Puzzles

Forum Archive : Puzzles

 Cube ownership determines correct play

 From: Kit Woolsey Address: kwoolsey@netcom.com Date: 31 January 1995 Subject: Re: Cube influence on moves - EXAMPLE PLEASE! Forum: rec.games.backgammon Google: kwoolseyD396Dn.JyH@netcom.com

```Bill Taylor wrote:
> This topic came up just recently as a sub-thread about the cube; it was
> one I'd been meaning to inquire about for some time. Various people said
> there were plenty of examples, but no-one has actually posted one!
> At least I didn't see any. So could someone please put their money where
> someone else's mouth is, and give an example.
>
> That is: an example of a position and roll, where the roll would be
> better played two different ways, depending on which side the cube's on.
>
> I would hope for as clear-cut an example as possible; preferably an
> end-game example, where the various expectations could be calculated
> exactly. But even if that isn't possible, then at least an example for
> which there would be very little difference of opinion among good
> players.

Sure enough.  Here's a simple example.  Suppose you have a closed board
with spares on your 3, 7, and 8 points, and you opponent has one checker
on the bar and his other 14 checkers deep in his home board someplace.
You have chosen to play on for the gammon (and why not, since nothing bad
can happen next roll and if you roll an awkward number you can then
reconsider and cash if you think it proper to do so).  Now you roll 5-5.
If you own the cube your proper play is 8/3, 7/2, 5/off(2).  The reason
is that you are planning on doubling next turn, so you want to minimize
the effect of your opponent's best roll now!  If you play "safe" by
moving two men from the 6 point and he rolls boxes, suddenly he has a
fighting chance in the race and can take a double.  It doesn't matter
that by taking two men off you are risking leaving a shot next turn
because of the gap, because that shot will never come -- you will turn
the cube before you roll, and your opponent will be forced to pass.
However if he already owns the cube, then your proper play is 8/3, 7/2,
6/1(2).  Now you will have to worry about leaving the shot next roll, and
the danger of that is greater than the danger of losing the race
outright.  There are other possible examples, some much more complex, but
this one should be pretty clear.

Kit
```

### Puzzles

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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.