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41$-33 and 51$-33, etc.

Posted By: Nack Ballard
Date: Sunday, 11 July 2010, at 8:15 a.m.

In Response To: 41$-33 4 ply RO (David Rockwell)

There's a lot to say about xxx-33 (double 3s replies, where xxx is one of the 28 strong opening plays -- within .02 of best).

For money, it's right to reply with B (Both, 13/10(2) 24/21(2)) against 1 or 3 splits (21S, 41S, 51S, 32S, 43Z) or point-makers (31P, 53P, 61P, 64P) or 65R. It's right to reply with A (Attack, 8/5(2) 6/3(2)) against any 2 or 4 split (32Z, 43S, 43U, 52S or 54S) or either lone 11pt play (52D, 64R) or 42P. It's right to reply with 7 (13/7*(2)) against a 6 split (62S, 63S or 64S). And it's right to reply with N (Near, 13/10*(2) 6/3(2)) against 63R. [Summary: 10, 8, 3 and 1 for B, A, P and N, respectively.]

That leaves just six opening plays: 21$, 41$, 51$, 32D, 43D and 54D. I'll touch on all of these, but to avoid too long a post I'll "analyze" just two.

Against the $'s (5pt slots), it is prudent to anchor in anticipation of Opp's quick-developing prime, and for the other two 3s, it is a great opportunity to make the strongest inside point. That is, C (Cross, 24/21* 8/5*(2)) is the indicated reply. Under other circumstances paying off to 7s (24/17*) is too expensive, but as Neil and David have noted, the richness of return shots (despite some 5 duplication) causes C to rise to the top. The frequently played B is a mistake.

The "agg" (bot aggregate) values for the xx$-33 replies are:

21$-33 [C B25 E42 A48]
41$-33 [C=E B18 A77]
51$-33 [C A20 E35 B37]

Key: C = Cross (24/21(2) 8/5(2)), E = Each (24/21(2) 6/3(2)), B = Both (24/21(2) 13/10(2)), A = Attack (8/5(2) 6/3(2)). Error sizes are in thousandths. For example, "[C=E B18 A77]" means that C and E are exactly tied for best, B is -.018 and A is -.077.

Let's compare the second and third of these positions (difference of 9/8 or 1 pip for White) and isolate the C and E plays. There is a swing of .035 in the margins. In the diagrams below, Blue has played the anchoring half of the play and has two 3s left to play.


 ' ' '2O1X4X '3X1X ' '5O

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

41$-33: Blue to play only two 3s



 ' ' '2O1X4X '4X ' ' '5O

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

51$-33: Blue to play only two 3s


Why is making the 5pt tied with making the 3pt on the left, but making the 5pt is so much stronger on the right?

It mainly comes down to (a) blocking 4s on the right, and (b) blocking key 2s on the left.

(a) On the left, White is using all her 4s to cover the 5pt (including 41, which makes both the 9pt and 5pt), which means that she will not immediately benefit from Blue's 5pt being vacant, except with double 4s. By contrast, on the right, White can clearly gain by splitting with 4s, whether they cover the 5pt or not.

(b) By making the 3pt on the left, Blue causes more damage to White's 52 (she has to make the 3pt instead of hitting on the 17pt). That same 52 is more palatable on the right, because White can unstack a four-checker 8pt instead of stripping it and leaving the 9pt blotted. And even swingier is 22: when White can make the 5pt with only two deuces (as on the left), preventing her 22pt anchor is a big gain, whereas on the right she needs all four deuces to make the 5pt anyway.

You can remember this position pair by focusing on the biggest swing number, 42, which falls under both (a) and (b) categories. White wants to play 24/22 9/5 on the left and 24/20 13/11 (duping aces) on the right. Blue can foil those aims by making the 3pt on the left and the 5pt on the right.

Blocking 4s is relevant not only for 51$-33 but also for 21$-33 and 32D-33 (the latter position was discussed by David), and to a lesser degree 43D-33. It is NOT at all true for 54D-33: making the 3pt (or 10pt) is much better because it duplicates vital 4s, whereas the 3pt blocks (and therefore creates some awkward) 2s.

41$-33 shares the 4-duplication aspect with 54D-33 (where E is clearly better than C), but White's slotted 5pt gives Blue additional justification in leaving the 8pt blot, which has enough influence to promote C to a tie. Note, though, for 41$-33 at DMP, E is definitely better.

Nack

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