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 Kansil: The Backgammon Quiz Book--Five problems

 From: Chuck Bower Address: bower@bigbang.astro.indiana.edu Date: 14 October 1997 Subject: Reliability of robot rollouts, part I Forum: rec.games.backgammon Google: 620u5r\$mju\$1@dismay.ucs.indiana.edu

```Part I. Motivation and History.

Frequenty there are posts asking "how can I best learn to be
a strong BG player?"  Standard answers are "read GOOD books, watch
good players, play against good players, study the games of good
players, etc."

Backgammon by the Bay has an excellent WEB page which falls
under the "...study games of good players..." category.  Several
annotated games can be found at:

http://www.backgammon.org/bgbb/games.html

From an aesthetics standpoint, I find the page appealing.  (But,
hey, I've been defending the Jellyfish GUI, so beware!)  Recent
improvements include a new color board layout.  Technically, the
choice of games and analysis are top notch.  The annotators make
use of Jellyfish rollouts to critique the plays made at the table.

The most recent game is from a match between Emil Malek and
Nick Ballard, with analysis provided by Ron Karr (and JF rollouts
by Richard McIntosh).  In the past I have questioned the use of
level-5 Jellyfish rollouts.  For play decisions, Richard does 7776
truncated trials with an horizon of 7.  ("Truncated rollouts" means
that JF will play the game for a set number of rolls and then
evalulate the position and keep a tally of the evaluated results.
The algorithm is repeated with random dice until 7776 truncated
games have been played--in Richard's case.  "Horizon" is the number
of rolls played for each side before the evaluation/tally.)

Four positions in the match caught my eye (meaning I wasn't at
all sure what the right play was, even after reading the rollout
results and Ron's analysis).  I decided to perform JF level-6
cubeless rollouts to see if the level-5 truncated results stood up.
I was quite surprised by the outcome!

For those not familiar with JF, level-5 means JF looks at the
postion, uses its neural net (brain) to assign an equity (cubeless
value of the game) for the various legal moves, and chooses the best
of these moves.  In "level-6", JF builds a tree.  For each legal
move, it looks at the equities of all of the opponent's possible moves
NEXT roll and then makes the choice, assuming the opponent makes
the "best" play.  Level-6 has (not surprisingly) been shown to play
a stronger game than level-5.

So why would anyone use truncated level-5 rollouts?  I can only
think of one answer:  speed!  JF level-6 takes a lot of time, partly
because it plays the games all the way through.  But even more
time consuming (by an order of magnitude) is the time it takes
looking one roll in the future.  Is the speed worth the sacrifice
in accuracy?  I've always been skeptical.

There is a "hand-waving" argument which goes like this:  "If
a rollout robot makes mistakes, that's OK for comparing two plays,
because it will make similar mistakes for each position (averaged
over the long run) so they cancel, and the true difference between
the plays emerges."  In a mathematics class, this kind of argument
would be lucky to receive the grade of D!

Now for some BG history.  Prince Joli Konsil wrote a book
in the 70's--The Backgammon Quiz Book (Playboy Press, 1978, sc.).
Some of his answers were controversial, but it was harder back
then to decide.  There was no JF!  Soon after his book was published
Konsil became BG editor for GAMES magazine.  In the July/Aug 1980
issue, he reprinted five of his more controversial positions.  BUT,
better yet, he had robot rollouts!  A non-commercial(?) program
was used to compare various plays for the five positions.  I quote:

David Rothman of Hawthorne, California ...uses a Data General
machine that can take a given backgammon situation and run
1000 trials in half an hour.  The computer doesn't play on a
very sophisticated level but this flaw is fairly minor since
it plays "equally poorly" for both players.

Does Konsil's last sentence sound familiar?!?!?!

Years later I ran Expert Backgammon (and recently JFv3.0) rollouts
on Konsil's five controversial positions.  See part II of this series
for the positions, surprises, etc.

