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"The first strong computer opponent was BKG 9.8. It was programmed by
Hans Berliner in the late 1970s on a PDP-10 as an experiment in
evaluating board positions. Early versions of BKG played badly even
against poor players, but Berliner noticed that the critical mistakes
the program made were always at phase changes. He applied basic
principles of fuzzy logic to smooth out the transition between phase
changes, and by July 1979, BKG 9.8 was ready to play against then
current world champion Luigi Villa. It won the match, 7-1, becoming the
first computer program to defeat a world champion in any game, although
this was mostly a matter of luck, as the computer happened to get
better dice rolls than its opponent in that match." --Wikipedia
7 point match
Game 1
Villa : 0 Gammonoid : 0
1) 61: 13/7 8/7 44: 24/20 24/20 13/9 13/9
2) 42: 13/9 6/4
Better is 42: 24/20 6/4
2) 44: 20/16* 20/16 6/2 6/2
Better is 44: 20/16*(2) 9/5(2)
3) 61: 25/24 24/18 Doubles => 2
4) Takes 42: 8/4 6/4
How about 42: 13/7*?
5) 43: 8/4 8/5 52: 16/11 9/7*
6) 41: 25/24 13/9* 54: 25/20* 20/16*
7) 53: 25/20 25/22 21: 7/5* 5/4
8) 33: 25/22 7/4 6/3 6/3 51: 16/11 9/8
9) 32: 13/10 24/22 22: 13/11 11/9 11/9 11/9
10) 62: 22/20 20/14 62: 8/2 13/11*
Better is 62: 13/7 9/7
11) 51: 25/20 13/12* 66:
12) 33: 12/9 10/7 9/6 6/3 11: 25/24 24/23 6/5* 6/5
13) 55: 31: 23/20 11/10
14) 43: 25/22 22/18 66: 20/14 14/8 10/4 8/2
15) 53: 18/13 13/10 64: 8/2 8/4
16) 51: 10/5 7/6 32: 9/6 6/4
17) 42: 6/2 7/5 62: 4/2
18) 54: 24/19 19/15
Better is 54" 22/13
18) 31: 4/1* 2/1
19) 55: 66:
20) 53: 25/22 15/10 42: 9/5 9/7
21) 65: 22/16 16/11 62: 7/5 5/0
22) 11: 10/9 9/8 8/7 7/6 21: 2/0 1/0
23) 61: 11/5 3/2 64: 5/0 4/0
24) 21: 4/2 2/1 65: 5/0 5/0
25) 55: 22/17 17/12 12/7 7/2 62: 4/0 2/0
26) 43: 22/18 18/15 32: 4/1 2/0
27) 22: 15/13 13/11 11/9 9/7 21: 2/0 1/0
Wins 2 points
Game 2
Villa : 0 Gammonoid : 2
1) 63: 24/18 18/15
Most players today would play 63: 24/18 13/10
1) 63: 24/18 13/10*
2) 52: 25/20 20/18 11: 8/7* 8/7 6/5 6/5
3) 54: 25/21 6/1* Doubles => 2
No double ...
4) Drops Wins 1 point
Easy take!
Game 3
Villa : 0 Gammonoid : 3
1) 52: 13/8 13/11 41: 13/9 6/5
2) 63: 11/5 8/5 44: 13/9 9/5 8/4 8/4
3) 54: 13/8 8/4 64: 8/2 6/2
4) 21: 6/4 6/5 54: 13/8 13/9
Better is 54: 13/8 9/5
5) 41: 8/4 13/12* 63: 25/22 8/2
Better is 63: bar/16
6) Doubles => 2 Takes
7) 51: 8/3* 4/3 66:
8) 63: 8/2 5/2 66:
9) 64: 24/18 18/14 66:
10) 61: 24/18 18/17 66:
11) 41: 17/13 12/11 66:
12) 22: 14/12 13/11 13/11 11/9 66:
13) 21: 11/9 9/8 66:
14) 32: 8/5 12/10 66:
15) 52: 10/5 6/4 66:
16) 53: 11/6 9/6 66:
17) 66: 6/0 6/0 6/0 6/0 62: 25/19 19/17
18) 52: 5/0 5/3 61: 17/11 11/10
19) 64: 5/0 4/0 31: 10/7 7/6
20) 61: 5/0 3/2 62: 24/18 18/16
Villa's next roll is the super antijoker 43, but that's not the only
reason 62: 24/16 is not right!
