Magriel VS. GNU (long)

I like Paul Magriel's classic book "BACKGAMMON" a lot, but I was always concerned about how some of the examples might stack up against modern, neural-network based advice. So, I went through the book with GNU, set on 2-ply, to take a look at the positions (I didn't want to make a career of it and do rollouts of the positions).

I have compiled the results, and decided to post them for whatever use they may be to others. A few points:

1. This shouldn't necessarily be construed as a list of Magriel errata, just a list of where GNU 2-ply disagrees.

2. I put all the positions into a 7-away, 7-away match, and used cubeful equity evaluations.

3. I have only given results for positions where GNU's recommended move is not the same as Magriel's. In most cases, the equities are pretty close (see stats below).

4. I only examined positions in chapters 12 through 29, excluding chapter 15 (openings). I excluded the backgame section of chapter 29, as bots are still suspect at backgames in rollouts, much less in 2-ply examinations.

5. For positions listed, the GNU recommended move is followed by the ordered list of other possibilities, with their equity differences from the GNU recommended move. The last move in the list is Magriel's recommended move. Occasionally when the list was long and I got lazy, I inserted an ellipsis (...) to show there were other moves between GNU's recommendation and Magriel's recommendation.

Please point out errors if you find them – thanks.

Randy

Statistics as follows:

Positions examined: 267
Positions where GNU's move agreed with Magriel's move: 175
Average equity loss of Magriel's move, all 267 positions: .026
Average equity loss of Magriel's move, only the 92 positions where GNU disagrees: .076
Median equity loss of Magriel's move, only the 92 positions where GNU disagrees: .046

Chapter 12 - Builders and Flexibility

Position 12.1
GNU prefers 1A or 1B to 1C
8/7 8/5
8/6(2) -.026
7/6 7/4 -.041

Position 12.4
GNU prefers 4A to 4B
10/9 6/4
10/8 6/5 -.142

Position 12.8
GNU prefers 8A to 8B
9/5
8/5 6/5 -.020

Position 12.11B
8/5* 6/5
6/5*(2) 8/7 -.016

Position 12.12
b/23 13/12*/11*
b/24 13/12*/11*/10 -.017
b/24 13/12*/11* 7/6 -.057

Position 12.16B
24/23
10/9 -.069

Position 12.18
8/5 7/5
7/4 6/4 -.048

Position 12.19
10/7 9/7
13/10 24/22 -.046

Position 12.20
10/2
10/8 10/4 -.004

Chapter 13 - Duplication and Diversification

Position 13.7D
9/3
9/8 9/4 -.028

Position 13.11
18/16 5/4
18/15 -.017
18/17 6/4 -.017

Position 13.14
24/18 13/11
24/22 13/7 -.002
13/7 6/4 -.011
13/11 13/7 -.038

Position 13.20
24/18 13/11
24/22 13/7 -.002
24/22 24/18 -.008
13/11 13/7 -.102

Position 13.24
b/21* 5/4
b/21* 6/5 -.034
b/21* 8/7 -.046

Position 13.25A
21/15 10/6
...
10/6 9/3 -.086

Position 13.25B
20/14 10/6
...
9/5 10/4 -.020

Chapter 14 - When You Are Forced to Leave Shots

Position 14.3
16/11 6/5
16/11 3/2 -.004
16/10 -.022

Position 14.4
8/7 8/2
8/1 -.118
11/4 -.163

Position 14.8
4/o 3/o
4/o 4/1* -.026

Position 14.12
20/18
4/2 -.040

Position 14.15A
8/4
7/3 -.033

Position 14.15B
8/4 6/4
14/8 -.137
7/1* -.207

Chapter 16 - Safe Play vs. Bold Play

Position 16.4
7/6 (what an ugly move)
6/5 -.001
9/8 -.088

Position 16.6
GNU agrees with the main point, don't slot, but
24/23
11/10 -.016

Position 16.7
24/23
11/10 -.016
6/5 -.019

Position 16.9
13/10
8/5* -.129

Position 16.10
13/11 6/5
13/10 -.006

Position 16.14
13/7 6/5
24/18 6/5 -.009
13/6 -.016

Chapter 17 - Slotting

Position 17.2
24/23
11/10 -.016
6/5 -.019

Position 17.8
13/10
24/23 13/11 -.045
24/23 8/6 -.050
8/5 -.095
13/11 6/5 -.118
3/2* 3/1 -.122
13/11 8/7 -.135

Position 17.12
GNU agrees that switching points 4/3*(2) is best but prefers to
play the last 1 as 24/23 rather than 8/7 equity difference -.034.

Position 17.13
6/5
8/7 -.072

Position 17.16A
GNU agrees that slotting 8/7 isn't good but has a slight preference
(.002 equity) for playing 11/10 rather than 6/5.

