Forum Archive :
Don Woods wrote:
> In _The Backgammon Book_ by Jacoby & Crawford, they discuss when to
> double/redouble/accept, and start out "by considering only cases
> in which there is no possibility of a gammon" (an automatically
> doubled stake that is not received if the game ends due to a double
> being declined). They suggest you "consider a first double" if
> your chances are 7-to-5 or better, and "definitely make a first double"
> at 9-to-5 or better. That's a range of about 58-64%. But if you have
> already accepted a double, their suggested range for the redouble is
> to consider it at 3-to-2, and definitely redouble at 2-to-1 (60-67%).
This thread has gotten rather involved, but I can see that there
are several previously published works which are being overlooked. First,
I believe Jacoby/Crawford was the SECOND book published in the
modern era of backgammon. First was Obelinsky (sp?) and James around
1969. As such, although probably the best book ever written on BG at
the time of its release, it is today no more than an introduction.
The above quoted doubling points are, in general, way too low, IMHO.
I suggest the interested readers seek out the following studies:
1) Articles published in Management Science and also in Operations
Research (two scholarly journals) by Keeler and Spencer and by
Kobliska (and a co-author whose name I can't recall at the moment).
Both of these articles refer to GAMMONLESS games. Initially they
treat "continous" games (perfect cube efficiency) but then go on to
simulations of volatile, discontinuous cases--more like real BG.
2) Work by Danny Kleinman, starting with "Vision Laughs at Counting,
with Advice to the Dicelorn" (two volumes, esp. volume II, both
available from Carol Colefirstname.lastname@example.org).
3) by far the most complete coverage of the money cube that I know
of has been done by Rick Janowski. His results--formulas for double,
redouble, beaver, drop/take, play on, etc. for Jacoby, non-Jacoby AND
all outcomes (simple games, gammons, and backgammons) were published in
three issues of Hoosier Backgammon Newsletter in 1993. Write Butch
Meese ( email@example.com ) if interested in obtaining those back
issues. As an example, the following is just one of the formulas (and
the only one I happen to have memorized) which applies to the money take
point (in percentage of wins):
L - 0.5
T = ---------------
W + L + 0.5x
where W = (s + 2g + 3b)/(s + g + b)
and s,g,b are simple, gammon, and backgammon win chances for the person
considering whether to drop/take. L is the similar expression for losses.
x is a cube efficiency factory which varies from 0 (dead cube) to 1
(perfectly efficient cube) and is typically set to somewhere between
0.6 and 0.7.
You should be able to quickly see that gammonless cubeless is 25% and
gammonless cubeful is 20%, both numbers being bandied about in this thread.
Janowski doesn't include the derivations (but it took 3 issues just to
describe and list the results!). I recommend his work to anyone serious
in delving into this complex topic.
c_ray on FIBS
- Against a weaker opponent (Kit Woolsey, July 1994)
- Closed board cube decisions (Dan Pelton+, Jan 2009)
- Cube concepts (Peter Bell, Aug 1995)
- Early game blitzes (kruidenbuiltje, Jan 2011)
- Early-late ratio (Tom Keith, Sept 2003)
- Endgame close out: Michael's 432 rule (Michael Bo Hansen+, Feb 1998)
- Endgame close out: Spleischft formula (Simon Larsen, Sept 1999)
- Endgame closeout: win percentages (David Rubin+, Oct 2010)
- Evaluating the position (Daniel Murphy, Feb 2001)
- Evaluating the position (Daniel Murphy, Mar 2000)
- How does rake affect cube actions? (Paul Epstein+, Sept 2005)
- How to use the doubling cube (Michael J. Zehr, Nov 1993)
- Liveliness of the cube (Kit Woolsey, Apr 1997)
- PRAT--Position, Race, and Threats (Alan Webb, Feb 2001)
- Playing your opponent (Morris Pearl+, Jan 2002)
- References (Chuck Bower, Nov 1997)
- Robertie's rule (Chuck Bower, Sept 2006)
- Rough guidelines (Michael J. Zehr, Dec 1993)
- Tells (Tad Bright+, Nov 2003)
- The take/pass decision (Otis+, Aug 2007)
- Too good to double (Michael J. Zehr, May 1997)
- Too good to double--Janowski's formula (Chuck Bower, Jan 1997)
- Value of an ace-point game (Raccoon+, June 2006)
- Value of an ace-point game (Øystein Johansen, Aug 2000)
- Volatility (Chuck Bower, Oct 1998)
- Volatility (Kit Woolsey, Sept 1996)
- When to accept a double (Daniel Murphy+, Feb 2001)
- When to beaver (Walter Trice, Aug 1999)
- When to double (Kit Woolsey, Nov 1994)
- With the Jacoby rule (KL Gerber+, Nov 2002)
- With the Jacoby rule (Gary Wong, Dec 1997)
- Woolsey's law (PersianLord+, Mar 2008)
- Woolsey's law (Kit Woolsey, Sept 1996)
- Words of wisdom (Chris C., Dec 2003)