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Forum Archive :
Puzzles
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Christopher Yep wrote:
> This leaves open questions which I have wondered about for awhile:
> Are there any backgammon positions (other than the initial position,
> before either player has rolled) where:
>
> 1. The equity is 0? [money play]
> 2. The player on roll has a 50% chance to win the game? [1 pt. match
> (no cube)]
1) I know of a couple. One which is very easy to see is as follows:
X has one checker on 9 point, O has one checker on 6 point, X owns cube,
X is on roll. X wins outright on 12 of his rolls. Since all of his
rolls get him to at least the 6 point (where he has a claim or break-even
on O's decision whether or not to take a redouble), in essence X wins 1/4
of the 24 rolls he fails to get off immediately (since O gets off on 3/4
of his rolls), which comes to the desired 18 out of 36.
Another example which is more complex but my trusty computer says is so is:
X has two checkers on 4 point and one checker on 6 point, O has three (or
four) checkers on ace point, X owns cube, and X is on roll. Check it out
if you want to spend some pencil and paper time.
An example of a contact position might be as follows:
X has a closed board -- his other three checkers are two on O's 3 point
and one on O's 7 point. O's position: 3 on 1 point, 3 on 2 point, 4 on 4
point, 4 on 5 point, 1 on 12 point. X is on roll, cube is in center
(money game, Jacoby rule in use). Note that X has exactly 18 hitting
numbers, and if he misses O certainly has a claim with the cube. If we
assume that after hitting X's gammon chances are less than half his losing
chances (which seems like a proper assumption to me) then it is not
correct for X to double now. Therefore X wins when he hits, loses when he
misses, for equity of 0.
2) With no cube in play, I don't know any zero equity positions. If there
were one in a race I'm sure our regurgitating computer programs would
have spit it out by now and I would have heard of it. I guess in theory
there could be one in a contact position, but that would be awfully hard
to prove -- keep in mind that "gin" positions just aren't 100% gin.
Kit
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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)
![[GammOnLine forum]](pics/GammOnLine.gif)
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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