This hand was presented by Michael Berkowitz in the column of Larry Cohen. These are experts I consider on the "aggressive side. Both vulnerable, the bidding was

South West  North East
1d    Pass  2d    pass 
2NT   Pass  3NT   pass 

(North's 2d was an inverted minor raise.)

The hands were:

s: A93
h: KQJ
d: QJ74
c: T83

s: JT72
h: A75
d: K832
c: A6

Berkowitz characterized this as a "normal 3NT with 13 opposite 12." But North has a 4-3-3-3 distribution, so shouldn't "12" really be 11, and "25" really be 24?

Sources such as this give N-S only a 37% of making 3NT with only 24 points. This includes hands with "24" that are really 23, not hands that are "25" really 24. Making this adjustment, the chances of success are about 40%. Using IMPS scoring, that's good enough, when vulnerable.

But Berkowitz/Cohen didn't make a qualifier for when one is non vulnerable. Should such a qualifier have been made? Am I right to feel misled by an assurance that this hand is a solid, rather than borderline, 3NT bid when "25" points is more like 24 because of the 4-3-3-3 distribution?


I think that your adjustment to HCP is perfectly fine for your own purposes, but it's not within the technical definition of "high card points" (which solely include the 4/3/2/1 point count, or whatever other numbers you want to assign each honor) and exclude distribution points. You're well within rights to consider distribution; but many automated programs will solely focus on HCP, including the link you sent, as far as I can tell - so when they say that two balanced hands with 25 points are optimally in 3NT, they mean the hand above to be in that collection.

I'd also say that those two hands look fine in 3NT. They're both solid hands with dense honors yet still largely controlling the suits; little wasted value ("Jxxx" type stuff) and lots of T/9/8s also to round out the hands. North can count 4 tricks in their hand even with basically nothing of value in South, and South similarly can count 3.5 tricks at least in theirs again with absolutely no help from North - 4 if you consider the diamond length to make the K fairly safe. Each expecting the other to have 4 solo tricks plus one trick from fitting honors seems reasonable, don't you think?


You can't just mix-and-match how you count the hands - consistency is key. HCP alone is easy, so consider a full evaluation for the two hands:

- 13 HCP
- -1 for 4333
- -0.5 for the Heart shape
- +0.5 for the Spade 9 and Club 8

Total: 11.5 Pts

- 12 HCP
- +1 for 4432
- Offsetting plus/minus for the weak Diamonds vs Spade 10

Total: 13.0 Pts

Yes; according to Goren (and many others) one absolutely counts one for the doubleton of a 4432 hand, even in NT - as it represents the advantage, both in suits and NT, of either two 4-card suits or one five-card suit as might apply.

One might quibble that 11.5 is not 12 - but every good player I've ever known has always rounded up an extra 0.5 after all considerations have been made.

Also, defending this hand correctly is non-trivial. Both North and South have denied major Suit interest; making it easy for West to lead the wrong black suit when the Spade honours are split and East has a broken Club suit without the Diamond Ace. Then a simple false card of the Spade 7 by South at Trick One might give the Defense conniptions.

  • I've never understood why you add +1 for 4-4-3-2. I was taught that was the "standard" or "par" shape. 4-3-3-3 is clearly -1, if you are making that adjustment, and depending on the cirstances, 5-3-3-2 could be +1, especially in NT. Put another way, relative to 4-3-3-3,(worth -1) I consider 4-4-3-2= +1, and 5-3-3-2= +2. More to the point, I consider 4-4-3-2 "intermediate" between 4-3-3-3 and 5-3-3-2, with 5-3-3-2 worth +2 over 4-3-3-3. I could make the case that 4-4-3-2 is worth +1.25 over 4-3-3-3, and 0.75 less than 5-3-3-2.
    – Tom Au
    Mar 7 '20 at 1:13
  • I also didn't count anything extra for intermediates because N-S have two Ts, one 9 and two 8s, versus an expectation of two Ts, two 9s, and two 8s. Now if they had, say, three Ts between them, that would be different. The hand is clearly makable, but at 24.5, less than 50-50 (an even 25 is just over 50-50). I would consider this a "borderline," not "solid" 3NT bid when not vulnerable.
    – Tom Au
    Mar 7 '20 at 1:21
  • @TomAu: As you noted: "These are experts I consider on the "aggressive side. Both vulnerable". Defensive errors occur even against the best opponents, particularly on opening lead. Top declarers expect to make a bit more often because of those errors. Mar 7 '20 at 1:41
  • I think I understand now. Aggressive Cohen/Berkowitz would consider this 24.5 3NT "normal" and conservative Frank Stewart might consider this "edgy," with the truth somewhere in between. Thanks for your help.
    – Tom Au
    Mar 7 '20 at 1:59

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