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I've seen a number of successful 3 NT contracts made with 23-24 HCPs (not 26). In most of these cases, the declarer's side had a solid five card suit that provided a large number of tricks. On the other hand, I've seen 3NT contracts fail with a combined 27-28 HCP points. Usually, this was because of "flat" distribution in declarer's and dummy's hands, (4-3-3-3, or 4-4-3-2), especially if they "mirror."

Conversely, it seems that the the defense has a very good chance to prevail against a 26 HCP 3NT if they have a reasonably solid eight card suit, say, QJTxxxxx or better divided 5-3, but not if they are divided 4-4. (With 6-2, it depends if the hand with 6 has enough entries to cash them.)

Is a good five card suit often a decisive factor in making or breaking a 3NT contract? It seems to me like that fifth card in a suit may be worth about 3 points, so 24+"3" will probably make, and 27-"3" will often fail.

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    Partner opens 3D. You hold S: A62; H: A73; D: K7; C: Q9753. What do you bid? – Alexander Woo Aug 11 at 21:39
  • @AlexanderWoo: In this case, I bid a "gambling" 3NT opposite a supposed QJxxxxx and a side honor. I count on 6 diamonds, 2 aces, and a side trick with less than 20 HCPs. My fear is that LHO has something like KQJxx of spades or hearts, plus the ace of diamonds. – Tom Au Aug 12 at 0:09
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    Then you know, for any practical purpose, the answer to your question. Count tricks, not points. – Alexander Woo Aug 12 at 0:58
  • I get on your case occasionally in regards your algorithms - but here are three sites discussing Barry Crane's Inviolable Partnership Rules: Grant Baze Tribute, Other tributes, Other Rules (in the comments) – Forget I was ever here Aug 30 at 10:52
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There are nearly as many ways to evaluate hand distribution as there are experts. In some cases, these methods are chosen to justify being passive or aggressive in certain circumstances. However everyone recognizes two distinct components to evaluating distribution: a) the core value of the distribution; and b) the fit with partner.

In the days of Goren, a relatively simple evaluation system, one evaluated short suits only, for both suit and Notrump contracts, as:

  • 3 for void;
  • 2 for singleton; and
  • 1 for doubleton.

However remember that Goren's NT openings were all one point stronger than today, and all experts deduct a full point for 4333 distribution, When we shift to modern NT ranges and properly downgrade 4333, we end up with something like this:

  • +3 for void;
  • +2 for singleton;
  • +1 for doubleton; and
  • -1 for 4333.

Now 4432 distribution (the most common) with 15-17 HCP exactly matches Goren's 16-18 Total Points; but we have a more accurate and precise evaluation for other distributions.

Every expert I know also counts one point for the fifth card in a suit, even if it is expressed as a shift in the opening NT range: ie "Don't open 1NT with a five card suit and 17 HCP." or "I open 1NT with 15 HCP and a five card suit."

We now have:

  • +3 for void;
  • +2 for singleton;
  • +1 for doubleton;
  • +1 for a fifth card in a suit; and
  • -1 for 4333

For additional cards in a suit, these are (at least usually) worth more than the single point for a fifth card - but how much more is unsure. Sheinwold recommended in Five Weeks to Winning Bridge to count every card past the fifth at two points each, but that may be a bit aggressive. it may be better to regard it as having value both intrinsically and due to fit (or lack of it) with partner. With this in mind, we couldsay something like this:

  • +3 for void;
  • +2 for singleton;
  • +1 for doubleton;
  • -1 for 4333;
  • +1 for a fifth card in a suit; and
  • +2 for a sixth card in a suit when partner shows at least two; and
  • +1 for a sixth card in a suit otherwise; and
  • +2 for seventh and subsequent card in the suit.

Back to your specific example, this evaluates 5332 distribution as (+1+1) - (-1) = +3 points better than a 4333 hand; but only 1 point better than a 4432 distribution - from 4432 to 5332 one has lost a four card suit to gain the five bagger.

