. World Champion ( Best in the world, usually rating of 2750> and the winner of a match recognized by FIDE )

14 KARPOV-KASPAROV LINARES 93

15 BOTVINNIK-CAPABLANCA Holland 1938 One of the most beautiful tactics of that era. Botvinnik was just becoming a top player, while Capablanca was still at his best. The game is also famous for being the 1 st game that a Chess Computer Pioneer in 1977 was able to solve not by calculating million moves but only few and choosing the best out of them.

16 BOTVINNIK-CAPABLANCA

17 The Opening

18 The Middlegame fight

19 The Tactical Calculation

20 Tactical Execution of the Idea

21 The Final Struggle by Black

22 Short Description of the Game 1. A Normal Chess Opening by both sides. 2. A power struggle on all 3 sides of the board. 3. White opens the center and aims at the Black King. 4. Black destroys white s Queen side. 5. White creates a strong Passed Pawn. 6. White Sacrifices 2 pieces to open the Black King and attack it. 7. White threatens a Checkmate or Queen Promotion of the E pawn. 8. Black seeks Perpetual Chess but cannot find it. 9. White wins.

23 HOMEWORK Set-up a chess board ( or use a Computer generated chess board ). Find this game (Botvinnik-Capablanca, 1938) in a chess book, use the full notation provided above or on-line. You can use sources such as Chessbase (Lite), chessgames.com, chesslab.com, chessbase.com or any other to find the game and possibly some commentaries about the game by Grandmasters. Go move-by-move over the game and find out what the opponents tried to do and what did they possibly miss. 1. What can you tell us about the Nimzo-Indian Opening that was used in this game. Its origination, strategic concepts, some examples, names of famous chess players who resorted to this defense when playing black. (15 Pts) 2. Was there a defense for Black anywhere after move 28? Think of your own suggestions, or use any sources to help improve Black s defense. Where do you think Black went wrong in the game? ( it could be on multiple points of the game ) (15 pts) 3. What can you tell me about the Pioneer Chess program developed by Botvinnik and what was so special about it? (Extra Credit-5 Pts) Should be typed, Between 1-2 pages per question. Sources cited.

C SC 483 Chess and AI: Computation and Cognition. Lecture 3 September 10th

C SC 483 Chess and AI: Computation and Cognition Lecture 3 September th Programming Project A series of tasks There are lots of resources and open source code available for chess Please don t simply copy