Strategy--Checker play

Forum Archive : Strategy--Checker play

 
Saving gammon

From:   Ron Karr
Address:   karr@best.com
Date:   13 December 1997
Subject:   Re: match winning chances & saving gammons
Forum:   rec.games.backgammon
Google:   3492D812.FA3@best.com

Morten Wang wrote:
> O vs X, score is 2-2 in a 5-point match.
> O owns 2 cube.
>   +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
>  8| O  O  X  O       |   |                  |
>  O|    O     O       |   |                  |
>  O|    O     O       |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>   |                  |   |                  |
>   |                  |   |                  |
>   |                X |   |                  |
>   |    X        X  X |   |                  |
>   |    X  X  X  X  X |   |                  |
>   |    X  X  X  X  X |   |                  |
>   +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
> X rolls 5-1.
>
> I ran the rollout, and the result was this:
>
> Runs (22-16):
>     Wins G/BG  BG
> O: 100.0 10.1 0.0
> X:  0.0   0.0 0.0
> Equity O: 1.101
> Sd: 0.002
> Eq to: 22699
>
> Stays and makes 1:
>    Wins G/BG  BG
> O: 96.2 25.4 0.2
> X:  3.8  0.0 0.0
> Equity O: 1.180
> Sd: 0.003
> Eq to: 32000
>
>
> looking at a single game it's clear one has to run.  this was in a
> match so I tried to calculate the match winning chances for both moves
> from the result of the rollouts.
>
> O loses, score 3-away, 1-away, 25% wins.
> O wins single game, score 1-away, 3-away, 75% wins.
> O wins gammon, wins game, 100% wins.
>
> (lengthy calculation deleted)

There are three parts to solving this problem (if you're a human being
and not Jellyfish):

1. What are your winning chances if you stay back?
2. What is the gammon price?
3. By how much do you reduce your gammon chances if you run?

None of these require Jellyfish to answer, although #3 isn't obvious
without some research, so it's useful to look at JF's results.

1.  It's easy to figure out winning chances, since this is pretty much a
one-roll situation. ( If O fails to clear but doesn't leave a shot, X is
definitely running next time). So: O leaves a shot 1/3 of the time (I
find the easiest way to see this is that O plays SAFELY with all 1s and
2s (20 #s) + 4 doubles. = 24 numbers)

X hits with any 1 (30%).  So 1/3 x 30% = 10%.  How often does X then
win?  Clearly he's an underdog since O has 9 or 10 off.  I'd have
estimated slightly lower than JF's 3.8%, but somewhere around there.

2.  The gammon price measures the relative value of a gammon vs. a
win-loss swing.  It's useful in play decisions like this one; it's also
useful in cube decisions for determining how much gammons affect the
take point.

If you lose a gammon, you blow 2 points, while if you win the game, you
gain 4 points (compared with losing the game).  Therefore the gammon
price for money is always 2/4 = 50%.

At different match scores, the gammon price can vary.  At 3-away/3-away,
you gain 50% by winning the game and lose 25% by getting gammoned, so
again the gammon price is exactly 50%!.  So there's really no difference
between this score and money as far as gammons are concerned.

The way to use this figure:  in order for it to be correct to stay back,
my wins need to be at least 50% of my extra gammon losses.  So if I'm
winning, say 4%, by staying back, am I losing an additional 8% gammons?
This requires some information.

3.  If a gammon is very close, a single roll makes a huge difference..
around 30% gammon chances, I think.  The number drops as the gammon gets
more likely or more unlikely.  In this position, X is a favorite to get
off the gammon regardless (plus the roll is only 6 pips, slightly less
than average), so the extra gammon loss is only 15%, according to JF,
which makes sense.  But this is still way more than twice as great as
the winning chances, so running is clearly right.

Ron
 
Did you find the information in this article useful?          

Do you have any comments you'd like to add?     

