Cube Handling in Races

 Calculating winning chances

 From: OpenWheel Address: none Date: 29 November 2005 Subject: Bearoff calculation techniques. Forum: GammOnLine

```Can someone steer me in the right direction as to how to figure my
winning chances in some lopsided bearoffs, such as one like the
following that came up for me today?

24  23  22  21  20  19      18  17  16  15  14  13
+---+---+---+---+---+---+---+---+---+---+---+---+---+
58  | O   O   O   O   O   O |   | O                     |
| O   O   O   O   O   O |   |                       |
|             O   O     |   |                       |
|                       |   |                       |
|                       |   |                       |
|                       |   |                       |
|                       |   |                       |
|     X           X     |   |                       |
|     X           X     |   |                       |
| X   X           X     |   |                       |  +---+
40  | X   X       X   X   X |   |                       |  | 2 |
+---+---+---+---+---+---+---+---+---+---+---+---+---+  +---+
1   2   3   4   5   6       7   8   9  10  11  12
```

 Raccoon  writes: ```I'll address the lopsided race, not adjusting for stacks and gaps and wastage. (1) For almost any race length, if you trail by 4 pips on roll, your GWC is about 50%. (2) For almost any race length, Leader's pipcount + 10% + 2 = about 78% GWC. (3) The value of each additiona pip beyond that declines quickly. Example: You trail on roll 50-46. You have about 50% GWC. You lead on roll 40-46. 40+4+2 = 46 -> you have about 78% GWC Going from 50-46 to 40-46, 10 pips better, gained you 28% GWC, so each pip was worth on average 2.8% GWC. Additional pips are worth much less than 2.8%. You could figure 40-46 = 78%, 40-50 = 85% (each additional pip being worth about 1.75%) and then I'd just add another 1% for each additional pip, so 40-58 comes to about 94% GWC. Of course you'd make an adjustment for the wasted pips. Check out Tom Keith's "Value of a pip" table at http://www.bkgm.com/rgb/rgb.cgi?view+1203 The table covers a range of leads from -14 to +10 and shows the average value of a pip at various race lengths. By going up and down the columns you can see how each pip's value changes depending on how close the race is. ```

### 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)