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Kangaroo Count (link)
Posted By: Nack Ballard
Date: Monday, 18 January 2010, at 9:36 p.m.
I know we've already had this thread on bgonline. I've created this post just so there is a decent link a Kangaroo Count search can find. I hope to create a better consolidation some day.
I first conceived the Kangaroo count about fifteen years ago. It was first published in Issue #277 of Flint Area BackgammoNews, Dec. 2005. If you want to know why I chose "Kangaroo" for the name, read the article. :)
I'm not as clever as Tom Keith is with graphics, so first click here (or better yet open it in a separate window).
Let's follow the four steps for counting the opening position. (Tom's diagrams illustrate how to group the checkers in the first three steps):
Step 1: 7 x 2 = 14
Step 2: Add 5 = 19, mult 2 = 38
Step 3: Add 7 = 45
Step 4: Mult 3 = 135, + 30 = 165.Steps 1 and 2 are represented by the first two lines of the Kangaroo poem. Steps 3 and 4 are combined in the third line of the Kangaroo poem, which goes
First you double the far side men
Add big diagonal, double again
Add small diags, times 3, plus 30,
And shifting to the middles is pertyIf you are satisfied with a halfcrossover count, you're finished after "diags."
If you want an approximate traditional count, stop after "30" (end of third line).
If you want an exact count, the fourth line refers to shifting to the middles of the halfquadrants (or "triples" as Doug Zare calls them), which are the second and fifth points in each quadrant.
If a checker is on the bar or borne off, it shifts 2 pips to get to the middle of its halfquadrant. All other checkers shift 0 or 1, but for an experienced counter its mostly 0's due to cancellations.
In Tom's example (opening position), the 8pt is already in the middle of its halfquadrant; no change. The fivechecker stacks on the midpoint and 6pt both shift right 1 pip, canceling out, so also no change. The only adjustment is that the 24pt shifts left a pip, adding +2 to the count. So, the 165 approximate count outlined above becomes 167.
[Usual shifting rules apply: Cancellations on the same side of the board shift/cancel towards each other. Cancellations on opposite sides of the board (near vs far) shift/cancel in the same left/right direction. With practice you can become very fast, and you can skip the last step (shifting) altogether if an approximate count will suffice for a position.]
Nack

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