Part II. Quiz.

The following five problems are taken from "The Backgammon Quiz
Book" by Prince Joli Konsil.  (Playboy Press Paperbacks, 1978.)
Also, these positions were republished (with more detailed
analysis by Konsil) in "GAMES" magazine July/August 1980 issue.
NOTE that cubes were NEVER shown in either the book or in the
magazine.  All games are \$ play with gammons and backgammons.

Problem 1 (quiz 40c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-|
11| O                |   |                  |
O| O                |   |                  |
O| O                |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
X|                  |   |                  |
X|                  |   |                  |
X|       X          |   |                  |
X|       X  X       |   |                  |
X|    X  X  X       |   |                  |
X| O  X  X  X       |   |                  |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 32

Problem 2 (quiz 76c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
|          X  O  O |   |    O           X |
|                O |   |    O           X |
|                O |   |    O             |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                X |   |    X           O |
| O        X  X  X |   |    X        X  O |
| O  O     X  X  X | O |    X        X  O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 41.

Problem 3 (quiz 29c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
|       O  O  O  O |   |          X       |
|       O  O  O  O |   |                  |
|             O  O |   |                  |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
X| X  X             |   |                  |
X| X  X             |   |                  |
X| X  X  X  O       |   |                  |
X| X  X  X  O  O    |   |             O    |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 22.

Problem 4 (quiz 15b in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O     O     O  O | X | O  O           X |
| O     O     O  O |   |                X |
|       O     O  O |   |                  |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|    X     X     X |   |                  |
|    X     X  X  X |   |                  |
| O  X     X  X  X |   |    X             |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 32.

Problem 5 (quiz 88c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
14|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
X|                  |   |                  |
X| X  X  X  X  X  X |   |                  |
X| X  X  X  X  X  X | O |                  |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 21.

Stay tuned for rollout results by THREE(!) bots, plus human
solutions and scoring key.  All will be in Part 3 of this series.

Part III. Solutions.

The following five problems are taken from "The Backgammon Quiz
Book" by Prince Joli Konsil.  (Playboy Press Paperbacks, 1978.)
Also, these positions were republished (with different
analysis by Konsil) in GAMES magazine July/August 1980 issue.
NOTE that cubes were NEVER shown in either the book or in the
magazine.  All games are \$ play with gammons and backgammons.

Problem 1 (quiz 40c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-|
11| O                |   |                  |
O| O                |   |                  |
O| O                |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
X|                  |   |                  |
X|                  |   |                  |
X|       X          |   |                  |
X|       X  X       |   |                  |
X|    X  X  X       |   |                  |
X| O  X  X  X       |   |                  |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 32

Play      Konsil   1980 bot     EXBG       JFv3.0 L6
score     rollout    rollout      rollout

3/0, 4/2      5      46(0.5)%   47.0(0.5)%   48.2(0.7)%
4/1*, 3/1     2      "close"    49.0(0.5)%   50.1(0.6)%
3/0, 2/0      0      39(0.5)%   39.3(0.3)%   40.3(0.7)%
3/0, 3/1*     0      39(0.5)%    ------      41.6(0.8)%

Running score:  1980 bot    5
JFv3.0     2

(NOTES ON SCORING:  "correct" answer is always 5.  Alternate plays can
be somewhere between 0 and 5, inclusive.  "close" means close to the
correct answer in terms of winning percentage, but not quite as good.)

Problem 2 (quiz 76c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
|          X  O  O |   |    O           X |
|                O |   |    O           X |
|                O |   |    O             |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                X |   |    X           O |
| O        X  X  X |   |    X        X  O |
| O  O     X  X  X | O |    X        X  O |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 41.

