Puzzles

Forum Archive : Puzzles

 
13 blots

From:   Timothy Chow
Address:   tchow8@hotmail.com
Date:   29 August 2009
Subject:   Blotfest puzzle
Forum:   bgonline

At Bob Koca's suggestion, I am posting a backgammon puzzle that I came up
with a few months ago.

Alice was playing backgammon. She was not on the bar. She rolled the dice
and discovered that, no matter how she played the roll, she would end up
with 13 blots. What was the position and the roll?

Remark: I used the word "the" but actually the solution is not unique. For
extra credit: Can 13 be increased to 14 or even 15? I don't think so, but I
don't have a proof.

Richard Munitz  writes:

I think this forces 13 blots ...

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

      X to play 5-5.

Or this, which both starts and ends with 13 blots ...

     24  23  22  21  20  19      18  17  16  15  14  13
    +---+---+---+---+---+---+---+---+---+---+---+---+---+
    | X   X   X   X   X   O |   | O   O   O   X       X |
    |                     O |   | O   O   O             |
    |                     O |   |                       |
    |                       |   |                       |
    |                       |   |                       |
    |                       |   |                       |
    |                       |   |                       |
    |                       |   |                       |
    |                     O |   | O   O                 |
XX  | X   X   X   X       O |   | O   O           X   X |
    +---+---+---+---+---+---+---+---+---+---+---+---+---+
      1   2   3   4   5   6       7   8   9  10  11  12
 
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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?
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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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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.
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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.
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)  [GammOnLine forum]
From the starting position, form a full 6-prime in three rolls.
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Quiz  (Martin Krainer, Oct 2003) 
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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)  [GammOnLine forum]
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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