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Cube Handling in Races
What's your favorite formula?

What's your favorite formula?
13 14 15 16 17 18 19 20 21 22 23 24
++++++++++++++
 O   O O O O O  56 pips
   O O O O 
   O O O 
   O 
   O 
    ++
     1 
    ++
   
   X 
   X X 
   X X X X X X 
   X X X X X X  59 pips
++++++++++++++
12 11 10 9 8 7 6 5 4 3 2 1
X on roll. Cube action?


Stick writes:
I would heavily prefer EPC to Keith in this type of situation in general.
EPC for blue I know as a reference position so there is no question that I
have that right. As for the opponent, I also have a similar high
wastage/gapped reference position that I believe will get me close to the
correct amount of wastage. Both formulas bottom line is the same, ND/T,
though the double is not far off.
 Estimate both players' epcs. In Timothy's example X's epc would be 68.5
(59 + 9.5 of wastage, flat position wastes 10 pips and I know this
specific one from reference). O's epc is ~71. (56 + 15 in wastage)
 Figure out the # of rolls to go by dividing the leader's/cubing player's
epc by 7. For instance in Timothy's example shown below Blue's epc is
68.5/7 = ~10.
 The point of last take for the trailer is equal to the number of rolls to
go (10) minus three. So the PoLT is 103 or 7 effective pips.
 You can send an initial cube when you're within 2 effective pips of his
point of last take and a recube when you are within 1 effective pips. We
know the PoLT = 75.5 (68.5 + 7) so to double our opponent would need to
have an epc of 73.5 or more.
For everyone who kind of read that and glossed over it I promise it isn't
as complicated as it comes off if you take a minute to understand what at
first looks like gobblety gook.


Taper_Mike writes:
Keith Count
Player on roll
59 Raw pip count
+2 One extra checker on 1pt
+1 One extra checker on 2pt

62 Subtotal
+8 Add 1/7 (rounding down)

70 Keith Count
Opponent
56 Raw pip count
+4 Two extra checkers on 1pt
+1 One extra checker on 2pt
+2 Two extra checkers on 3pt
+1 Gap on 4pt

64 Keith Count
Because 70 exceeds 64 by more than 4, the Keith Count rates this as a "no
double."
      
Market Losers
White will be fine so long as he can bear off a checker next turn. Fine,
that is, so far as a take is concerned. That means he needs to roll a 5 or
6 (except 54 64), or else roll any doublet except 11. But look what happens
when he throws 42 or one of the 9 numbers totaling 5 pips or less. Then we
are suddenly in a 7.5rollversus8roll position, with the leader Blue on
roll. That is "doublepass" territory. So, at least 30% of the time, Blue
will lose his market.
This is a conservative estimate. Blue could also roll big doublets, and
lose his market that way.
With so many market losers, it is clear that this is a double.


Timothy Chow writes:
I was playing against XG and took my time over this decision. I couldn't
see a good way of estimating White's EPC. Keith Count gave a very clear ND,
so I took a roll. I was quite surprised that the computer thought I had
erred. The discussion here has been very helpful; thanks.
Rollout (324 games with VR, moves and cube decisions 4 ply):
X's winning chances: 71.84%
Equity (no double): +0.671 (0.032)
Equity (double/take): +0.703
Equity (double/drop): +1.000
Best Cube action: Double / Take




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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