Position 17.16B
b/22 6/5
b/22 8/7 -.044

Chapter 18 - Action Play

Position 18.1
9/5 6/5
24/20 6/5 -.021

Position 18.2
24/22 13/7
9/1 -.003
24/18 9/7 -.013

Position 18.3
11/6
23/18 -.170

Position 18.4
8/4 6/5
8/7 8/4 -.007
13/9 6/5 -.024
24/20 6/5 -.037

Position 18.5
10/5 6/5
23/22 10/5 -.096
23/18 6/5 -.149

Chapter 19 - One Man Back

Position 19.2
11/5 6/5
13/7 8/7 -.098

Position 19.4
13/8 6/5
8/3 6/5 -.011
22/21 6/1* -.012
13/7 -.014
8/7 6/1* -.023

Position 19.5
15/11 13/8
13/9 6/1* -.004
15/11 6/1* -.013
15/10 13/9 -.017
11/7 6/1* -.025

Position 19.10
24/21 13/9
24/20 13/10 -.008

Chapter 20 - Golden Point

Position 20.1
24/22(2) 6/4(2)
13/11(2) 6/4(2) -.007
24/22 13/11 6/4(2) -.027
24/20(2) -.029

Position 20.5
20/14*
8/2 -.136

Position 20.7
b/16*
b/20 24/20 -.066

Position 20.8
24/20*
8/5 6/5 -.074

Position 20.11
No Double, Take
Double, Take -.052

Chapter 21 - Splitting

Position 21.1A
13/10 11/10
24/23. 11/8 -.017
13/10 6/5 -.024

Position 21.1B
13/10 11/10
13/10 6/5 -.024

Position 21.4
8/4 6/5
8/7 8/4 -.007
13/9 6/5 -.024
24/20 6/5 -.037

Position 21.12
13/11
24/22 -.060

Chapter 22 - Doubling Theory

Position 22.4
GNU believes X is too good to double by a hair.
No Double
Double, pass -.003
(Double, take +.449)

Position 22.5
Double, take
Double, pass +.258
(that is O should take and loses .258 equity by passing)

Chapter 23 - No Possible Contact

Only positions 8A and 8B were checked - both OK

Chapter 24 - Avoiding Contact

Position 24.11
10/5
8/3 -.149

Position 24.15
6/o 2/o
6/o 3/1 -.077

Position 24.24
6/4 6/2*
...
6/2* 4/2 -.017

Position 24.40
8/6 5/1
9/5 8/6 -.211
9/3 -.216

Position 24.42
12/6 11/6
12/1 -.000
12/7 11/5 -.111

Position 24.43
16/10 11/10
16/15 11/5 -.076
16/10 6/5 -.083
16/9 -.087

Position 24.44
18/17*/15
18/17* 6/4 -.002
...
18/16 6/5 -.259

Position 24.46
18/16*/13
...
18/13 -.085

Position 24.47
3/o
6/5 6/4 -.045

Position 24.49
10/4 8/4
7/1* 5/1 -.033

Position 24.52
18/16* 13/8
...
18/11 -.192

Position 24.58
6/3
9/6 -.030

Chapter 25 - After Contact

Position 25.1
16/13
20/17 -.005
17/14 -.012

Position 25.2
11/9
6/4 -.057

Position 25.5
18/14
16/12 -.046

Position 25.6
18/13
9/4 -.131

Position 25.7
24/22 13/7
13/5 -.069
13/11 13/7 -.118

Position 25.16
20/16 13/7
20/10 -.006
20/14 13/9 -.006
13/7 5/1 -.023

Position 25.17
20/16 19/13
20/10 -.003
20/14 19/15 -.004
19/9 -.006
19/13 5/1 -.022

Position 25.22
13/10 6/1*
19/16 6/1* -.010
13/5 -.013

Chapter 26 - Priming and Blocking

Position 26.10
24/22 13/9
24/20 11/9 -.013
13/9 11/9 -.033

Position 26.11A
9/4 8/4
13/9 13/8 -.033

Position 26.12A
24/22(2) 13/11(2)
...
13/9(2) -.126

Position 26.14
14/9 13/8 6/1*(2)
8/3(2) 6/1*(2) -.028
13/8(2) 6/1*(2) -.031
14/9 13/3 8/3 -.073

Position 26.15
6/4 6/3
13/8 -.016
8/3 -.031
13/11 6/3 -.087

Position 26.17
24/18
24/23 11/6 -.048
13/7 -.068
13/8 11/10 -.070

Position 26.18
13/10 5/3*
24/21 5/3* -.029
11/8 5/3* -.046

Chapter 27 - Control of the Outside

Position 27.8
8/5
6/3 -.082

Position 27.14
11/7 10/7
24/20 13/10 -.039

Chapter 28 - Timing

Position 28.2
18/13
7/2* -.151

Position 28.4
24/13
24/18 7/2* -.151

Position 28.7
13/8
6/1* -.030

Position 28.9A
6/2 4/1
10/7 10/6 -.117

Position 28.11A
8/6 8/3
...
20/13 -.259

Position 28.14
10/6 4/2
9/5 4/2 -.053
10/6 9/7 -.058

Position 28.15
24/23*
10/9 -.469

Position 28.19
8/6 8/2*
...
8/2* 3/1* -.371

Chapter 29 - Holding Game and Backgame
(only positions 1 - 9 examined - no backgames)

Position 29.2
24/16(2)
24/20 13/9(2) 8/4 -.026
24/20(2) 13/9(2) -.030
24/20 13/5 13/9 -.033

Position 29.8
13/11 13/7
7/1 3/1 -.042

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