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Thanks for the citation. The work by Nack and Paul is one of the good ones. Every serious player should read it. Just as interesting (for purposes of this thread) is your thought process. What play(s) were you favoring before checking the book? More importantly, what are the cues in the two positions that allow you to discriminate between them over the board? After posting my ideas, I also found this pair in Backgammon Openings. One point made there that was not brought out in my analysis is just how good the opponent’s 6s are when you do not hit, playing 65R-41$-31P instead. He can make his 5pt with 61, 62, 63, and 64. With 65 he makes his 3pt; and with 66, both bar points. What I did note is that his 6s become very poor after 65R-41$-31H. The more complete story is the swing. Hitting demotes the opponent’s 6s from good rolls into very poor rolls. With 65R-21$-31, there is no such swing. With the exception of 66, hitting merely changes your opponent’s 6s from one kind of good roll into another kind of good roll. Mike |