Here are overall evaluations for some frequent hand distributions (where the distributional evaluation is the same value, I have ordered them weaker followed by stronger according to my personal subjective assessment):

  • -1 4333
  • +1 4432
  • +2 5332
  • +2 4441
  • +3 5422
  • +3 5431
  • +4 6322 w/o 2+ fit from partner
  • +4 5440
  • +5 6322 w/ 2+ fit from partner

A reminder - this system is a means of assessing the potential for establishing length tricks due to the intrinsic shape of the hand. This is absolutely not an acceptable or accurate means of assessing ruffing potential in the hand with shorter trumps.

As a final note, Goren recommended not bidding 3NT until the partnership was known to have 26 total points. This is regarded as overly cautious by modern standards. Players are better overall than they were two generations ago, and as we see above modern evaluation is more refined. The modern standard is 25 points for Matchpoints, Rubber, and Not Vulnerable at IMPS; and 24 points Vulnerable at IMPS. As I have discussed in other answers, a partnership should agree that the one point variation for vulnerability at IMPS (and the complementary adjustment for slam bidding) is made only by the hand inviting game, or bidding it without an invitation. This is the only agreement for it I am aware of that is both unambiguous and simple to describe and remember.

  • "Players are better overall than they were two generations ago," While I can imagine this is true, I'm not an avid bridge player, so I don't know that this is true. Do you have a reference for that claim? It's pretty a pretty interesting claim. – John Aug 11 at 19:36
  • @John: It is largely the result of Charles Goren's writings, who greatly simplified both hand evaluation and bidding for novices. Ely Culbertson and his wife Josephine had made the game popular, but their Quick Trick evaluation system was difficult for learners as it relied excessively on the user's judgement. Everything changed after Goren. This was followed up in USA in the 1960's with seminal works by Alfred Sheinwold and Edgar Kaplan. – Forget I was ever here Aug 11 at 19:42
  • @John: If you are interested in more detail, ask a question on it. There are other strong bridge players on this site, some not from North America I believe, and they would be able to give a broader perspective than my North American one. I don't believe any of them would dispute my statement. – Forget I was ever here Aug 11 at 19:47
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    @John: The long run of success by the Italian Blue Team starting in 1957 demonstrated forcefully that while Goren's system was fun and easy for beginners, Four Card Majors was an inadequate bidding system for IMP play at the World level. Experts in North America soon began developing natural five card major systems that could compete, led by Kaplan-Sheinwold with their eponymous East Coast style system and Richard Walsh with his West Coast style that became Two Over One Game Forcing. By 1970 North American experts had caught up. – Forget I was ever here Aug 12 at 18:13
  • @John: I'm not sure if players are actually better than they were before. What IS true is that the nuances of the game are better understood than before. An example, from Larry Cohen's "Law of Total Tricks" is the value of "intermediate" cards. For instance, if you have JT98x in a NT contract, it's worth a lot more than one high card point, because you can take two tricks with it. At least three tricks, if partner has one of the three top honors. – Tom Au Aug 30 at 20:44
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It is - but only marginally.

Here is a simulation comparing 5-3-3-2 hands with 4-3-3-3 hands

A five card suit is only going to be beneficial IF it can be set up - in which case it will make an extra trick compared to a four card suit. This means that a very weak 5-card suit might actually be a handicap as declarer tries to set it up. If the 5 card suit is in a weak hand then declarer may not have the entries to set up the suit and finally - the fact that there is a 5 card suit in a hand also means that there will be a 2-card suit in the hand, which increases the chances that the opponents might also have a 5 card suit in their hand to set up.

If a player holds a decent 5-card suit then they are fully entitled to look on it favourably when considering a relatively low-count 3NT contract. Equally a defender with a decent 5 card suit needs a good reason to look elsewhere for the opening lead. Four tricks from the suit and One trick to get in to cash it makes 5 - enough to defeat 3NT. (6 card suits aren't quite as effective unless the hand is quite strong since partner is likely to only hold one and declarer can more easily break communications).

  • +1 for the observation that the quality of the fiver is the key. – Jyrki Lahtonen Sep 3 at 6:09

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