Cube Handling in Races

 Value of a pip

 From: Tom Keith Address: tom@bkgm.com Date: 26 June 2004 Subject: Re: Two articles on cube handling Forum: rec.games.backgammon Google: wUaDc.2132\$H0G1.330@news04.bloor.is.net.cable.rogers.com

```The following chart shows the probability of winning for the
player-on-roll at different length races and various leads.
The chart is an average of the positions I rolled out.

---------------- Length of Race -------------------
Lead     20    30    40    50    60    70    80    90   100

-14:  .101  .154  .193  .222  .244  .258  .270  .285  .297
-13:  .114  .177  .214  .238  .265  .280  .290  .305  .317
-12:  .149  .211  .246  .273  .295  .307  .315  .325  .334
-11:  .177  .247  .279  .298  .319  .329  .338  .349  .357
-10:  .210  .283  .309  .328  .347  .354  .363  .371  .375
-9:  .250  .312  .338  .356  .369  .377  .382  .389  .395
-8:  .288  .340  .359  .377  .387  .397  .408  .413  .415
-7:  .333  .380  .410  .423  .422  .425  .430  .432  .435
-6:  .384  .426  .442  .449  .450  .449  .452  .456  .459
-5:  .430  .470  .480  .478  .475  .474  .477  .480  .482
-4:  .494  .505  .503  .504  .508  .503  .501  .501  .500
-3:  .530  .537  .540  .531  .529  .529  .526  .524  .521
-2:  .569  .555  .553  .557  .559  .555  .549  .547  .547
-1:  .616  .614  .600  .588  .577  .574  .573  .568  .565
0:  .648  .643  .635  .619  .610  .604  .594  .588  .583
1:  .691  .672  .654  .643  .634  .624  .616  .610  .602
2:  .727  .707  .693  .671  .655  .645  .636  .630  .622
3:  .762  .735  .712  .693  .676  .667  .657  .648  .641
4:  .782  .760  .741  .718  .700  .690  .677  .667  .661
5:  .806  .780  .764  .741  .726  .712  .698  .689  .680
6:  .835  .805  .786  .767  .748  .732  .717  .708  .698
7:  .856  .828  .800  .776  .765  .753  .734  .720  .712
8:  .871  .850  .828  .800  .780  .767  .753  .739  .728
9:  .890  .866  .842  .816  .799  .786  .770  .755  .744
10:  .907  .883  .856  .831  .815  .802  .786  .775  .763

AvgPip:  .033  .029  .027  .025  .024  .022  .021  .020  .019

Tom
```

### 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)