Cube Handling in Races

 EPC example

```What's the best way to calculate the effective pipcount in the accompanying
position? The way I did it turned out to be somewhat inaccurate.

24  23  22  21  20  19      18  17  16  15  14  13
+---+---+---+---+---+---+---+---+---+---+---+---+---+
O  | O   O   O   O         |   |                       |
O  | O       O             |   |                       |
O  | O       O             |   |                       |
O  | O                     |   |                       |
O  | O                     |   |                       |   X on roll.
|                       |   |                       |   Cube action?
X  |                       |   |                       |
X  |                       |   |                       |
XX  |                     X |   |                       |
XX  |                 X   X |   |                       |
XX  |         X   X   X   X |   |                       |
+---+---+---+---+---+---+---+---+---+---+---+---+---+
1   2   3   4   5   6       7   8   9  10  11  12
```

 John O'Hagan  writes: ```O's position is a little worse than a 5-roll position so his EPC is a little over 36. If you're a member of Gammonvillage, read the late Walter Trice's June 2008 article. It tells you how to estimate EPC's for almost n- roll positions like O's. Per this article, Walter would recommend adding a 1 pip penalty to O's EPC which makes it 37. X's position has very little wastage. Another of Walter's GV articles mentioned that (IIRC) the minimal wastage once you get down to a few checkers left was around 5 or 5 1/2. That suggests an EPC of 40 or so for X. Another EPC tool for X's position can be found at the linked article below which is from Kit's GammOnline magazine. http://www.bkgm.com/articles/GOL/Dec00/pipples.htm As far as the cube action, Walter sez the trailer's point of last take occurs when he trails by no more than n-3 effective pips. Since the leader's EPC is 37, n = about 5 so X could take if he trailed by 2 or less. He actually trails (if my estimates are correct) by 3 or 4, so it's redouble/pass. ```

 Matt Cohn Geier  writes: ```> X's position has very little wastage. Another of Walter's GV articles > mentioned that (IIRC) the minimal wastage once you get down to a few > checkers left was around 5 or 5 1/2. That suggests an EPC of 40 or so for > X. One of my abandoned projects was working on rules to estimate EPC. One thing I did note was that a few checkers left will waste about 5 pips, but only very few checkers left--2 or 3. 7 checkers is quite a bit more than 2 or 3 (and quite a bit less than 15), and usually wastes ~6 pips. ```

 John O'Hagan  writes: ```Another way to estimate the rolls side is as follows: Add 2/10 of a pip for every missing roll and add this to what the EPC would be for a pure n-roll position. Here 3-3 counts as a miss since it leaves you in a 4-roll position whereas you'd have a 3-roll position in a pure 5-roll position. That's 1 miss. 2-2 also misses. It counts as 1.3 misses since you'll miss again if you next roll a 2. If you roll a single 2, you're probably a favorite to roll another missing 2 so maybe this counts as 6 misses. That's 8.3 misses for a 1.66 pip penalty which makes the EPC 36 + 1.66 = 37.66, close to what GNU says. This method (and others for estimating EPC) is explained in Doug Zare's 4/25/03 GV article. ```

 Stick  writes: ```(* From http://www.bkgm.com/articles/EffectivePipCount/) * "Rule 1: For an N-roll position, the EPC is 7N + 1." +---+---+---+---+---+---+---+---+---+---+---+---+---+ O | O O O O | | | O | O O | | | O | O O | | | O | O | | | O | O | | | This position is a bit worse than a 5 roll position. If it was a straight 5 roll position the EPC would be 7(5) + 1 or 36. Depending on how well you can estimate how often it's a 6 roll (epc of 43) and a pure 5 roll you should pick an epc somewhere in between there. 38 matching GNU's estimate seems right. * "Rule 2: Nice positions waste 7 pips." X | | | | X | | | | XX | X | | | XX | X X | | | XX | X X X X | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+ Even though X has 8 checkers off here the wastage won't be much lower than 7 pips. How to know that? Once you look at many such positions you get a good feel for how much these standard looking positions waste. I would have estimated this position still wastes ~6.5 pips so the EPC would be 35 + 6.5 or 41.5. ```

### 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)