Improved Cube Handling in Races
Posted By: Axel Reichert
Date: Saturday, 14 June 2014, at 5:51 p.m.
I have just finished an article about cube handling in races that heavily builds (and improves considerably) upon the Keith count. Tom was so generous to host it on his page, so you can find it here:
My investigation also picks up themes from Walter Trice's EPC article, Joachim Matussek, and Michelin Chabot (can be found in the same section of the "Cube Handling" articles on Backgammon Galore).
As an appetizer for you, please find below the abstract and a short discussion/summary.
You are an ambitious backgammon player? You like the Keith count, but wish it were simpler? You like the Keith count, but think it lacks accuracy? You like the Kleinman count or Trice’s Rule 62, but have no idea how their accuracy compares with the Keith count? You like the Keith count, but would prefer a method that gives winning percentages and works even in match play? You like Bower’s interpolation for the Thorp count, but like the Keith count better? You like the concept of the EPC, but have no idea how to calculate it for a complicated position? You have heard rumors about a “gold standard table”, but do not want to calculate square roots over the board or distinguish between long and short races? You want a method for cube handling in races that can be used for positions with wastage? You want a method for cube handling in races that can be abused for mutual two-checker bear-offs?
Then you should read this article.
This paper presented a general, parametrized framework for adjusted pip counts and decision criteria for cube handling in pure races without contact. The positional features considered for adjusted pip counts were checkers already borne off, high stacks on low points, gaps on high points, and crossovers needed before the bear-off starts. For decision criteria a distinction between long and short races was considered, but turned out to be unnecessary, since long races are rare. The point of last take was determined using a denominator and a further shift. In turn, doubling and redoubling point were shifted from the point of last take.
Having the framework in place, lower and upper limits for all the parameters were specified. Two objectives were defined: The total cube error should be minimized (tested against a database containing the correct cube actions for around 50000 real life endgame positions), and the total effort should be minimized (quantified using the total number of pips added/subtracted by the adjustments). Several multi-objective optimizations were done using the software solution Isight. First, an adjusted pip count and a decision criterion were found. The resulting method for cube handling in races has both a lower effort and error than existing methods. It can be reasonably used even for cub-offs. It is crucial that the decision criterion be valid for positions with wastage in order to match an adjusted pip count successfully. Second, a method for approximating EPCs was found, with both a lower effort and EPC error than existing methods. This method is not suitable for cube handling. Third, a method for approximating CPW was found, with a decision criterion that resulted in exactly the same cube action as the method found before.
Indeed, a connection between these two methods was found: The trans- formation formula describing it can be used to convert any decision criterion based on a point of last take and a (re)doubling window into an equivalent method working with percentages. This allows for the use in match play, for which the percentages will have to be adapted based on score.
Questions and comments are very welcome!
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