21) 43: 4/0 4/1* 41: 25/24* 16/12
22) 41: 25/24 63: 9/3 6/3
23) 53: 31: 12/9 2/1*
24) 66: 55: 24/19 19/14 14/9 6/1
25) 66: 21: 9/7 9/8
26) 66: 44: 9/5 8/4 7/3 4/0
27) 66: 53: 5/0 3/0
28) 66: 66: 6/0 6/0 5/0 5/0
29) 62: 25/19 19/17 41: 4/0 1/0
Double/pass already.
30) 21: 17/15 15/14 Doubles => 4
31) Drops Wins 2 points
Game 4
Villa : 0 Gammonoid : 5
1) 54: 13/8 13/9 42: 8/4 6/4
2) 52: 9/4 6/4 42: 13/9 13/11
3) 44: 24/20 24/20 20/16* 20/16 21: 25/23 6/5
4) Doubles => 2 Drops
Wins 1 point
A well-played game! In the next and final game, Gammonoid's moves 5, 18
12 and 19 are particularly stinky.
Game 5
Villa : 1 Gammonoid : 5
1) 21: 13/11 6/5
2) 21: 13/11 24/23 61: 11/5 6/5
3) 64: 13/7 11/7 21: 6/4 5/4
4) 61: 13/7 23/22 32: 8/5 5/3*
5) 31: 25/22* 24/23 42: 25/23 13/9
6) 62: 22/16* 16/14 53: 25/20 23/20
7) 51: 23/18 14/13 63: 13/7* 13/10
8) 43: 25/22 22/18* 55: 25/20 20/15 8/3 8/3
9) 63: 18/12* 13/10* 32: 25/22 25/23
10) 41: 13/9 10/9 32: 23/20 24/22
11) 42: 8/4 6/4 61: 20/14 14/13*
12) 62: 25/23 13/7 51: 13/8 3/2*
13) Doubles => 2 Takes
14) 32: 25/22* 6/4 42: 25/23 10/6
15) 21: 4/2* 2/1* 53: 25/20 25/22
16) 42: 22/18 18/16 55: 20/15 15/10 10/5 8/3
17) 31: 7/4 16/15 43: 6/2 5/2
18) 41: 15/11 11/10 42: 5/1 5/3
19) 21: 4/2 2/1 22: 22/20 22/20 22/20 3/1
20) 41: 10/6 7/6 55: 20/15 20/15 15/10 15/10
21) 53: 9/4 9/6 33: 10/7 10/7 7/4 7/4
22) 51: 8/3 8/7 32: 20/17 17/15
23) 53: 7/2 6/3 53: 20/15 20/17
24) 33: 7/4 7/4 3/0 3/0 66: 17/11 15/9 15/9 11/5
25) 51: 6/1 1/0 64: 9/3 9/5
26) 51: 6/1 1/0 64: 6/0 4/0
27) 51: 6/1 1/0 42: 4/0 2/0
28) 62: 6/0 2/0 41: 4/0 1/0
29) 54: 6/2 4/0 41: 4/0 1/0
30) 11: 2/1 1/0 1/0 1/0 62: 6/0 2/0
31) 61: 4/0 4/3 21: 2/0 5/4
32) 31: 4/1 1/0 55: 5/0 4/0 3/0 3/0
Wins 2 points and the match
Gammonoid knew that backgammon is a race!
