Cube Handling in Races

 EPC examples: stack and straggler

 From: Carlo Melzi Address: camelzi@tiscali.it Date: 15 December 2008 Subject: Effective Pip Count with stragglers Forum: BGonline.org Forums

```I seem to have problems in handling cubes in bearoff positions with
stragglers.

Here are 2 examples that recently gave me some troubles.

- - - - - - - -

Example 1.

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

X doubles to 4. Should O take?

X has an EPC of about 29 (4*7+1). O has a pip count of 25. How can you
calculate O's wastage?

GnuBG estimates O's wastage as 6.675, for an EPC of 31,675.  O is then
trailing by 2.675 in the EPC. How do you use this number?  Is this a pass
or a take?

- - - - - - - -

Example 2.

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

X doubles to 4. Should O take?

X has an EPC of about 36 (5*7+1).  O has a pip count of 19.  How can you
calculate O's wastage?

GnuBG estimates O's wastage as 18.885, for an EPC of 37,885.  O is then
trailing by 1.885 in the EPC.  How do you use this number?  Is this a pass
or a take?

- - - - - - - -

I remember reading in Backgammon Boot Camp by Walter Trice a formula to use
to understand EPCs and related doubling decisions when stragglers are
present.  However, I don't have access to the book now.  Can anybody post
the formula or a link to where I can find it?

Many thanks for your help, Carlo Melzi
```

 Gregg Cattanach  writes: ```The formula to estimate the EPC of a stack + straggler (stack should be super-speed board with basically no misses) is: (#checkers * 3.5) + straggler pip count. If there are two stragglers: (#checkers * 3.5) + both stragglers total pip count - 4. ```

 Walter Trice  writes: ```In Example 1, I would treat O's position simply as 3 checkers with a pip count, not stack-and-straggler. (Where's the stack??) Boot Camp chapter 23 suggests using wastage = 4.7 for a one checker far outfield position and 5.2 for two checkers (like what you have after a coup classique), and of course it's something more than 7 for 15 checkers. Mindless linear extrapolation from 4.7 and 5.2 would yield 5.7 for three checkers, which is probably not so bad here. For sure GBUBG's 6.675 is too high. As for Zare's method, if you use it here you get EPC = 3*3.5 + 10 + 13 - 4 = 29.5. 29.5 means wastage = 4.5, which has got to be too low. With the 5.7 estimate we get 30.7 for White's epc, which puts him down 1.7. The pips-vs.-rolls guideline says that in a 4-roll position you can take down 1, so it looks like I'm predicting a close pass. ```

 Keene  writes: ```OK, according to my best guesstimates, I have Example 1 as a 4-roll position (or transpose to 4 rolls for each side), and Example 2 as a 5-roll position. Each roll average is 8 pips, so by playing 8 pips per figurative roll to get in, then whatever its going to take to bear them off. My reference point here is the 4-roll positions for each side are redouble/take. So Example 1 is a redouble/pass for me, and Example 2 is a redouble/take for me. Just because there are fewer sets that will work as "bearoff sets" in the short term in Example 1 is where you are losing enough equity to make it a pass. The way I worked it out was to calculate how many rolls to get the stragglers into the homeboard, then how many rolls to bear them off, then the same for X. After some brief checking, I can see that my answers are at least half right ... but, nonetheless, this is how I looked at it, and how I would assess it OTB. Although much less precise than Gregg's numbers, I feel its a reasonable way to go about it, and will give you at least a good approximation. ```

### 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)