Cube Handling in Races

Forum Archive : Cube Handling in Races

Thorp count

From:   Simon Woodhead
Address:   simon@Aus.Sun.COM
Date:   11 September 1991
Subject:   Re: Edward Thorpe on running games?
Google:   1991Sep11.003958.7062@Aus.Sun.COM

Edward Thorpe worked out a formula for calculating race doubles
(an elaborated pip-count) which is claimed to be 99% accurate. There
are certain positions (described in Bill Robertie's "Advanced Backgammon")
where it falls down a little. On the whole, it is extremely accurate
for medium and long races, and has the advantage of being easily (:-)
calculated over the table.

This is the formula:

. Compute the leader's doubling number as follows:
    1) The leader's pip count,
    2) plus two for each of the leader's remaining checkers,
    3) plus one for each checker on the ace point,
    4) minus one for each point covered in the home board,
    5) plus 10% of the total so far, if that total is greater than 30.

. Call the final result L, the leader's adjusted pip count.
. Compute the trailer's doubling number by following steps 1-4, but
  omitting step 5. Call this result T, the trailer's adjusted pip count.

. If T > L-2, the leader should double.
. If T > L-1, the leader should redouble.
. If T > L+2, the trailer should pass.

Looks harder than it is. Anyone serious should be able to do a
normal pip count fairly quickly. Adding/subtracting the other bits
just takes a bit of practise.

If you want something a little easier, try this:

. Compute both player's pip count. Find the difference and compare
  that difference to the leader's count.

. With a difference of 8% or more, the leader has an initial double.
. With a difference of 9% or more, the leader has a redouble.
. With a difference of 12% or less, the trailer has a take.

Note that these formulae apply to money-game races, and do not take
any account of match-play scores. Use at your own risk!

Simon simon@Aus.Sun.COM
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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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