Play      Konsil   1980 bot     EXBG       JFv3.0 L6
score     rollout    rollout      rollout

7(2)          5        2nd        ----      0.951(0.019)
6/2*, 20*     4        1st        ----      1.074(0.018)
6/2*, 8/7     2        4th        ----      1.041(0.019)
11/7, 20*     0        3rd        ----      0.964(0.020)

Running score:  1980 bot    9
JFv3.0     6

Problem 3 (quiz 29c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
|       O  O  O  O |   |          X       |
|       O  O  O  O |   |                  |
|             O  O |   |                  |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
X| X  X             |   |                  |
X| X  X             |   |                  |
X| X  X  X  O       |   |                  |
X| X  X  X  O  O    |   |             O    |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 22.

Play      Konsil   1980 bot     EXBG        JFv3.0 L6
score     rollout    rollout       rollout

15/11*,1(2)   5       equal    1.066(0.012)  0.891(0.020)
15/11*/7      2       equal    1.184(0.016)  1.138(0.018)

Running score:  1980 bot   12.5  (avg. this problem's scores)
JFv3.0     8

Problem 4 (quiz 15b in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O     O     O  O | X | O  O           X |
| O     O     O  O |   |                X |
|       O     O  O |   |                  |
|                O |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|    X     X     X |   |                  |
|    X     X  X  X |   |                  |
| O  X     X  X  X |   |    X             |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 32.

Play      Konsil   1980 bot      EXBG        JFv3.0 L6
score     rollout     rollout       rollout

b/23, 8/5     5    50%(more G) -0.186(0.008)  -0.187(0.015)
b/23, 4/1*    2    50%(less G)  0.142(0.004)   0.117(0.015)

(NOTE:  "more G" or "less G" refers to gammon losses for X.
"50%" is X's total game winning chances.)

Running score:  1980 bot    17.5
JFv3.0     10

Problem 5 (quiz 88c in "The Backgammon Quiz Book")

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
14|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
O|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
|                  |   |                  |
X|                  |   |                  |
X| X  X  X  X  X  X |   |                  |
X| X  X  X  X  X  X | O |                  |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

X to play 21.

Play      Konsil   1980 bot     EXBG       JFv3.0 L6
score     rollout    rollout      rollout

3/0           5        5+%      7.3(0.22)%    8.4(0.1)%
2/0, 1/0      4       <4 %      5.9(0.19)%    6.8(0.1)%
6/4, 6/5      2       ----      8.2(0.08)%    8.8(0.1)%
2/0, 2/1      0       ----      7.6(0.13)%    9.0(0.1)%

Final score:    1980 bot    22.5
JFv3.0     10
(out of a possible 25)

I did not score EXBG, because apparently back then I didn't
feel it was reliable enough on the backgame problem to perform a
rollout--maybe unfair of me.  And notice that EXBG agrees rather
well with JF on the other problems.  Konsil had a ranking which
he assigned to the scores.  I've transposed his ranking to %-ages
and here is what that gives:

>83%     Tournament Grandmaster
75--83%     Club Champion
66--74%     Very Good
58--65%     Good
50--57%     Fair

Below 50% he gave no designation.  We can see that the 1980 bot
ranked as "Tournament Grandmaster" but Jellyfish is not even "Fair".

Now for some commentary.  Let's NOW assume that JF is right.  On
which problems did Konsil and his bot have trouble?  The two bearoff
problems have candidate plays which are close, according to JF.
And you might expect primitive robots to be able to handle bearoffs,
since typically these positions are easier.  In problem 1, the 1980
bot also said the plays were close, but got the order reversed.
Konsil apparently didn't see JF's "correct" answer as being very
close since he only gave it 2 out of a possible 5 points.  In
absolute terms (X's winning percentage) the 1980 bot was off by
about 2-4% (getting 46% instead of JF's 48-50%), not too bad.

For problem 5, Konsil didn't consider the correct play worthy
of comment in his book (thus the 0 score).  At the end of his GAMES
article, he gave a quiz in which one of the problems was to explain
why 2/0, 2/1 was "much poorer" than 3/0.  He missed the boat.
