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Most contracts can succeed with some distributions and defenses of the 26 opposing cards, and fail with others. If a contract (except a grand slam) makes against any defense and distribution you've underbid. If one never makes against any distribution and perfect defense, you've overbid. The latter two are clearly "non optimal" contracts.

When I learned bridge in the early 1970s, I was taught to "bid to make." With a standard eight card trump fit and 26 points, one should be in a four level contract that would make if e.g. the trump suit broke 3-2 (a 68% chance) but would often fail if the suit broke 4-1 or 5-0. Other equivalent (68%) chances were a combination of 3-3 suit break followed by a finesse.

More recently, scoring rules have changed, especially for IMPs, so that you will come out ahead if your contracts have a 50% chance of making, and in some cases, even 40%. Have bidding systems adjusted to these changes, requiring say, 24 points instead of 26, so that your contract hinges on 50-50 finesses rather than the 68% chance situations described above?

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    50% of 200 points is worth more than 75% of 120, but 75% chance to win a game is worth more than 50% chance. But your definition of optimality makes both of them optimal at the same time. This doesn't make sense as a word for this situation, and has no further mention in the point of the question anyway. I suggest removing it entirely as a source of multiple potential confusions. – Nij Nov 14 at 3:02
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Bidding systems, particularly ones experts use against experts, are built around optimizing results overall, not contracts.

Half the time, the opponents have better hands than you do, and you are still trying to make their results as bad as possible. Sometimes this is by sacrificing - getting to a contract that goes down but for which the opponents score less for setting you than they would for making their own contract. Often, this is simply by disrupting the bidding enough that the opponents cannot exchange enough information to decide on their best contract.

At the slam level, and even frequently for games, experts are frequently thinking about the entire probability distribution of what partner's hand could be, what opponents' hands could be, looking at their hand, and calculating if there is at least a 50% or 35% (depending on form of scoring and vulnerability) for the contract to make. They are not counting points.

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    Great answer - but I take issue with your final statement "They are not counting points.". Perhaps "They are not just counting points." instead. I am no expert, but have played with and spent hundreds of hours discussing hands with others who are true experts. All, without exception, translated their total assessment of points and intangibles back into the point framework of their bidding system - except in rare circumstances of very unusual distribution. – Forget I was ever here Nov 15 at 11:17
  • @ForgetIwaseverhere: I start with points, and then make adjustments for e.g. the fifth card in the suit, the probable location of adverse honors based on the bidding, etc. But my evaluation is "anchored" in points. – Tom Au Nov 15 at 23:18
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Alexander Woo's answer well addresses the direct question at issue - but there are numerous statements made (and implied) in the question body which are based on misunderstanding at best. Let's take them one by one:

  1. Most contracts can succeed with some distributions and defenses of the 26 opposing cards, and fail with others.

    No, there is no basis for this in fact. For any contract at a level above 1NT there is in general far less than a 50% chance that our side has a chance to make it. Further, double dummy cooperative defenses have no bearing on any sane analysis of Bridge. Even very weak players are out to attempt success, and typically will get at least a couple of good results over a 26 board evening.

  2. If a contract (except a grand slam) makes against any defense and distribution you've underbid.

    No. There is for example no point to bidding contracts of:

    • Three of any suit;
    • Four of a minor; and
    • Five of a major

    except in a (actual or potential) competitive auction to obtain the best tactically achievable score. Sound bidding guidance, for good reason, advises against bidding these levels for constructive reasons other than to invite the next higher "bonus level": game or slam as the case may be.

  3. If one never makes against any distribution and perfect defense, you've overbid. The latter two are clearly "non optimal" contracts.

    No; the object if the game is to maximize one's score. As a tactical means of approaching that goal one will occasionally, in the auction, judge that losing a small amount going down is better than risking a much larger loss allowing the opponents to set the contract. This is a optimal score rather than an optimal contract by your definition.

  4. When I learned bridge in the early 1970s, I was taught to "bid to make."

    This is sensible advice to give a novice beginner. If you passed through that stage without being introduced to preemptive openings and reopening (ie balancing) calls then your instruction was sorely lacking.

  5. With a standard eight card trump fit and 26 points, one should be in a four level contract that would make if e.g. the trump suit broke 3-2 (a 68% chance) but would often fail if the suit broke 4-1 or 5-0. Other equivalent (68%) chances were a combination of 3-3 suit break followed by a finesse.

    Novices never arrive with intuition - as that is only developed in any sound sense with hundreds (for the very fortunate) or even thousands (for the less fortunate) hours of play and study. For some it never arrives at all. This guidance is to enable, in the interim, a modicum of success that will enable the acquiring of sound intuition. You are conflating an improvement in Point Count Evaluation, that occurred in North America contemporaneous with the arrival of "scientific" systems into North America in the late 1950's (see below), with those systems themselves.

  6. More recently, scoring rules have changed, especially for IMPs, so that you will come out ahead if your contracts have a 50% chance of making, and in some cases, even 40%.

    The only scoring change I am aware of since the early 1970's, IMPs or otherwise, is the change for fourth and subsequent non vulnerable doubled undertricks from 200 each to 300 each. This was instituted to discourage over-competitive non vulnerable contracts at both IMPs and other tournament formats; and certainly not for the reason you ascribe.

  7. Have bidding systems adjusted to these changes, requiring say, 24 points instead of 26, so that your contract hinges on 50-50 finesses rather than the 68% chance situations described above?

