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This was recommended by author Terence Reese (and several members of the site).

But I was taught differently, at least as declarer.

That is, I was taught to count "trumps and honors." So, if you are declarer in a trump contract, with, say, 26 high card points and an eight card trump fit, you will be most concerned about the five outstanding trumps, and the outstanding five or so, of the 16 face cards in your opponent's hands. Assuming no overlaps, your primary concern would be over TEN opposing cards, not 26.

If there is a critical side suit in the play, you might worry about five or so additional cards in that suit as well. Then I have worry about 15 of my opponents' cards, but not all 26.

On the other hand, suppose you have a singleton, x in the dummy of your opponents' best suit, and xxx in your own hand. They start off with AK of the suit, and you ruff the second round. You've seen four of your opponents cards, and you don't have to worry about the remaining five cards in the suit (assuming that both follow when you ruff your last x). Then you only have to worry about the remaining 19 opposing cards. And of these, the most important ones are the outstanding trumps, and the two honors or so, outside their main suit.

Is this right, at least regarding a trump contract (no trump is a different animal)? Or is there something that I am missing?

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Terence Reese is widely regarded as amongst both the best bridge players of the 20th century, and the best bridge writers of the 20th century. When you can legitimately aspire to one of those achievements, your proposed new approach to declarer play can be taken seriously. –  Pieter Geerkens Apr 27 '13 at 2:22
    
Care to play for money, say 10 cents a point. Rubber or Chicago, your choice. You can choose any partner who will play with you, and I will do likewise. After my partner and I have shaved your bank account a bit, we can discuss your new approach of counting hands to less than a full 13 cards. Perhaps over the dinner that yo will have so kindly treated us all to. –  Pieter Geerkens Apr 27 '13 at 2:27
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@PieterGeerkens: Maybe it was a badly worded question, which was really about the (economic) "law of diminishing returns." Of course "more is better than less" and 52 is better than 51 or 50 (nonsatiation). But if Reese is 100, can one get to e.g. "90" by counting 35-40 cards, or does one need to count 46-48? Put another way, while the ability to go from 26 to 36 increases your skill by a LOT, is there all that much difference between say, 46 and 52? –  Tom Au Apr 27 '13 at 15:38
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@Tom: What exactly do you mean by all 52? Down to the spots? Or are you talking about the hand distribution, with possibly not knowing all the x's, like "LHO has AJTxx"? –  Aryabhata Apr 27 '13 at 16:37
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I sense a misunderstanding here. On the one hand, remembering every card played in every hand is a good thing, as there is always a small chance that the setting trick will turn on the 4 against the 5. This does not mean that striving for this perfection is the best way to improve your bridge, nor that anyone who can't do it is a bad player. On the other hand, it is only necessary to keep track of significant cards; but the 4 as against the 5 may be significant as a signal or indicating a split (assuming a defender played his lowest trump under the A). You're not actually disagreeing. –  TimLymington Apr 29 '13 at 22:16

2 Answers 2

It's not completely a matter of the number of cards that you know as much as knowing the important features of the cards. For instance, it might be valuable to know that East holds one more small heart even if you don't need to know precisely which one it is.

As Pieter Geerkens says, every card is potentially important, so it's definitely worthwhile to locate as many as you can as accurately as you can.

In the interest of prioritizing, here are my suggestions for what is most important. There are two axes: One is which cards to pay most attention to, and the second is what methods to use to locate them.

For which cards to pay attention to, I would suggest the following priorities:

  1. High cards and distribution: Honors are probably self-explanatory, but distribution (and not just of trump) is frequently even more important. You often need to know if a suit is set up, if someone can ruff, etc. At this level, you just want to know how many cards in a suit are out/are held by someone, and don't care too much about which ones they are.

  2. Potential signals: If you are defender, you need to know if your partner is playing high-low or low-high, and as declarer, you also want to be able to read defenders' signals.

  3. High spots: It's very common that the 9 or 10 is high after a suit has been played twice, so you need to know that and where they are.

  4. Other spots: Usually you can get away with not knowing the exact values of the rest of the cards (although remember, you want to know how many each person has), but occasionally it still becomes important.

Whether #2 or #3 is more important depends on the hand. #1-#3 are all pretty important, but I think you start to face diminishing returns by #4.

Methods:

  1. Know which cards have been played already and which are in play: This is a critical beginner skill. I have seen many beginners miss tricks simply because they didn't remember that their Q was high. I still get bitten by this myself occasionally if I don't remember whether someone sluffed an 8 (making my 7 high) or a 6 (meaning the 8 is still out).

  2. Assemble a picture of the hand: At this level, you start doing deducing distributions from the two hands you can see and the cards already played. For instance, if you know East started with 2 hearts because he has shown out, and can have started with only 1-2 spades because you and dummy have 10 and West has already played 1, then you also know that East started with 9-10 cards in the minors. As you get more information, update the picture. E.g., West turns out to have a singleton club, meaning East has 6. Therefore East started with 3-4 diamonds.

