Puzzles

Forum Archive : Puzzles

 All-time best roll

 From: Kit Woolsey Address: kwoolsey@netcom.com Date: 20 December 1997 Subject: Re: puzzle Forum: rec.games.backgammon Google: kwoolseyELHAu3.4Kq@netcom.com

```> Anyone know what position and roll give the maximum equity change from
> pre-roll to post-roll? How about a twe roll sequence (a rolls then b)?
> Does allowing a double with a legimate take (then bad roll for
> doubler, then good roll for taker) produce the greatest change? Does
> the greatest single roll change include a game ending roll? I haven't
> thought much about this, but I know that the fertile minds of the
> regular posters will produce some fascinating situations (bonus points
> awarded for events that actually happened at the table). I can't wait
> to see the results.

Best I could come up with off the top of my head was the following:

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

O is on roll.  According to Jellyfish level 7, O's equity on a 1-cube is
-1.557.  However, if O rolls 6-6, his equity becomes +1.841.

Kit
```

 Paul Epstein  writes: ```The +1.841 after 66 seems much too low. Surely the equity is over 2. O has plenty of time to put enough checkers on the bar for a gammon and possibly for a backgammon. ```

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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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