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Here's why 43S-61X and 54S-63H

Posted By: Nack Ballard
Date: Saturday, 3 April 2010, at 11:49 a.m.

In Response To: I forgot to say why is H best with 63 after 54S? (neilkaz)

Why is X better than H after 43S-61, but H is better than X after 54S-63?

I have no explanation for this. thx . neilkaz .


H is better than X for both 54S-63 and 54S-61. I'll use the latter position for this analysis so that the number of checkers on the 8pt and 6pt are the same.

We'll be looking at opening 43S and 54S, with replies of 61X and 61H. The four resulting positions are shown below, with discussion.

White on roll165


1O ' ' ' '5X1O3X '1X '5O

1X ' ' '1O4O '3O ' ' '4X

43S-61X160


White on roll163


1O ' ' ' '5X1O4X ' ' '5O

1X ' ' '1O4O '3O ' ' '4X

54S-61X160


After 43S-61X (upper left diagram), there are 10 numbers (54 32 41 42 43) with which White hits one blot on her 20pt, after which Blue can hit with 3s on his 15pt. He doesn't have this resource in the same variation following 54S-61X (upper right). In short, splitting with the 6 exploits White's 10pt blot.

Another factor is that 7 numbers (31 51 21 11) allow White to unstack a fourth checker off her 8pt in the upper right (not so in the upper left). Of these, 31 is an extra-large swing because White has a decent use for her 31 (i.e., Bar/24 13/10) in the lower left-hand diagram she does not have in the lower right.

I believe the only roll that substantially swings the other way is White's 53, which hits twice in the upper left versus only once in the upper right.

White on roll165


2O ' ' ' '5X '3X '1X '4O

1X ' ' '1O4O1O3O ' ' '4X

43S-61H160


White on roll163


2O ' ' ' '5X '4X ' ' '4O

1X ' ' '1O4O1O3O ' ' '4X

54S-61H160


The position you asked about is actually 54S-63 (instead of 54S-61). The difference is Blue's 8pt/6pt distribution in the two right-hand diagrams (five on 6pt and two on 8pt, instead of four/three). This difference partially mutes the effects I described above, but the explanation (of why splitting with the 6 is thematically right against 43S but not against 54S) is sufficient for our purposes.

For reference, here are bot-averaged values for the three positions, with plays other than H or X omitted:

43S-61 [X H16]
54S-61 [H X28]
54S-63 [H X11]

(Re-including other competitive plays, values are: 43S-61 [X P10 H16], 54S-61 [P H34 X62], and 54S-63 [H X11 R14].)

Hope that helps.

Nack

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