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Benjamin Colorless Counting--New Elegant and Brilliant Counting System

Posted By: Phil Simborg
Date: Monday, 27 March 2017, at 3:00 p.m.

In preparing for our lecture in Cleveland, Art Benjamin and I talked about counting methods including, of course, Cluster Counting and Colorless counting. I told him how it amazed me that after so many years Bob Urquhart (with a little help from me) came up with such an elegant new idea. And then Art said he felt the same way, but found an even more elegant approach.

He thought about how colorless counting works, and why it works, and then decided there is a much faster and easier way to apply it.

Simply count the total pips of the first 15 checkers on one side, and then the remaining 15 checkers for the other side, WITHOUT CARING ABOUT THE COLOR OF THE CHECKERS, and the difference is the difference in the pip count. Usually, that's all we need to know. And of course, when you need exact totals, after you use the Benjamin Count, then count either side and you have the actual counts.

Look at the position below. If you start with Blue's checkers, you can quickly see that the first 15 checkers add up to 78 (40 inside, 4 checkers on the 7 and 8 is 30, plus 8). Then in a couple of seconds you can see that the remaining checkers total 91 (41 inside and 50 outside). So in a few seconds you know the pip count difference is 13 and the blue side is the lower side.

As you can see, you can do this very quickly and accurately and generally don't have to add very large numbers.

As for checkers on the bar, you can count you opponent's checkers on the bar a 0, as among the set of 15 checkers for you, along with any checkers you have borne off.

 White is Player 2 score: 0 pip: 103 Unlimited GameJacoby Beaver pip: 90 score: 0 Blue is Player 1
XGID=--BBBBBbC---bB-----bbbbba-:0:0:1:43:0:0:3:0:10
Blue to play 43

eXtreme Gammon Version: 2.19.211.pre-release

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