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Gapped Crunched Bearoffs

by Walter Trice
15 November 2007

Walter Trice

In the bearoff phase of a game of backgammon the checker play is nearly trivial, but determining the proper cube action can be quite difficult. Mental arithmetic is almost always necessary. Sometimes a pip count for each side is sufficient. In fully crunched positions, with all checkers stacked on low points, a count of the checkers may tell you all you need to know.

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Subject: Re: Gapped Crunched Bearoffs

From: johnoh Member has a photo available

Date: 09 Dec 2007 22:31 EST

Walter,

Thanks for another great article. I now have a better understanding of these positions. I'm not real clear on one thing though and I wonder if you could clarify it for me.

It has to do with the trailer's point of last take. If I understand it correctly, your rule is that the trailer can take as long as his deficit in effective pips is 3 less than the number of effective rolls, right? In problem 1, you estimate the EPC'S at 48 and 52.625 and conclude that the trailer should pass since this is a 7 roll position and he's down by more than 4 pips. But 48 pips is a little less than 6 rolls and 52.625 is around 6 1/2. Likewise in Problem 3, the EPC'S are 56 and 61 which you refer to as an 8-roll position.

If I had to guess, I would say that you're supposed to calculate the trailer's EPC, then divide by 8 1/6, and then round up to the next whole number (at least this works in the 2 examples above). Is this correct?

John O'Hagan

Subject: Re: Gapped Crunched Bearoffs

From: trice

Date: 17 Dec 2007 21:37 EST

Hi John,

I guess I should have made that a little clearer. When I refer to n as "number of rolls" in the context of a pips-vs-rolls or rolls-vs-pips problem I mean something more or less equivalent to a 2*n stack on the ace. So I'm calling 48 a seven roll position because 48 is close to 50, which is 7*7+1. Similarly 56 is nearly 57, which is 8*7+1, so it has an epc close to what it would be for 15 men on the ace.

I originally stated the rule of thumb this way because in the "basic" pips-vs.-rolls situation I wanted to be able to just count the checker-pairs for the rolls side and be done with the math.

Walter Trice

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