Forum Archive :
Cube Handling in Races
I have just written an article on cube handling in noncontact positions.
http://www.bkgm.com/articles/CubeHandlingInRaces
It compares several pipcounting methods to see which ones work best. To
compare the methods, I collected positions from real games and rolled them
out using GnuBG.
Five pipcounting methods were evaluated: Thorp count, Keeler/Gillogly
count, Ward count, Lamford count, and my own "Keith" count. The formulas
are judged on their ability to account for wastage and on how good they
are at making accurate cube decisions.
There is lots of interesting information there, and several pretty graphs.
Please let me know what you think.
Tom


Tom Keith writes:
Chuck Bower asks:
> 1) What are the strict requirements to make the database:
> a) any noncontact position?
Yes.
> b) include positions with players owning their own midpoints (nearly
> noncontact)?
No, though that would be interesting to do too.
> c) was there any requirements/restrictions on how many checkers were yet
> to be borne in? Already borne off?
No.
> d) I assume that a single game typically generated many entries to the
> database, since after each play a new valid situation results. True?
True.

HappyJuggler0 asks:
> I am also intrigued that the colored line graph of the various methods
> at different pip counts seem to show all the counting methods except the
> Keith Count to be inferior than a straight, unadjusted pip count once
> you get to the 80+ range. Or did I read that wrong?
Yes, I assume the reason for this is that some adjustments such as
"subtract 1 pip for each occupied homeboard point" really aren't useful
in longer races.


Michael Sullivan writes:
I'd like to see this compared to a heuristic using effective pips a la
Trice and Zare, but it's hard to see how to get that into an algorithm and
a function that's easily coded. In practice there's a lot of handwaving,
but I find I get results (without being especially good at it yet) that
are closer to database values that way than with any other count I've
tried, especially for positions with <25 pips, and I note that *all* of
Tom's heuristics tested, including the Keith Count have a fairly large RMS
error at these small pip counts. A .05 error in assessing cwc can easily
translate into a whopper of a double or take decision.
It looks to me like Keith count works about as well for midrange races as
it's competition, but it's the only one that is as good or better than
plain pipcount in long races. OTOH, in short races, it looks still to be
worthwhile to do a full analysis from a decent mental database of known
positions.
This isn't all that surprising really. Edge effects average out better the
longer the race. In really long race, the pip count is a pretty good
estimate, in medium races, taking care of the large scale effects (simple
heuristics) is good enough to get a good estimate. In really short races,
the details pay.
Michael


Rob Adams writes:
24 23 22 21 20 19 18 17 16 15 14 13 54 pips
++++++++++++++
O  O O O O O   
O  O O O O O   
 O O   
 O   
   
 X   
 X   
 X   
 X X   
 X X X X   
 X X X X X X    [2]
++++++++++++++
1 2 3 4 5 6 7 8 9 10 11 12 39 pips
I had this position yesterday online. So please let me know if this is how
the Keith Count should work or not.
X has 39 plus 10 for the acepoint checkers plus 1 for the 2pt is 50 plus
1/7 is about 57.
O has 54 plus 2 for the acepoint checker is 56. Nothing for having a gap
on the 2pt or having 2 off right?
So ahead 5756 would be a redouble/drop as X isn't ahead by 2.


Tom Keith writes:
Yes, that's how to do it. Now I hope a rollout doesn't show this to be too
far wrong!
...
A rollout shows dropping is a 0.089 error here.
Even though the formula was wrong, in a way this is a good example because
it reminds us that the formula gives only approximate answers and will
make its share of errors.
Cubeful equities:
1. Double, take +0.911
2. Double, pass +1.000 (+0.089)
3. No double +0.844 (0.067)
Proper cube action: Redouble, take


Douglas Zare writes:
Very well done. I hope you also publish this in backgammon periodicals. If
you don't mind, I'd like to include a hyperlink to your page in my next
GammonVillage column, but I think you could write an article or series of
articles based on your work.
I like the simplicity of the Keith count, but I suspect its accuracy in
relevant positions could be improved by tweaking some of the parameters
and adding a couple of items (e.g., reduce the penalty for checkers on the
3 point, but penalize the difference between the number of checkers on the
lower three points and the number on higher points).


Bob Koca writes:
Good article Tom. It should be mentioned though that some of your
recommendations apply only to longer races. You state that if cubeless
chances are between 30% and 70% then a pip is worth about 2.5%. The
length of the race is important here as well. If the pipcount is 104
to 100 then gaining one pip is worth about 2% whereas if the pipcount
is 50 to 54 then a gaining one pip is
worth nearly 5%. Similarly the 68%, 71% 78% rule is for longer races.
As the race gets shorter all those numbres decrease.
,Bob Koca


Tom Keith writes:
Thanks for the comments, Bob. You make some good points.
For the value of a pip, you are right that the length of the
race matters, though I don't get as big a difference as you do.
The following chart shows the probability of winning for the
playeronroll at different length races and various leads.
The chart is an average of the positions I rolled out.
According to the chart, the average value of a pip in a 100pip
race (pip count of playeronroll) is 1.9%, which is about the
same as you said. For a 50pip race, the chart shows gaining
a pip is worth about 2.5%, larger than a 100pip race but not as
much as your 5%.
 Length of Race 
Lead 20 30 40 50 60 70 80 90 100
14: .101 .154 .193 .222 .244 .258 .270 .285 .297
13: .114 .177 .214 .238 .265 .280 .290 .305 .317
12: .149 .211 .246 .273 .295 .307 .315 .325 .334
11: .177 .247 .279 .298 .319 .329 .338 .349 .357
10: .210 .283 .309 .328 .347 .354 .363 .371 .375
9: .250 .312 .338 .356 .369 .377 .382 .389 .395
8: .288 .340 .359 .377 .387 .397 .408 .413 .415
7: .333 .380 .410 .423 .422 .425 .430 .432 .435
6: .384 .426 .442 .449 .450 .449 .452 .456 .459
5: .430 .470 .480 .478 .475 .474 .477 .480 .482
4: .494 .505 .503 .504 .508 .503 .501 .501 .500
3: .530 .537 .540 .531 .529 .529 .526 .524 .521
2: .569 .555 .553 .557 .559 .555 .549 .547 .547
1: .616 .614 .600 .588 .577 .574 .573 .568 .565
0: .648 .643 .635 .619 .610 .604 .594 .588 .583
1: .691 .672 .654 .643 .634 .624 .616 .610 .602
2: .727 .707 .693 .671 .655 .645 .636 .630 .622
3: .762 .735 .712 .693 .676 .667 .657 .648 .641
4: .782 .760 .741 .718 .700 .690 .677 .667 .661
5: .806 .780 .764 .741 .726 .712 .698 .689 .680
6: .835 .805 .786 .767 .748 .732 .717 .708 .698
7: .856 .828 .800 .776 .765 .753 .734 .720 .712
8: .871 .850 .828 .800 .780 .767 .753 .739 .728
9: .890 .866 .842 .816 .799 .786 .770 .755 .744
10: .907 .883 .856 .831 .815 .802 .786 .775 .763
AvgPip: .033 .029 .027 .025 .024 .022 .021 .020 .019
Tom




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)
From GammOnLine
Long message
Recommended reading
Recent addition

 
