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If we add a play prior to the 21$-31 sequence, the decision becomes much closer. In fact, if the position is 65R-21$-31 (shown on the right), P is slightly better than H! (See page 55 of the same book.)
Adding a two-down play prior to 21$-31 is not enough of a change to make P a better play, though it goes a long way. 52D-21$-31 (not diagrammed) cuts the margin roughly in half, to [H P54] ~1t.
An even closer decision is 54D-21$-31, diagrammed below on the left, with a result of [H P18] ~5.
Paul and I chose not to publish 54D-21$-31 in Backgammon Openings because the best play didn't differ from that of the more basic 21$-31, and our goal was to cherry pick the most instructive positions. For purposes of this post, however, it is useful to know that the margin narrows all the way from about .100 to .018. The reasons are:
- Blue's 8pt has an extra spare that can be unstacked,
- his 9pt checker is a builder that increases his chances to win a priming battle, and
- His 9pt checker is also a blot that can be picked up in an exchange of hits.
The first of these three reasons fully applies to 52D-21$-31 (the undiagrammed position discussed earlier with the midway H/P margin), the second reason less so, and the third reason much less so. All three fully apply to 54D-21$-31 (below, left).
That brings us to the original position of this thread: 52D-54D-21$-31, diagrammed below right. It is the same as the position to its left except that 52D has been added to White's position. I was certain that P would now be better than H, though I rolled it out and the margin is even bigger than I guessed: [P H50] "<=5. As I see it, the main reasons are:
- White is 7 pips more advanced (without having a newly diversified builder); she will not fare as well in a battle of primes.
- White's stripped midpoint makes her less flexible. If White is left alone, rolls of 43 and 53 played on her near side leave a shot.
- In a hitting battle, White has more ammunition.
Nack
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