Forum Archive :
Puzzles
TarHeelFan recently posted an amusing infinite loop.
> 13 14 15 16 17 18 19 20 21 22 23 24
> +---+---+---+---+---+---+---+---+---+---+---+---+---+
> | | | O |
> | | | |
> | | X | |
> | | | |
> | | | |
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> +---+---+---+---+---+---+---+---+---+---+---+---+---+
> 12 11 10 9 8 7 6 5 4 3 2 1
>
> X rolls 5-5.
Inspired, I found another amusing loop with a similar flavor.
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| X | | |
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| O | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
12 11 10 9 8 7 6 5 4 3 2 1
X rolls 1-1 and plays 13/12*/9
12 11 10 9 8 7 6 5 4 3 2 1
+---+---+---+---+---+---+---+---+---+---+---+---+---+
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| | O | |
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| X | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
13 14 15 16 17 18 19 20 21 22 23 24
O rolls 3-3 and plays bar/16*/13.
13 14 15 16 17 18 19 20 21 22 23 24
+---+---+---+---+---+---+---+---+---+---+---+---+---+
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| | X | |
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| O | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
12 11 10 9 8 7 6 5 4 3 2 1
X rolls 3-3 and plays bar/13.
12 11 10 9 8 7 6 5 4 3 2 1
+---+---+---+---+---+---+---+---+---+---+---+---+---+
| X | | |
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| O | | |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
13 14 15 16 17 18 19 20 21 22 23 24
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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?
- All-time best roll (Kit Woolsey+, Dec 1997)
What position and roll give the greatest gain in equity?
- All-time 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.
- All-time 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 (Robert-Jan 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 (Robert-Jan 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.
- Not-so-greedy bearoff (Kit Woolsey, Mar 1997)
Find a no-contact position where it is better to move a checker than bear one off.
- Not-so-greedy bearoff (Walter Trice, Dec 1994)
Find a no-contact 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 6-prime 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.
- Three-cube 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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