Presumably he didn't even have the 1980 bot roll the correct play
out, so we can't blame the bot here.  But it said the other plays
should win 4-5%, while in actuality they win almost twice as much.
Not good.

Ironically, the backgame problem is where the 1980 bot seemed
to do best!  Luck?  Some think JF is weak at backgames.  Could it
be that the 1980 bot is as good as JF in this position?  Ha, ha.

Problems 3 & 4 are the most surprising of all.  Jf says the
candidate plays are not even close in either problem, yet Konsil
and the 1980 bot got them both wrong.  Has BG evolved this much
in 20 years?  I don't think so.

In the margins of my copy of "BG Quiz Book" I wrote (back in
1978 or 79) that Konsil's solution for problem 4 was "WRONG!"  And
for problem 3 I questioned his choice.  I wasn't that great of a
player back then, either...
```

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### Books

Bagai: Classic Backgammon Revisited  (Gregg Cattanach, Feb 2002)
Bagai: Classic Backgammon Revisited #100  (Raccoon, Nov 2004)
Bagai: Classic Backgammon Revisited--Errata  (Jeremy Bagai+, Apr 2005)
Ball: Alpha Backgammon  (James Takahashi+, May 1994)
Ballard & Weaver: Backgammon Openings Book A  (Marty Storer, Jan 2008)
Ballard & Weaver: Backgammon Openings Book A  (Mislav Radica, Nov 2007)
Ballard & Weaver: Backgammon Openings Book A  (Rob Adams+, Oct 2007)
Ballard & Weaver: Backgammon Openings Book A  (Gregg Cattanach, Oct 2007)
Ballard & Weaver: Backgammon Openings Book A  (Neil Kazaross+, Jan 2005)
Ballard & Weaver: Backgammon Openings--Volunteers needed  (Nack Ballard, June 2007)
Barr: Barr on Backgammon  (Walter Swan+, Feb 1996)
Becker: Backgammon for Blood  (Gus, Mar 2003)
Becker: Backgammon for Blood  (PTaber+, June 1999)
Becker: Backgammon for Blood  (Michael Fuhrmann, Aug 1997)
Becker: Backgammon for Blood  (Daniel Murphy, July 1997)
Becker: Backgammon for Blood  (Durf Freund+, May 1994)
Bell: Winning with the Doubling Cube  (&Atilda;˜ystein Johansen+, Apr 2006)
Bell: Winning with the Doubling Cube  (André Nicoulin, Oct 2000)
Bell: Winning with the Doubling Cube  (David Montgomery, May 1999)
Bell: Winning with the Doubling Cube  (Peter Bell, Aug 1998)
Bell: Winning with the Doubling Cube  (Jacques Torrione, Feb 1998)
Bell: Winning with the Doubling Cube  (Robert Scibelli, Dec 1997)
Bell: Winning with the Doubling Cube  (Kevin Bastian, Nov 1997)
Bray: Backgammon for Blood  (Chris Bray, Sept 2007)
Bray: Backgammon to Win  (Chris Bray, June 2007)
Bray: Backgammon to Win, second edition  (Chris Bray, Aug 2012)
Bray: Backgammon--An Independent View  (Chris Bray, May 1998)
Bray: Backgammon--An Independent View Revisited  (Chris Bray+, Jan 2005)
Bray: Second Wind  (Chris Bray, May 2007)
Bray: What Colour is the Wind?  (Chris Bray+, June 2002)
Bray: What Colour is the Wind?--Rerelease  (Chris Bray, Sept 2006)
Brooks: Backgammon's Best Openings and Replies  (Chuck Bower+, Dec 2004)
Clay: Backgammon Winning Strategies  (Michael Strato, Nov 1999)