  3. Make inferences from the bidding and play: Put in information you have from bids and plays that were made. If someone overcalled hearts, they probably have 5+ hearts -- that narrows the distribution down further. If West lead and East put in the K, East should not have the Q (unless East is a beginner or using some unusual signalling conventions, or conceivably has KQ doubleton).

  4. Make inferences from things that were not bid or played: For instance, if East chose not to open, and if you have located 10 HCP with East and you are trying to identify the location of a king, you can probably infer that West has the missing K. Ask yourself questions like: Why didn't West lead partner's suit? Or I know East has 6 diamonds, why didn't he bid them? (Too weak for a weak two, perhaps?)

In this axis, #1 through #4 are all very valuable, it's just that the later ones tend to be harder. #3 and #4 tend to involve some inherent uncertainty, which means you have to be a bit cautious in inferring information. You should try to evaluate how likely it is that your inferences are correct, and perhaps try to identify alternate scenarios.

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Declarer never needs to count all 52 cards, just like declarer never needs to make the contract. To be consistently successful declarer simply needs to be counting more cards than defenders are counting. Of course if the defenders are counting at least 26 each, declarer should be counting a full 52.

There are two fundamental reasons why one must aspire to count all 52 cards:

  • You get expanding returns, not diminishing returns, as every card you count increases the ability to locate and count the next card. The reason for this is that each located card reduces the number of cards remaining to be counted.
  • All of the advanced play techniques (single-, double-, and repeating-squeezes; throw-ins, etc.) require an exact, or nearly exact, count. One cannot aspire to perform any of these reliably without an exact count; neither can one effectively defend against them without an exact or nearly exact count.

The gain in play by having a solid familiarity of advanced techniques, can approach a trick over the play of a good intermediate player who has not studied these techniques. That is like being dealt 2 or 3 extra points every hand. If your partner has likewise studied these, (s)he also gets these extra points.

Imagine how many more successful contracts you will bid, and how many more opposing contracts you will set, if you and your partner are each dealt an extra queen each hand. That is the advantage one obtains by first learning to get an exact count early in the hand, and then studying the advanced techniques that allow you to take full advantage.

This analysis may also bear o your question here concerning cycles of over- and under-bidding. If one considers the very aggressive bidding of the Meckwell partnership (Eric Rodwell & Jeff Meckstroth), it is their excellent declarer and defender play, combined with superb table feel and intuitive hand evaluation, that allows them to be successful playing this way. Barry Crane played a similarly aggressive style in his day.

Weaker players tend to emulate the best known successful players of the day, without having the skill set to support the style. Goren addressed this by developing a more conservative system for weaker players, which was popular for many years. However don't be misled to think that Goren played passively in tournaments; Goren played his own system very aggressively, because of possessing the intuition and skill to do so successfully.

Update:
Yes, there are in many hands low spot cards that one does not need to remember exactly; thinking of an x is sufficient. However, the bridge literature is chock full of examples where the careless play of a deuce or trey instead of 5 or 6 has blocked a key suit. One never knows for sure which low spots are irrelevant until the full hand is counted.

I remember well an argument between two mentors, during my formative bridge years, as to where two small diamond spots had been, on a hand played 4 years earlier. Yes, that was the key hand in an important hand in a lost final; but one cannot even attempt to remember that far back if one doesn't remember at the conclusion of the hand. (Corollary: they both agreed on the location of the other 50 cards.)

Remember this: As declarer, the opponents are using those spot values to communicate with each other; as defender, your partner is using those spot values to communicate with you, and you are using those spots to communicate with partner. Nothing is more frustrating than to lead a small spot to partner asking for the suit to be returned, and having partner return another suit instead allowing a FAMOUS declarer to make an unmakeable contract (Sorry Dan! Too good an anecdote to leave out; I'll buy you a beer.)

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I think your count, and Tom's count mean different things. Counting distribution and location of relevant cards is all one needs to do. Not necessarily all the 52, down to the spots, which is what Tom is getting at I presume. –  Aryabhata Apr 27 '13 at 16:40
    
@Aryabhata: I think you need to re-read my post, without preconceptions. –  Pieter Geerkens Apr 27 '13 at 16:42
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Ok, please clarify by what you mean by count? Do you mean down to the spots? (like at trick 7, you know who holds the spade 4?) –  Aryabhata Apr 27 '13 at 16:43
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@Aryabhata: Yes, every spot of every suit until one knows the spot-value is irrelevant. This will happen sooner in some suits, and on some hands, than on others. I will not claim to be that good (yet), but I do aspire to that level because I understand the value of doing so. –  Pieter Geerkens Apr 27 '13 at 16:50
    
@PieterGeerkens: It seems like "how many cards do you count?" is tied to "how far do you want to go?" Maybe "26 to 36" gets you from beginner to high intermediate, while "36 to 52" gets you from high intermediate to world class, with "advanced" somewhere in the 40s. –  Tom Au Apr 27 '13 at 16:58

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