 

Strategy--Checker play

Avoiding major oversights  (Chuck Bower+, Mar 2008) 
Bearing off with contact  (Walter Trice, Dec 1999) 
Bearing off with contact  (Daniel Murphy, Mar 1998)  [Long message]
Blitzing strategy  (Michael J. Zehr, July 1997) 
Blitzing strategy  (Fredrik Dahl, July 1997) 
Blitzing technique  (Albert Silver+, July 2003)  [GammOnLine forum]
Breaking anchor  (abc, Mar 2004) 
Breaking contact  (Alan Webb+, Oct 1999) 
Coming under the gun  (Kit Woolsey, July 1996) 
Common errors  (David Levy, Oct 2009) 
Containment positions  (Brian Sheppard, July 1998) 
Coup Classique  (Paul Epstein+, Dec 2006) 
Cube ownership considerations  (Kit Woolsey, Apr 1996) 
Cube-influenced checker play  (Rew Francis+, Apr 2003)  [GammOnLine forum]
Defending against a blitz  (Michael J. Zehr, Jan 1995) 
Estimating in volatile situations  (Kit Woolsey, Mar 1997) 
Gammonish positions  (Michael Manolios, Nov 1999) 
Golden point  (Henry Logan+, Nov 2002) 
Hitting loose in your home board  (Douglas Zare, June 2000) 
Holding games  (Casual_Observer, Jan 1999)  [Long message]
How to trap an anchor  (Timothy Chow+, Apr 2010) 
Jacoby rule consideration  (Ron Karr, Nov 1996) 
Kamikaze plays  (christian munk-christensen+, Nov 2010) 
Kleinman Count for bringing checkers home  (Øystein Johansen, Feb 2001) 
Late loose hits  (Douglas Zare+, Aug 2007)  [GammOnLine forum]
Mutual holding game  (Ron Karr, Dec 1996) 
Pay now or pay later?  (Stuart Katz, MD, Nov 1997) 
Pay now or pay later?  (Stephen Turner, Mar 1997) 
Pay now or play later?  (Hank Youngerman+, Sept 1998) 
Play versus a novice  (Courtney S Foster+, Apr 2004)  [GammOnLine forum]
Playing doublets  (Grunty, Jan 2008) 
Playing when opponent has one man back  (Kit Woolsey, May 1995) 
Prime versus prime  (Albert Silver+, Aug 2006)  [GammOnLine forum]
Prime versus prime  (Michael J. Zehr, Mar 1996) 
Saving gammon  (Bill Riles, Oct 2009) 
Saving gammon  (Ron Karr, Dec 1997) 
Splitting your back men  (KL Gerber+, Nov 2002) 
Splitting your back men  (David Montgomery, June 1995) 
Trap play problem  (Brian Sheppard, Feb 1997) 
When in doubt  (Stick+, Apr 2011) 
When to run the last checker  (Stick Rice+, Jan 2009) 
When you can't decide  (John O'Hagan, Oct 2009) 

[GammOnLine forum]  From GammOnLine       [Long message]  Long message       [Recommended reading]  Recommended reading       [Recent addition]  Recent addition
 

  Book Suggestions
Books
Cheating
Chouettes
Computer Dice
Cube Handling
Cube Handling in Races
Equipment
Etiquette
Extreme Gammon
Fun and frustration
GNU Backgammon
History
Jellyfish
Learning
Luck versus Skill
Magazines & E-zines
Match Archives
Match Equities
Match Play
Match Play at 2-away/2-away
Miscellaneous
Opening Rolls
Pip Counting
Play Sites
Probability and Statistics
Programming
Propositions
Puzzles
Ratings
Rollouts
Rules
Rulings
Snowie
Software
Source Code
Strategy--Backgames
Strategy--Bearing Off
Strategy--Checker play
Terminology
Theory
Tournaments
Uncategorized
Variations

 

Return to:  Backgammon Galore : Forum Archive Main Page