Clay: Backgammon Winning Strategies  (Gary Wong, Jan 1998)
Cooke & Bradshaw: Backgammon--The Cruelest Game  (Chuck Bower+, Aug 1998)
Cooke & Orléan: Championship Backgammon  (Timothy Chow+, Apr 2011)
Cooke & Orléan: Championship Backgammon  (Marty Storer, Sept 2004)
Cooke: Paradoxes and Probabilities  (Neil Kazaross+, Sept 2004)
Cooke: Paradoxes and Probabilities  (Peter van Arkel+, Sept 2002)
Cooke: Paradoxes and Probabilities  (Donald Kahn, Dec 1998)
Cooke: Paradoxes and Probabilities  (Stephen Turner, Apr 1996)
Corbett: Backgammon Problems  (Stick+, Jan 2008)
Deyong: The Playboy Book of Backgammon  (Shuman Lloyd Lee, Aug 1991)
Dwek: Backgammon for Profit  (Bob Stringer, Sept 2002)
Euler: Everyday Errors in Checker Play  (BaronGossettEulerPhD+, June 2012)
Garal: Fair Backgammon Tournament Rules  (Jakob Garal, June 2007)
Heinrich & Woolsey: New Ideas in Backgammon  (Douglas Zare, Mar 2003)
Heinrich & Woolsey: New Ideas in Backgammon  (Craig E. Groeschel+, Sept 1998)
Heinrich & Woolsey: New Ideas in Backgammon  (David Montgomery, May 1997)
Heyken & Fischer: The Backgammon Handbook  (Martin Fischer, Sept 1998)
Heyken & Fischer: The Backgammon Handbook  (Marina Smith, Feb 1998)
Hickey & Storer: What's Your Game Plan?  (Timothy Chow, May 2011)
Jacoby & Crawford: The Backgammon Book  (Patrick Wilken, Aug 1991)
Kansil: The Backgammon Quiz Book  (Daniel Murphy, July 1997)
Kansil: The Backgammon Quiz Book--Five problems  (Chuck Bower, Oct 1997)
Kennedy & Papazian: Backgammon Master Games  (Ben Fairbank+, Apr 1999)
Kershaw: Backgammon Funfair  (Tom Keith+, July 2012)
Kershaw: Backgammon Funfair  (Peter Bennet, May 2012)
Lamford: 100 Backgammon Puzzles  (Harold Simon+, Oct 2001)
Lamford: 100 Backgammon Puzzles  (Mark Driver, July 2001)
Lamford: 100 Backgammon Puzzles--Snowie analysis  (Michael Schell, Oct 2001)
Lamford: Improve Your Backgammon  (Alef Rosenbaum, May 2003)
Leet: Winning Backgammon  (Ryan Long, Apr 2002)
Leet: Winning Backgammon  (MW Book Review, July 1999)
Lortz: Double ... now: An Authentic Cube Remedy  (Chuck Bower+, Jan 2004)
Mabardi & Luce: Vanity Fair's Backgammon to Win  (Paul Tanenbaum, Feb 1998)
Magriel: Backgammon  (Baldo+, Mar 2004)
Magriel: Backgammon  (Neil Kazaross, July 2003)
Magriel: Backgammon  (Chuck Bower, Nov 1999)
Magriel: Backgammon  (Dean Gay, Sept 1999)
Magriel: Backgammon  (David Montgomery+, Aug 1997)
Magriel: Backgammon--2004 Edition  (Tom Keith+, Dec 2004)
Magriel: Backgammon--GnuBG evaluations  (Randy, July 2008)
Martyn: Phillip Martyn on Backgammon  (Steve Brorens+, Nov 1996)
Munchkin: Gambling Wizards  (Chuck Bower, Aug 2003)
Obolensky & James: Backgammon the Action Game  (Edward D. Collins+, Oct 1999)
Reese & Brinig: Backgammon: The Modern Game  (Al Mirpuri+, Sept 2011)
Robertie: 501 Essential Backgammon Problems  (Paul Epstein, July 2005)
Robertie: 501 Essential Backgammon Problems  (Albert Silver, Nov 2002)
Robertie: 501 Essential Backgammon Problems  (Tore Fredriksen, July 2002)