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Adam Tansley writes:
Thanks Raccoon. And here's what a modern day bot thinks of all that
(gnubg 2-ply analysis):
Chequerplay statistics
Villa Gammonoid
Total moves 91 90
Unforced moves 78 73
Unmarked moves 0 0
Moves marked good 87 75
Moves marked doubtful 2 6
Moves marked bad 1 4
Moves marked very bad 1 5
Error rate (total) -0.617 (-7.332%) -2.433 (-22.671%)
Error rate (per move) -7.9 (-0.094%) -33.3 (-0.311%)
Chequerplay rating Expert Beginner
Luck statistics
Villa Gammonoid
Rolls marked very lucky 0 3
Rolls marked lucky 2 5
Rolls unmarked 86 81
Rolls marked unlucky 3 1
Rolls marked very unlucky 0 0
Luck rate (total) +0.025 (-8.596%) +4.438 (+54.568%)
Luck rate (per move) +0.3 (-0.094%) +49.3 (+0.606%)
Luck rating None Good dice, man!
Cube statistics
Villa Gammonoid
Total cube decisions 50 52
Close or actual cube decisions 21 8
Doubles 3 3
Takes 1 2
Passes 2 1
Missed doubles (below CP) 3 (-0.048 (-0.351%)) 0
Missed doubles (above CP) 0 1 (-0.038
(-0.505%))
Wrong doubles (below DP) 0 1 (-0.151
(-1.006%))
Wrong doubles (above TG) 0 0
Wrong takes 0 0
Wrong passes 1 (-0.674 (-4.504%)) 0
Error rate (total) -0.723 (-4.855%) -0.189 (-1.511%)
Error rate (per cube decision) -34.4 (-0.231%) -23.6 (-0.189%)
Cube decision rating Beginner Casual player
Overall statistics
Villa Gammonoid
Error rate (total) -1.340 (-12.187%) -2.622 (-24.182%)
Error rate (per decision) -13.5 (-0.123%) -32.4 (-0.299%)
Equiv. Snowie error rate -7.4 -14.5
Overall rating Intermediate Beginner
Actual result -50.00% +50.00%
Luck adjusted result +13.16% -13.16%
Luck based FIBS rating diff. +177.04
Error based abs. FIBS rating 1924.4 1616.6
Chequerplay errors rating loss 98.5 414.8
Cube errors rating loss 27.1 18.6
Worth noting that although Gammonoid got very lucky, and Villa had by
far the better checker play, Gammonoid actually did better with the
cube, according to gnubg.
tansley
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Programming
- Adjusting to a weaker opponent (Brian Sheppard, July 1997)
- Anticomputer positions (Bill Taylor+, June 1998)
- BKG 9.8 vs. Villa (Raccoon+, Aug 2006)
- BKG 9.8 vs. Villa (Andreas Schneider, June 1992)
- BKG beats world champion (Marty Storer, Sept 1991)
- Backgames (David Montgomery+, June 1998)
- Blockading feature (Sam Pottle+, Feb 1999)
- Board encoding for neural network (Brian Sheppard, Feb 1997)
- Bot weaknesses (Douglas Zare, Mar 2003)
- Building and training a neural-net player (Brian Sheppard, Aug 1998)
- How to count plies? (Chuck Bower+, Jan 2004)
- How to count plies? (tanglebear+, Mar 2003)
- Ideas for improving computer play (David Montgomery, Feb 1994)
- Ideas on computer players (Brian Sheppard, Feb 1997)
- Introduction (Gareth McCaughan, Oct 1994)
- Measuring Difficulty (John Robson+, Feb 2005)
- Methods of encoding positions (Gary Wong, Jan 2001)
- N-ply algorithm (eXtreme Gammon, Jan 2011)
- Neural net questions (Brian Sheppard, Mar 1999)
- Pruning the list of moves (David Montgomery+, Feb 1994)
- Search in Trees with Chance Nodes (Thomas Hauk, Feb 2004)
- Source code (Gary Wong, Dec 1999)
- TD-Gammon vs. Robertie (David Escoffery, June 1992)
- Training for different gammon values (Gerry Tesauro, Feb 1996)
- Training neural nets (Walter Trice, Nov 2000)
- Variance reduction in races (David Montgomery+, Dec 1998)
- Variance reduction of rollouts (Michael J. Zehr+, Aug 1998)
- Variance reduction of rollouts (Jim Williams, June 1997)
- What is a "neural net"? (Gary Wong, Oct 1998)
- Writing a backgammon program (Gary Wong, Jan 1999)
From GammOnLine
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