Cube Handling in Races

Forum Archive : Cube Handling in Races

Kleinman count

From:   André Nicoulin
Date:   4 September 1998
Subject:   Re: Kleinman count
Google:   6so821$8c4$

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:

Winning chances
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.
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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)  [GammOnLine forum]
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)  [GammOnLine forum]
Effective pipcount and type of position  (Douglas Zare, Jan 2004)  [GammOnLine forum]
Kleinman count  (Øystein Johansen+, Feb 2001) 
Kleinman count  (André Nicoulin, Sept 1998) 
Kleinman count  (Chuck Bower, Mar 1998)  [Recommended reading]
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)  [GammOnLine forum]
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) 

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