Forum Archive :
Puzzles
> Maybe we could hold a contest: find the position & dice roll which has
> the most possible moves.
Here's my entry:
white on roll
Black: 1 checker on his 24 point
White: single checkers his 3,5,7,9,11,13,15,17,18,19,20,21,22,23,24 point
dice: 11
2220 moves.
Kees


Douglas Zare writes:
It's not too hard to show that the positions with the most number of moves
possible will involve 11: Any move you can make with 22 can be made with
11 if you order the points 242220...2232119...1. There are too few
moves possible with nondoubles or checkers on the bar or the bearoff.
The most I have found is 2226, with checkers on the 24, 23, 21, 20,...6,5,
and 3. There are a few variations possible in this ordering, e.g., pushing
the checker on the 5 to the 4. An easy upper bound on the number of moves
possible is 18 choose 4=3060, which would be the number of ways to
distribute 4 moves to 15 distinct objects, but I think that the 2226 is
optimal.
[Ray Kershaw writes:]
I interpret Zare has having 15 checkers on the 24, 23, 21, 20, 18, 17, 15,
14, 12, 11, 9, 8, 6, 5 and 3 points. Can you explain how he counts to
2,226?


Ian Shaw writes:
13 14 15 16 17 18 19 20 21 22 23 24
++++++++++++++
 O X X O X X   O X X O X X 
   
    ++
     1 
    ++
   
 X X O X X O   X X O X O O 
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1
X to play 11. (2,226 legal plays)
X to play 21. (224 legal plays)
You can find this many moves using gnubg. The default move limit must be
increased with the command "set analysis limit 3000" or the Settings,
Analysis, Move Limit dialogue box. Make sure you've selected only 0ply!




Puzzles
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Find a position that goes from White being too good to double to Black being too good to double.
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What position and roll give the greatest loss in equity?
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How can you go from the backgammon starting position to Nackgammon?
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Find a position and roll where the correct play depends on who owns the cube.
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What is the highest possible gammon rate in an undecided game?
 Infinite loops (Timothy Chow, Mar 2013)
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Position that's a redouble but not a double?
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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.
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Find a position that can be legally reached but never through optimum play.
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Go from the starting position to the mirror position (colors reversed)
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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.
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Find a nocontact position where it is better to move a checker than bear one off.
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Find a nocontact position where it is better to move a checker than bear one off.
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From the starting position, form a full 6prime in three rolls.
 Pruce's paradox (Alan Pruce+, Dec 2012)
 Quiz (Martin Krainer, Oct 2003)
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 Returning to the start (Nack Ballard, May 2010)
What is the least number of rolls that can return a game to the starting position?
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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?
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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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