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Author Terence Reese wrote that the difference between amateurs and professional was that the former could "see" (locate) only 26 cards, while professionals could "see" 52 before the hand was over. Another commentator on this site once remarked that this could occur by the sixth or seventh round (out of 13).

Suppose you're declarer. An opening lead comes from West, and dummy goes down. Now you can actually see 27 cards. More to the point, West probably led from a suit in which he and partner hold 8 or 9 cards, meaning that they are likely distributed 5-3 if eight cards, and 6-3 or 5-4 if nine cards. By the rule of sequences or the rule of 11, you can probably guess WHICH five cards west holds, especially after East plays. So you can now "see" 34-35 by the time the cards reach your hand. If West led his partner's (bid) suit, that factors into the equation.

What happens next? That is, how do you bring your knowledge of 34-35 cards up to 52, and in (roughly) how many rounds. It might be fairly easy if one or both opponents bid. But what if they haven't?

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5 Answers

up vote 8 down vote accepted

To make a quick stab at this, first consider that there are distinct steps towards learning how to perform this visualization feat:

  1. Train your memory to know (i.e. be able to recite exactly) where all 52 cards were at the end of the deal. The rest is irrelevant until you can do this (though it can be practiced simultaneously).

  2. Practice (and practice and practice) visualization of the opponent's hands at every call and play. As each deal starts there will obviously be 13 blanks in each opponent's hand, but every bid, call and play should be adding constraints to each card. A 1-level overcall in spades by the opponent should immediately trigger a visualization like:
    KJ9xx xx Axx xxx
    in your mind.

  3. Practice using the deductions you are making about the opponents' hands. This will help develop the habit of paying close attention, by providing yourself with an occasional carrot for good analysis.

  4. Remember to always pay particular attention when you have a weak hand. Most of the field at almost any event will be asleep with those poor cards, so the opportunity to make a big gain on the field is greater than usual. Tournaments can be won on these hands.

Update:
Richard Pavlicek has an excellent online site chock full of useful lessons for Beginners, Intermediate Players, and Experts. Here are two links to an expert example of good card reading and to an analysis of some important considerations when reading the opponents actions:
(1) http://www.rpbridge.net/7c04.htm
(2) http://www.rpbridge.net/7z75.htm

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This is a huge subject, and I think the answer is divided equally between experience and analysis. But to answer your last sentence: failure to bid can be as illuminating as an actual bid. Suppose you are missing three aces, and one opponent has shown up with two of them; with all three he would have bid something, so you can place the last accurately. More generally, if your side have 25 points and you reckon on 8 or 9 for an overcall, it's safe to assume that a lack of bidding indicates that the high cards are split quite evenly.

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"High cards split quite evenly." So if one opponent shows up with "a bunch," (like two aces) figure on the other opponent for (most of) the rest. Is that right? –  Tom Au Apr 22 '13 at 20:22
    
@TomAu: Yes. Obviously you have to take into account what opportunities each opponent had, but with two aces and two other honours, most people would bid. This person did not bid: therefore, he did not have two aces and two other honours. –  TimLymington Apr 22 '13 at 21:34
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If the opponents are using standard defense signals, there may be ways to read the count in the discards that they play. High-Low being the signal for even count while Low-High is the signal for an odd count. Thus, you need to get a couple of discards in various suits in order to get an idea of where other cards are as over the course of the first handful of rounds, it may not always be possible to look for the signals though there is something to be said for reading into what defense is playing and extrapolating from that.

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Unless opponents are playing upside down discards; or odd-even discards; or upside-down odd-even discards. Yes, everything the opponents do is important data, but it is the process of understanding and cataloguing it that transforms it into information. The bidding, and lack of it, is even more important in analyzing the opponents cards because that information is available several tricks earlier than the opponents carding signals; namely as the opening lead is made. –  Pieter Geerkens Aug 22 '13 at 22:06
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Having the possible distributions of a suit in one's mind is a shortcut way of working out what cards a player has left in their hand. So if you are declarer with 5 cards in your trump suit and dummy has 3 trumps, the remaining 5 trumps are probably divided 3 2 or 4 1 between the two opponents. (You work this out quickly by having the patterns 5332 and 5431 in your mind.)

Now you test your guess. If both opponents follow to two rounds of trumps, there is only one trump left, whereas if one opponent shows out on the second round, his partner had 4 trumps initially, and still has 2 left.

On most hands it is usually only relevant to keep a count of two suits: your trump suit and the main side suit which you need to establish.

A further help for working out the missing cards is to focus on the missing key cards. For instance, if you have the A 10 5 4 of hearts and dummy has the K 9 3, the missing key cards are the Q and the J. You need to focus on when these fall in order to determine if your 10 (or 9) is good.

The two more difficult types of hands that I face most frequently are those that require an end play and No Trump contracts where there are missing high cards in two (or even three!) suits. With my present level of expertise, I cannot seem to anticipate where an end play is the technique required, but at least akqbridge.com has allowed me to practice these in retrospect.

Where an "end play" is needed to make the contract, you need to use one's knowledge of patterns such as 5431 to keep track of the cards remaining in the hand of the opponent you wish to end play. Basically, you are stripping them of the cards in their escape suits so that, when you "throw them in" (i.e let them win a trick), they are forced to lead the suit you want.

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Your difficulty with endplays stems from your belief in this error: "On most hands it is usually only relevant to keep a count of two suits: your trump suit and the main side suit which you need to establish." –  Pieter Geerkens Aug 18 '13 at 13:22
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@PieterGeerkens We are in agreement: for an endplay you need to track the distribution of all four suits. However, if I recall correctly, I only needed to use an endplay in 2 of the first 50 declarer play deals on akqbridge. In other words, most hands do not require all the cards and their distribution to be tracked. One of the aims of my web site is get a better feel for how frequently the different play strategies occur. –  soupman55 Aug 19 '13 at 4:57
    
If you haven't counted the hand, how do you know what play strategies will work? –  Pieter Geerkens Aug 19 '13 at 5:14
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The principle is actually quite simple. Everyone time a new suit is lead, you can "see" a new set of cards.

In the question, you can see 27 cards after the opening lead, and since it's from your opponent's "best" suit, probably eight or nine cards above your 26, after one or two rounds of play. That's 34-35.

Suppose you win the second trick and lead a new suit (your eight-carder) on trick three. After one or two rounds, you can see your opponents' four or five cards, bringing up the total to 39.

Suppose a third suit is introduced on trick five. After one of two rounds, you can see your opponent's cards in that suit as well.

Once you've seen the layout of three suits in all four hands, you can pretty much infer the fourth. That happens typically, after trick six or seven. Which is why you can "see" all 52 cards (or nearly all of them) about halfway into the play.

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