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43D-42P-52P-63H-21 | |||||
Above is the first position in the set of three related positions that Mochy posted, but here it is intended to represent TWENTY-FOUR possible positions. The other ones are with Blue owning his 5pt, 3pt or 2pt (instead of his 4pt), and/or with White's blot being on her 16pt, 14pt, 13pt, 11pt or 10pt (instead of her 15pt).
Blue has rolled 21, and for the purposes of this study, he has a choice of two plays: U (Up, bar/22), and @ (anchor, bar/23 24/23). [Occasionally, another move is best but irrelevant to the study.] It is very tedious for both writer and reader to have to keep referring to the plays by traditional notation, so please memorize what U and @ mean (if you don't already know Nactation)!
The compactness of the table below is important for readability. The row header tells you the point Blue owns, the column header tells you the location of White's blot, and the cells tell you by how many thousandths of a point in equity that U is better than @. A red number is negative and means that @ is better.
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............16pt..15pt..14pt..13pt..11pt..10pt
.....5pt.....17....10....25 ...26....22.....3 ---------------------------------------------------
.....4pt......7....26.....8 ....2.....3....26
.....3pt.....30....33....37....27....25....10
.....2pt.....14....18.....5 ....1.....5.....7
In all cases except three (where the number is small anyway), U beats @ when Blue owns the 4pt or 2pt, and @ beats U when Blue owns the 5pt or 3pt. This data supports Maik's theory: With the 3pt made, Bar/23 24/23 makes your 33 and 55 work efficiently, while Bar/22 duplicates your 22, 42 and 64.
I would add 44 to Maik's even-number duplication list. When added to the 5pt or 3pt, A (Attack, 8/4(2) 6/2(2)) makes a powerful board, and will be significantly stronger than non-20pt-making alternatives. So, that's six swing rolls altogether.
[Note that with the 5pt (instead of 3pt) made, the near-side redundance of 33 still applies while the one for 55 does not, and the softer swing reflects that. That is, @ beats U by more in the 3pt row than in the 5pt row.]
Suppose we want to measure the effect of one of these Blue swing rolls. That's easier said than done, because it's hard to find an "average roll" in the interim for White. Her roll of 52 may seem an ideal choice because 15/8 is best regardless of whether Blue has the 5pt, 4pt, 3pt or 2pt, and/or whether he has played 21U or 21@. However, a "do nothing" roll isn't really average -- it's actually on the static end of the range. If White makes a point (either offensive, or by linking with 54/63), Blue's duplication/diversification will be reduced or diminished in importance. Still, it helps greatly to assign some roll, and by using 52, I guesstimate the effect won't be exaggerated by more than 20 (or 25?) percent overall.
So, let's give White 52 (played 15/8), and Blue 42 (with which he'll choose to anchor over making the 4pt, though as you are about to see in one situation he can't do either). In the case of Blue starting with his 4pt and having played 21U, his anchoring position is worth ¡V.139 (by XGR++ evaluation). If he has instead played 21@ -- shown below, Blue now has nothing better than S (Split, 24/20 13/11), yielding a value of ¡V.455. In other words, this particular contrast chalks up a (huge) gain of .316 for 21U.
I executed the same set of comparisons (for the same White 15/8 play and Blue 42 roll) on the positions where Blue owns a different inside point. For the 5pt, 4pt, 3pt and 2pt, the 21U play yields respective gains (vs 21@) of .087, .316 (as already noted), .104, and .134. If we multiply these gains by 1/18 (the chance of 42 being rolled) and reduce it by 20% (referenced two paragraphs back), the impact of 42 can be estimated at .0039, .0140, .0046, and .0060. In short, the 42 effect boosts 21U (vs 21@) for the 4pt position by about .010 (10 thousandths) over the parallel scenario in the 5pt position, a bit more than .009 (9 thousandths) over that of the 3pt position, and .008 over that of the 2pt position.
Now look at the 15pt column of the table shown earlier. The biggest difference in that column is between the 4pt position (+26) and the 3pt position (¡V33). At the end of the paragraph just above, I concluded that 42 is responsible for 9 of that 59 swing, and it seems quite believable to me that most -- if not all -- of the remaining 50 thousandths are accounted for by the other swing rolls (55, 33, 22, 64 and 44) first mentioned underneath the table.
Similar operations can be performed on the other columns. It may seem tedious, but I recommend taking a stab at this exercise (or one like it) some time. Doing so can greatly help develop your intuition for the size of duplication/diversification (or whatever) effects. Otherwise, it's easy to over- or under-adjust for various factors you notice in the course of play.
Nack
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43D-42P-52P-63H-21@-528-42 | |||||