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Colorless CountingA clever concept
Posted By: Phil Simborg
Date: Wednesday, 26 December 2012, at 3:12 p.m.
If you subscribe to Gammon Village, please read my new article on the Urquhart Colorless Counting approach...it truly is fascinating, and anyone who enjoys the mathematical beauty of the game will appreciate the idea, even if you don't wish to use it over the board. I take no credit for the concept other than helping Robert Urquhart put the concept into words and a framework that we "laymen" can understand.
For those who can't access GammonVillage, if you truly love the game, I highly recommend it...there are great articles by the likes of Jake, Steve Sax, Stick, Mary, Zare, and many others, and I use it a lot (along with Backgammon Galore) to review articles and concepts to help me and my students understand the game better.
Urquhart Colorless Counting (UCC) is a quick, accurate method of determining the pip count difference in any position, and how he figured out you could do this while totally ignoring the color of the checkers is a mystery to me, and to most of us. It's the kind of concept we might have thought about while under the influence of something but quickly discarded once we were back to normal.
UCC looks at crossovers (using a quick method that ignores which checkers are who's), then looks at checkers in the near half of each quadrant, and then looks at checkers on the near point in each of the three points on each half of each quadrant. You can quickly count most of these three totals in 20 to 30 seconds with a little practice, never have to use large numbers, and you have a pip count difference.
Of course, for cube action we also need to know the total pip count, and I wouldn't recommend UCC for that, but for most checker play situations, for back games and racing games, for DMP, and when the cube is not in question and you simply need to know where you are in the race, UCC is terrific.
But there is a human side to this that I also find fascinating. Robert is a retired IBM Software Engineer, in his late 70's, and though he has enjoyed backgammon for some time, he is recently diving into it more seriously with the goal of truly understanding the game more deeply, and that includes really understanding the underlying math involved in all cube and checker decisions.
I am proud to say he has looked to me as his teacher, and that has given me the opportunity to get to know him and work with him, adding greatly to my job satisfaction (which I get from all of my students, one way or another).
I also find it interesting to see that there is still plenty of room for discovering new concepts and approaches to understand backgammon. I have heard some say that since Robertie and Magriel's great books, we've only added "refinements" or adjustments to their concepts, and few really new ideas have come forth. I know that is not true, but I believe that ideas like UCC, even if they don't change the game, prove that there are other ways to look at the game we might not have even considered. (Danny Kleinman wrote me a note saying: "Why didn't I think of this three decades ago?")
For those of you who do not subscribe to Gammon Village, again, I suggest you join, but you can also email me at psimborg@sbcglobal.net and I will send you the UCC method and formula.

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