In the left-hand reference position (ignore that White blundered with her 64), Blue should definitely not hit with his deuce, because he cannot do anything special with the other half of the roll. Anchoring on the 20pt overshadows any other single objective.
However, two moderately strong objectives will often override. Honestly, I'm not sure if that is the case in the right-hand position (Leobueno's) above, because the 22pt is only a semi-advanced anchor and Blue's reduced midpoint (four checkers instead of five) weakens the value of the hit. While most humans routinely hit (overestimating its relative value) and often when it is wrong, hitting might actually be right in this specific position (though if so, barely); the decision seems closer than the great majority of examples I've seen.
Let's ponder a third-roll diagram pair from Backgammon Openings (pp. 42–43) with a similar two-beats-one theme. (This time the 5pt is the center of attention instead of the 20pt.) What move would you play in each of the two positions below?
Finally, some additional brain food from the same book: If we nudge Blue's 21pt checker up to his 20pt (forgiving that 42S is a never-played opener and treating it as a reference position), how should Blue play 31 and how should he play 41?
Nack
