Forum Archive :
Cube Handling in Races
I am not sure if you refer to the Kleinman formula to estimate cubeless
winning chances in race based on normal distribution theory. If it is the
case, here is a brief description. It comes from the help section of Snowie
Professional version 1.1 (Under preparation, mainly a patch of V1.0)
André Nicoulin, Oasya.
The Kleinman Rule
In match play, the score will strongly affect the value of the take points.
Hence you need in this case a more precise formula, which will provide you
a probability of winning the race. In "Vision Laugh at Counting" (1992),
Dany Kleinman develops such a formula. His formula is based on a concept
very familiar to statisticians named normal distributions. The rule is
expressed has follows.
Compute the player pipcount, and decrease it by 4 for taking into account
the fact that he is on roll. This leads to the corrected player pipcount P.
Compute the opponent pipcount as usual, O.
Compute the difference D equal to O minus P. It represents the lead in the
race of P over O.
Compute the sum S equal to O + P. It represents the total length of the
Compute the Kleinman metric D * D / S, i.e. D square over S. You then have
to compare the Kleinman metric with reference figures in order to know the
winning chances of the opponent:
of the opponent 17% 20% 21% 22% 24% 25% 30%
Kleinman metric 1.8 1.4 1.3 1.2 1.0 0.9 0.55
A more detailed table can be found in in "Fascinating Backgammon, Antonio
Ortega, second edition,1994. A description of how you reach this formula
can be found in "Vision Laugh ...", Dany Kleinman.
Cube Handling in Races
- Bower's modified Thorp count (Chuck Bower, July 1997)
- Calculating winning chances (Raccoon, Jan 2007)
- Calculating winning chances (OpenWheel+, Nov 2005)
- Doubling formulas (Michael J. Zehr, Jan 1995)
- Doubling in a long race (Brian Sheppard, Feb 1998)
- EPC example (adambulldog+, Jan 2011)
- EPC example: stack and straggler (neilkaz+, Jan 2009)
- EPC examples: stack and straggler (Carlo Melzi+, Dec 2008)
- Effective pipcount (Douglas Zare, Sept 2003)
- Effective pipcount and type of position (Douglas Zare, Jan 2004)
- Kleinman count (Øystein Johansen+, Feb 2001)
- Kleinman count (André Nicoulin, Sept 1998)
- Kleinman count (Chuck Bower, Mar 1998)
- Lamford's race forumla (Michael Schell, Aug 2001)
- N-roll vs n-roll bearoff (David Rubin+, July 2008)
- N-roll vs n-roll bearoff (Gregg Cattanach, Nov 2002)
- N-roll vs n-roll bearoff (Chuck Bower+, Dec 1997)
- Near end of game (Daniel Murphy, Mar 1997)
- Near end of game (David Montgomery, Feb 1997)
- Near end of game (Ron Karr, Feb 1997)
- One checker model (Kit Woolsey+, Feb 1998)
- Pip count percentage (Jeff Mogath+, Feb 2001)
- Pip-count formulas (Tom Keith+, June 2004)
- Thorp count (Chuck Bower, Jan 1997)
- Thorp count (Simon Woodhead, Sept 1991)
- Thorp count questions (Chuck Bower, Sept 1999)
- Value of a pip (Tom Keith, June 2004)
- Ward's racing formula (Marty Storer, Jan 1992)
- What's your favorite formula? (Timothy Chow+, Aug 2012)