Forum Archive :
Puzzles
Marc Gray wrote:
> In the Guinness Book of World Records there appears the following
> re: the shortest backgammon game possible: "Alan Malcolm Beckerson
> (b. 21 Feb. 1938) devised a game of just 16 throws in 1982."
> Does anyone know what the 16 shakes and their corresponding moves
> are?
That's shortest game cubeless, of course. But I claim it's impossible.
Each player starts with 34 tables to change, which can't be done in
fewer than 9 throws. So the shortest game most be at least 17 moves.
I'll try and remember to ask Alan at the next BIBA tournament.
No, I don't know what the moves were, but it's quite easy to devise
some. What's not so easy is to devise a game where each player plays
the correct moves all the time and it ends in 17 moves. Here is an
attempt at such a game. I believe all the moves to be correct except
X's 3rd move. (Though that's not so wrong that it's implausible that
anyone might play it). Can anyone devise one were the indisputably
right move is played all the time?
Score is 00 in a 1 point match.
Opponent is X  Turner is O
O: (6 3) 2418 1310
X: (3 5) 1722 1922
O: (6 6) 2418 137 137 104
X: (5 5) 1217 1217 1217 1722
O: (6 6) 137 137 82 82
X: (5 5) 1217 1722 1924 1924
O: (6 6) 1812 1812 126 82
X: (2 3) bar3 13
O: (6 6) 71 71 71 71
X: (3 3) bar3 85 85 85
O: (6 6) 126 6off 6off 6off
X: (2 3) 35 58
O: (6 6) 6off 6off 6off 6off
X: (6 5) 813 1319
O: (5 5) 4off 2off 2off 2off
X: (4 3) 37 36
O: (1 1) 1off 1off 1off 1off

Stephen R. E. Turner
Stochastic Networks Group, Statistical Laboratory, University of
Cambridge
email: sret1@cam.ac.uk
WWW: http://www.statslab.cam.ac.uk/~sret1/home.html


Kit Woolsey writes:
Ok, Steve, I think I've found one (wasn't easy) which involves correct
play. All the moves were deemed correct by jellyfish level 5 (and
only the opening 43 play was close), so how bad can that be.
X: 43 13/10, 13/9
O: 55 13/3(2)
X: 55 13/3, 10/5, 8/3
O: 55 13/3, 13/8(2)
X: 66 24/18(2), 13/7(2)
O: 33 24/21(2), 8/5(2)
X: 66 18/12, 18/6, 9/3
O: 66 21/9(2)
After that, X just rolls 66 each roll.
I think this meets the stipulated conditions.
Kit




Puzzles
 13 blots (Timothy Chow+, Aug 2009)
Alice, who is not on the bar, discovers that however she plays she ends up with 13 blots. What is her position and roll?
 Alltime best roll (Kit Woolsey+, Dec 1997)
What position and roll give the greatest gain in equity?
 Alltime worst roll (Tim Chow+, Feb 2009)
Find a position that goes from White being too good to double to Black being too good to double.
 Alltime worst roll (Michael J. Zehr, Jan 1998)
What position and roll give the greatest loss in equity?
 Back to Nack (Zorba+, Oct 2005)
How can you go from the backgammon starting position to Nackgammon?
 Cube ownership determines correct play (Kit Woolsey, Jan 1995)
Find a position and roll where the correct play depends on who owns the cube.
 Highest possible gammon rate (RobertJan Veldhuizen+, May 2004)
What is the highest possible gammon rate in an undecided game?
 Infinite loops (Timothy Chow, Mar 2013)
 Is this position reachable? (Timothy Chow+, Feb 2013)
 Janowski Paradox (RobertJan Veldhuizen+, Nov 2000)
Position that's a redouble but not a double?
 Least shots on a blot within direct range (Raymond Kershaw, Dec 1998)
Find a position with no men on bar that has the least number of shots out of 36 to hit a blot within direct range.
 Legal but not likely (David desJardins, July 2000)
Find a position that can be legally reached but never through optimum play.
 Lowest probability of winning (masque de Z+, Apr 2012)
What is the smallest win probability in backgammon, greater than zero.
 Mirror puzzle (Nack Ballard, Apr 2010)
Go from the starting position to the mirror position (colors reversed)
 Most checkers on the bar (Tommy K., May 1997)
What is the maximum total possible checkers on the bar?
 Most possible plays (Kees van den Doel+, May 2002)
Find the position and dice roll which have the most possible plays.
 Notsogreedy bearoff (Kit Woolsey, Mar 1997)
Find a nocontact position where it is better to move a checker than bear one off.
 Notsogreedy bearoff (Walter Trice, Dec 1994)
Find a nocontact position where it is better to move a checker than bear one off.
 Priming puzzle (Gregg Cattanach+, May 2005)
From the starting position, form a full 6prime in three rolls.
 Pruce's paradox (Alan Pruce+, Dec 2012)
 Quiz (Martin Krainer, Oct 2003)
 Replace the missing checkers (Gary Wong+, Oct 1998)
 Returning to the start (Nack Ballard, May 2010)
What is the least number of rolls that can return a game to the starting position?
 Returning to the start (Tom Keith+, Nov 1996)
What is the least number of rolls that can return a game to the starting position?
 Shortest game (Stephen Turner+, Jan 1996)
What is the shortest (cubeless) game in which both players play reasonably?
 Small chance of ending in doubles (Walter Trice, Dec 1999)
Find a position where the probability of the game ending in doubles is less than 1/6.
 Threecube position (Timothy Chow+, Sept 2011)
Find a position and roll for which three different checker plays are best, depending on the location of the cube.
 Trivia question (Walter Trice, Dec 1998)
What is the symmetric bearoff with the smallest pip count that is not an initial double?
 Worst possible checker play (Gregg Cattanach+, June 2004)
What position and roll have the largest difference between best and worst play?
 Worst possible opening move (Gregg Cattanach, June 2004)
What is the worst possible first move given any choice of dice?
 Worst symmetric bearoff of 8 checkers (Gregg Cattanach+, Jan 2004)
What symmetric arrangement of 8 checkers in each player's home board gives roller least chance to win?
 Worst takable position (Christopher Yep, Jan 1994)
What position has lowest chance of winning but is a correct take if doubled?
 Zero equity positions (Kit Woolsey, Apr 1995)
Find a position with exactly zero equity in (1) money play or (2) cubeless.
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