Forum Archive :
Puzzles
What are the fewest number of rolls to rereach the starting position?
The answer to the above question is five (or four if doubles are allowed on
the first roll). However, to make it easier in one way but more difficult
in another, I divided the problem into three parts: In each case, you are
to find the startpositionrepeat sequences that meet the conditions below.
(a) Six rolls, if played well throughout.
(b) Five rolls, if all but one roll are played well.
(c) Four rolls, if doubles now legal on first roll.

Part (a): Six rolls are played well throughout. My solution is
62: 24/18, 13/11 41: 24/20, 8/7*
43: bar/18* 61: bar/24, 20/14*
51: bar/24, 18/13 51: 14/8
The second and sixth plays are errors of only .003 and .013 according to
Snowie evals, or .005 (full) and .019 (trunc) according to rollouts. The
fifth play is almost exactly tied. The other plays  first, third and
fourth  are clearly best. (The 43, which hits bar/18*, can just as well
be 52 or 61.)
Here is the sixroll sequence in full diagram illustration:

Part (b): Five rolls, one big error allowed. My solution is
61: 24/18, 8/7 62: 24/18*, 13/11
41: bar/24, 18/14* 51: bar/24, 18/13
51: 14/8
My allowed big error is on the first play. The other plays are played
"well." According to Snowie eval, the second play is .002 and the fifth is
.013.

Part (c): Four rolls, with doubles legal on first roll. I found only one
solution.
44: 24/16, 13/5 22: 24/20*/18, 13/11
11: bar/24, 16/14*/13 51: bar/24, 18/13




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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