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Cube Handling in Races
EPC examples: stack and straggler

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
superspeed 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 stackandstraggler. (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 pipsvs.rolls guideline says that in a 4roll 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 4roll
position (or transpose to 4 rolls for each side), and Example 2 as a 5roll
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 4roll 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 (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)
 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)
 Nroll vs nroll bearoff (David Rubin+, July 2008)
 Nroll vs nroll bearoff (Gregg Cattanach, Nov 2002)
 Nroll vs nroll 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)
 Pipcount 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)
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