Forum Archive :
Cube Handling in Races
EPC example: stack and straggler

After I waited to cube we arrived at a typical Trice Formula EPC position.
24 23 22 21 20 19 18 17 16 15 14 13
++++++++++++++
OO  O   
OO  O   
OO  O   
OO  O   
O  O   
   
X    
X    
X  X X   
X  X X X X   
X  X X X X   O 
++++++++++++++
1 2 3 4 5 6 7 8 9 10 11 12


Christian MunkChristensen writes:
Looks like a roll vs stack and stragler: 5 rolls * 7 + 1 = 36 for X and 3.5
* 6 + 17 = 38 for O. D/T.


Neil Kazaross writes:
We think alike but, Blue's position is clearly worse than an EPC of 5n+1
since not all doubles work.


stw writes:
Rummer asks:
> I understand how to derive blues's epc: 7n + 1. Please explain the rest
> of your formula as I don't know what how the 3, works. Also, in Trice's
> book, I didn't understand how to determine wastage and how that is
> applied to problems.
The effective pip count for stack and straggler positions with 1 straggler
given by Trice is 3.5 * the total number of checkers left plus the pip
count of the straggler. i.e. if there are p men on the acepoint and 1 man
on the q (outfield) point then the effective pip count is 3.5(p+1) + q.
So in the position below White has an epc of 4 (total checkers left) * 3.5
+ 16 (pip count of straggler) = 30.
24 23 22 21 20 19 18 17 16 15 14 13
++++++++++++++
OOO  O   
OO  O   
OO  O   
OO    
OO    
   
X    
X  X X   
X  X X   
XX  X X   
XX  X X   O 
++++++++++++++
1 2 3 4 5 6 7 8 9 10 11 12


Bob Koca writes:
A pure 5 roll setup gives 7n + 1 = 36 and this needs to be incremented
since the given position is not a pure 5 roll position. I checked and
obtained +1.9 for a total of about 38. White's EPC is about 3.5*6 + 17 =
38.
The guideline is that for a 5 roll position vs. a pip position that the pip
player has a take down 2 in EPC. The roll player can redouble one pip
earlier than that and initialdouble 2 pips earlier. So it looks like a bare
initial double using that guideline.
How to account for the fact that the guideline is for a pure 5 roll
position? There are a couple reasons to think that blue should double
slower. The first is that since this is slightly longer than a pure 5 roll
position the trailer has more time to catch up. The second is that blue has
a greater deviation in number of rolls to bearoff. That extra variability
usually is in favor of the trailer in the race.
Here though exactly how the extra 1.9 pips creeps in is important. Some of
it comes from swinging 3 roll getoffs to 4 roll getoffs but those would win
for blue almost always anyways. Most of it comes from swinging 4 roll
getoffs to 5 roll getoffs and those have some chance of saving the win for
white but remember that white was given 2 extra pips also. The swing that
really helps white of 5 roll getoffs for blue becoming 6 roll getoffs
hardly happen at all. If the position is an initial double for 5 roll
position up 2 effective pips it will still be an initial double for the
given position.
For pure five roll position:
Off in 3 = 7.4%. Off in 4 = 44.4%. Off in 5 = 48.2%. Off in 6 = 0%.
For given position:
Off in 3 = 3.4%. Off in 4 = 32.5%. Off in 5 = 60.8% .Off in 6 = 3.4%.




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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