Robertie: 501 Essential Backgammon Problems  (Erik M Sørensen, May 2000)
Robertie: 501 Essential Backgammon Problems  (Daniel Hollis, May 2000)
Robertie: 501 Essential Backgammon Problems #75  (Hardy Hübener+, Nov 2005)
Robertie: Advanced Backgammon  (Doni+, Jan 2005)
Robertie: Advanced Backgammon  (Scott Steiner+, Sept 2002)
Robertie: Advanced Backgammon  (James Eibisch, Jan 1998)
Robertie: Advanced Backgammon  (Allen R. Adams, Nov 1995)
Robertie: Advanced Backgammon #165  (Peter Grotrian+, Mar 2005)
Robertie: Advanced Backgammon--Errata  (Matt Senecal+, Nov 2004)
Robertie: Advanced Backgammon--JF rollouts  (Øystein Johansen, June 2001)
Robertie: Advanced Backgammon--JF rollouts  (Alexander Nitschke, Feb 1997)
Robertie: Advanced Backgammon--JF rollouts  (Peter Fankhauser, Jan 1996)
Robertie: Backgammon for Winners  (Carl Tait, Aug 1998)
Robertie: Backgammon for Winners  (Gerry Tesauro, Oct 1993)
Robertie: Modern Backgammon  (Mattias+, Apr 2003)
Robertie: Modern Backgammon  (Gregg Cattanach, Oct 2002)
Robertie: Modern Backgammon  (Frank Mazza+, May 2002)
Robertie: Reno 1986  (AH+, Aug 2007)
Shiina: Cube Action 1000  (Mochy, Feb 2013)
Steed: Backgammon: The Meanest Game  (Albert Steg, Aug 1998)
Stern: Backgammon: The Quick Course to Winning Play  (Mark Driver, May 2001)
Storer: Backgammon Praxis  (Chase+, Apr 2007)
Storer: Backgammon Praxis  (Marty Storer+, May 2004)
Thorne's Backgammon Tactics (Reprint)  (Sam Sloan, July 2012)
Tremaine: Amazing Book of Backgammon  (Jim Wallace, Feb 1998)
Trice: Backgammon Boot Camp--2nd edition  (Jeremy Bagai+, June 2007)
Tzannes brothers: Backgammon Games and Strategies  (Mark Driver, Apr 2001)
Tzannes brothers: Backgammon Games and Strategies  (Albert Steg, May 1994)
Tzannes brothers: How Good Are You at Backgammon?  (Mark Driver, July 2001)
Wiggins: Boards, Blots, and Double Shots  (Ned Cross+, Mar 2004)
Williams: Backgammon Live in London  (Sean Williams+, June 2008)
Woolsey & Beadles: 52 Great Backgammon Tips  (Paul Epstein+, Dec 2007)
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Woolsey & Jones: Understanding Backgammon  (Jon Nall+, Feb 2004)
Woolsey: How to Play Tournament Backgammon  (John Bazigos, Oct 1994)
Woolsey: The Backgammon Encyclopedia Vol 1  (Dean Gay+, Feb 2004)

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 Book Suggestions Books Cheating Chouettes Computer Dice Cube Handling Cube Handling in Races Equipment Etiquette Extreme Gammon Fun and frustration GNU Backgammon History Jellyfish Learning Luck versus Skill Magazines & E-zines Match Archives Match Equities Match Play Match Play at 2-away/2-away Miscellaneous Opening Rolls Pip Counting Play Sites Probability and Statistics Programming Propositions Puzzles Ratings Rollouts Rules Rulings Snowie Software Source Code Strategy--Backgames Strategy--Bearing Off Strategy--Checker play Terminology Theory Tournaments Uncategorized Variations

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