21S-21 d[S U1 $1] "<31 41S-21 d[$ S5 W5] "<31 51S-21 d[$ U13 S19] "<20*15 52S-21 d[$ S2 H5] "<31 1. Why is slotting even on the radar for 21 reply against a minor split?
2. Why is slotting best against 41S and 51S, while it is very close to splitting against 21S and 52S at DMP?
21S-21 g[$ S8] "<31
41S-21 g[$ S10] "<31
51S-21 g[$ D25 U34 S38] "<15*10 5
52S-21 g[$ H7 S16] "<31*20
Earlier, I gave a brief response to question 1. I've delayed posting a response to the question 2 because I've been busy elsewhere, but your thread deserves some action, so here goes.
In analyzing third and fourth roll positions, it is often useful to build, interpolate or extrapolate on known first and second roll results. For first and second roll positions, we typically just accept the rollout results as they are, but when asked to explain them we sometimes have no better approach than to look for swing rolls and hope we don't miss anything important.
I do not intend to look at all twenty-one dice rolls that stem from all eight $ and S positions (21S-21$-xx, 21S-21S-xx, 41S-21$-xx, 41S-21S-xx, 51S-21$-xx, 51S-21S-xx, 52S-21$-xx, 52S-21S-xx) at DMP, let alone the other four with U, W and H). However, I will examine and compare the latter four of those eight, which represent the two second roll positions with the largest $/S margin contrast (.002 vs .019), and point out the larger swing rolls I find.
There are four positions diagrammed below. It is highly recommended that you widen your window (or use Ctrl- to zoom out) so that you can view them as a pair of side-by-side positions, to minimize scrolling. You'll find my analysis below the first pair and above the second pair.
Henceforward, I will refer to 51S-21$-xx as "1a" (i.e., Position 1a), 51S-21S-xx as "1b," 52S-21$-xx as "2a," and 52S-21S-xx as "2b." (This abbreviated scheme associates the opening play of 51S with "1" and 52S with "2," and the reply of 21$ with "a" and 21S with "b.")
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| XGID=-b----E-D---dDa--c-da--AA-:0:0:1:00:0:0:0:1:10 | |||||
Position 1a: ...51S-21$-xx.. (Blue on roll) | |||||
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| XGID=-aa---E-D---dDa--c-e---AA-:0:0:1:00:0:0:0:1:10 | |||||
Position 1b: ...51S-21S-xx.. (Blue on roll) | |||||
Now consider the inverse: 62 is a terrible roll in both 1a and 1b, and 63 is a fine roll in both 2a and 2b. I don't perceive the gain of 1a-over-1b as being noticeably greater than the gain of 2a-over-2b, nor vice versa. Hence, I will wash the effects of 63 and 62 in both paragraphs.
The largest swing in favor of White's 2a-over-2b (and yes, I've remembered to mentally halve the effect for doublets) appears to be 55, which runs to the midpoint in 1a but not in 2a. That is, slotting frustrates Blue's 55 in 2a more than in 1a.
Also supporting of 2a-over-2b is 33 (Blue can hit in 1a but not in 2a). You can think of this as the 24th number that hits in 1a but not 2a.
Ignoring the several rolls that favor one paradigm or the other in a lesser way, the remaining "major" swings (and all look larger than the 55 or 33 doublet) seem to be in favor of White's 1a-over-1b:
- In 1a, Blue has no constructive play with 52. The counterpart in 2a is 53, which makes the 3pt.
- Blue can hit with 54 in 1b but not in 2b
- There are duplications of 42 and 66 in 2b (that do not meaningfully exist in the other positions).
- 32 is duplicated (hit or advance-anchor) in 1a.
In short, the explanation (or double-check) that I offer for 51$-21$ being clear (at DMP) while 52$-21$ is tied (at DMP), is that there are more swing rolls, and more sizable swing rolls, that favor White's 1a-over-1b than her 2a-over-2b.
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| XGID=-b----E-D---dDa--c-da-A-A-:0:0:1:00:0:0:0:1:10 | |||||
Position 2a: ...52S-21$-xx.. (Blue on roll) | |||||
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| XGID=-aa---E-D---dDa--c-e--A-A-:0:0:1:00:0:0:0:1:10 | |||||
Position 2b: ...52S-21S-xx.. (Blue on roll) | |||||
Nack
P.S. I see now that Mike replied, evidently while I was writing this post. I look forward to reading his.