    No. What actually happened is that the Goren Point Count Evaluation was refined by making a clearer distinction between High Card Points and (Total) Points. This resulted in an reduction in the evaluation of the average hand by one Total Point, and thus in the total points by a partnership by two Total Points.

    The change involves the distinction in how one evaluates the distinction in playing strength between hands of 4333, 4432, and 5332 distribution, the most common holdings:

    • Goren Point Count:
      A 4333 hand is assessed at 0 points of distributional strength (counted at both NT and Suit contracts). A 4432 hand is assessed at 1 points of distributional strength (counted at both NT and Suit contracts). A 5332 hand is assessed at 1 points of distributional strength (counted at both NT and Suit contracts).

    • Modern Point Count:
      A 4333 hand is assessed at -1 points of distributional strength (counted at both NT and Suit contracts). A 4432 hand is assessed at 0 points of distributional strength (counted at a NT contract) and 1 points of distributional strength (counted at a suit contract). A 5332 hand is assessed at 1 points of distributional strength (counted in either NT or its doubleton suit) and at 2 points of distributional strength (otherwise).

    • Impact of above:
      This evaluation change better recognized the weak playing value of a 4333 distribution relative to the more common 4432 and 5332 distributions - and when matched across both partnership holdings allowed the specification of 24 points (instead of 26) as the recommended minimum combined partnership holding for a sound 3 NT game contract. Likewise again it allowed a reduction in the recommended minimum for an eight-card-fit Major game contract from 26 to 25 points (as presumably not both partners were holding 4333 hands where a 3NT contract might be better).

    Examples:

    • The hand AJxx QTx Kx AJxx evaluates to 16 Goren Points and 15 Modern Points for a 1NT opening. The hand AJxx QTx Kxx AJx evaluates to 15 Goren Points and 14 Modern Points for a 1NT opening. Thus under both systems the first hand is suitable for a 1NT opening while the latter is not.
    • The hand AQx KTx Kx AQxxx evaluates to 19 Goren Points and also to 19 Modern Points, thus in both cases being too strong for a 1NT opening. Note that Goren counts 1 point for the doubleton, Modern one point for the sound 5-card suit.

    • The hand AJx KJT AQ Qxxxx evaluates to 18 Goren Points and to 17 Modern Points, thus meeting the upper limit requirement in both cases for a 1NT opening. (Modern doesn't count the five-card suit with only medium honour as being worth a point for NT.)

    Note how the evaluation process for hands has improved - not the bidding system itself.


Also your implication that these ideas are post 1970's is blatantly incorrect. By the mid 1950's Tobias Stone and Alvin Roth, soon joined by Kaplan, Sheinwold, Kay, Walsh and others, are already formulating these ideas into Eastern and Western variants of a new Scientific approach for North American Standard bidding that would evolve into Kaplan-Sheinwold and Two-Over-One Game Force respectively. Kaplan and Sheinwold publish the material elements of their system (described in How to Play Winning Bridge) in two installments, 1958 and 1962, more than a decade before your claimed beginning of these developments.

  • I did fail to make the distinction between freely bid contracts and "competition." I meant first that most people (unless pushed) bid contracts they think they can make. I also didn't allow for deliberate overbidding to block opposing contracts in the earlier version. I have made these two changes in the question. – Tom Au Nov 15 at 22:46
  • @TomAu: You know better - Don't change questions to invalidate existing answers. Changing questions in response to comments is fine - but to invalidate existing answers destroys the whole purpose of a Q & A. – Forget I was ever here Nov 15 at 23:04
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    On the money, as always. A minor blemish is in your item 6. The increased penalty of 300 per undertrick only applies to fourth and subsequent undertricks. Down three doubled, non-vul, is still 100+200+200=500 for the opponents. This is a natural spot for a change IMVHO. The possibly most common application is that if we are non-vul and they are vul, it still pays to sac and go down three vs. game making their way. – Jyrki Lahtonen Nov 24 at 7:30
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    (cont'd) According to 1935-87 scoring rules going down eleven non-vul would show a plus in comparison to a vulnerable grand making their way, and that is surely ridiculous. – Jyrki Lahtonen Nov 24 at 7:35
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    @JyrkiLahtonen: Good catch; thank you . corrected. Yes, once it was thought of I don't think anyone regarded it as a bad idea. – Forget I was ever here Nov 24 at 12:07
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Absolutely - but I think it's more complex than just changes in scoring. I was taught in the 1990s, and 26 point games would definitely be overly conservative in that time even. 24-25 points was much more reasonable.

I don't think it's just scoring, though; I think it's due to people learning better strategies, particularly through statistical analysis. More aggressive bidding systems in general have become more in vogue - look at the interference over strong 1NT, for example, that's currently used as opposed to the older methods that required much more unusual hands. Even the 1NT opening range has adjusted - 15-17 not 16-18, even in fairly standard systems.

  • One thing people are learning about are "side" factors. For instance, it might be possible to make 3NT with 23-24 and a solid five card suit, or a "gambling" 3NT with 21-22 and a sold six card suit, but you may need 25-26 with 4-4-3-2 distributions in both hands. That's because the "long" cards provide extra tricks. In a trump contract, a 4-4 distribution could be advantageous (trump from either side) but not NT. – Tom Au Nov 14 at 16:11

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