Cube Handling in Races

 Near end of game

 From: David Montgomery Address: monty@cs.umd.edu Date: 22 February 1997 Subject: Re: Over the Board Bearoff Analysis Forum: rec.games.backgammon Google: 5eo4oo\$off@twix.cs.umd.edu

```Dean Gay writes:
>   +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
> 13|          X  X    |   |                  |
>  X|                  |   |                  |
>  O|             O    |   |                  |
> 12|    O        O    |   |                  |
>   +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
>
> O on roll.
> Should O double?
>
> I'm wondering, what is the
> thought process that a good player goes through *over the board* to
> figure out these type of decisions?
>
> Dean

Here was my thought process: My pipcount is 12, my opponent's 9,
so I'm down 3 pips.  I'll probably waste more than my opponent,
so I really trail by about 4 pips.  In a long race, trailing by
about 4 pips and being on roll makes the chances about equal, but
here the race is so short that I think I'm the favorite even if
I'm down 4.  Still, I can't be a big favorite, definitely less
than 60% cubeless.

This would be as far as I would go unless doubling were a close
decision with a cpw of more than 50% to less than 60%.  For most
scores, it's not enough to double, especially since I can get
many efficient cubes after taking a roll.  (For example, after
53 or 63, with two on the deuce point, vs your opponent's one
roll position, you have a very efficient money cube.)

Reality check:
Sconyers CD says O is only a little over 52% here, at the low
end of my rough guestimate.  O's effective lead in the race is

David Montgomery
monty on FIBS
monty@cs.umd.edu
```

### 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: 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)