Cube Handling in Races

 EPC example: stack and straggler

 From: neilkaz Address: neilkaz@earthlink.net Date: 6 January 2009 Subject: Typical Trice Formula EPC position Forum: BGonline.org Forums

```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 Munk-Christensen  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 ace-point 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: 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)

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