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Four-score positions

Posted By: Timothy Chow
Date: Thursday, 21 July 2011, at 12:25 a.m.

In Response To: 2nd roll differences (Nack Ballard)

To make the search for four-score positions more of a "sport," I suggest the following.

1. Suppose that the best plays for money, DMP, GG, and GS are A, B, C, and D respectively. Let Err(DMP,A) denote the size of the error (measured in EMG) of playing A at DMP, and similarly for other score/play pairs. Then define the value of a four-score position to be

min(Err(money,B), Err(money,C), Err(money,D) +
min(Err(DMP,A), Err(DMP,C), Err(DMP,D)) +
min(Err(GG,A), Err(GG,B), Err(GG,D)) +
min(Err(GS,A), Err(GS,B), Err(GS, C)).

In other words, the bigger the blunder it is to make the wrong play, the higher the value of the position. (The above formula may seem unnecessarily complicated; why not just take the error of the second-best play at each score and add up these errors? The problem with this is that it doesn't properly value positions such as the one that Nack gives in Backgammon Openings, where, according to Nack, the top two plays for money are very close but are mistakes at the other three scores.)

2. I propose keeping track separately of positions where the dice roll is a doublet and positions where the dice roll is not a doublet. It's obviously easier to construct a four-score position when the roll is a doublet, so keeping doublets and non-doublets separate gives some incentive to find examples with non-doublets.

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