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Such a system might be too complex for a human to consistently/safely implement, but I am curious if they exist. I am imagining a system where your choice of suit or rank to lead or follow with could convey additional information mid-hand.

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Isn't that the very definition of illegal communication? Or do I misunderstand the question? Not a bridge expert. –  Affe Dec 13 '13 at 17:52
    
@Affe no more illegal than communicating through weird bidding, I would expect. –  Sparr Dec 13 '13 at 19:42
    
@Affe: With some exceptions, any partnership agreement on the meaning of a legal bid made or card played, or sequence of such, that is well explained in advance of the round/match to the opponents is legal. The exceptions generally cover methods deemed too complex, in the context of the competition being held, for the opponents to defend and understand. Generally there are few restrictions in 10-day World Team Championships, and very many in 3 hours novice match-point games. –  Pieter Geerkens Dec 14 '13 at 3:11
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For a starter, it is obvious that such signalling only applies on defence - Declarer has no need to communicate with his partner (Dummy), and such communication is anyways illegal. Let's start with the basic defensive systems and progress from there. All of these are perfectly legal when fully explained to the opponents (except some of the more complex techniques are restricted in limited-master-point events).

  1. Basic Signals:
    • Lead highest of touching honours (except King from Ace-King) either at the top of a suit or from an interior broken sequence; fourth-best from length; highest of a doubleton; low to show interest in having the suit lead back and high to deny interest in having the suit lead back; Lead high for partner to rough asking for a higher-ranked side-suit lead back an low to ask for a lower-ranked side-suit lead back.
    • Follow in trumps high-low on first two rounds to show a 3rd trump and interest in a rough; follow high-low to partner's lead suit to express interest in continuation, low-high to ask for a switch; follow high-low in other suits lead by Declarer to show an even number, low-high to show an odd number; Follow high-low as suit preference for a higher-ranked side-suit and low-high as suit preference for a lower-ranked side-suit.

You will of course notice that many of these are contradictory or ambiguous - that is the cost of asking a very restricted language to convey a rich amount of information. Established partnerships discuss the priority of these signals at great length, but the general gist is (usually): Attitude first; Count once attitude is known; Suit-preference once count is known, or when obligatory. Deciphering that consistently with your partner is one of the most highly rewarded skills in Bridge, as most of your opponents are so very bad at it.
;-)

More complex signals involve adding a mixture of these variations to the basic scheme:

  1. Second-highest from touching honours. Sometimes only at the top; sometimes only from interior sequence (Coded 9's & 10's); sometimes both.
  2. Upside-Down signals - reversing the meaning of high-low and low-high sequences;
  3. Odd-Even signaling - replacing high-low and low-high combinations with the play of either an odd-spot or an even-spot, sometimes combining attitude with suit-preference so that an odd-spot encourages; a low-even spot asks for a lower side-suit switch; and a high-even spot asks for a higher side-suit switch.
  4. Round-the-corner suit preference in place of absolute suit-preference.

That's all I can recall off the top of my head, but I have seen attempts to play even more unusual combinations. Myself, I don't think the benefit is worth the risk of a disaster from misunderstanding.

Update: With some exceptions, any partnership agreement on the meaning of a legal call made or card played, or sequence of such, that is well explained in advance of the round/match to the opponents is legal. The exceptions generally cover methods deemed too complex, in the context of the competition being held, for the opponents to defend and understand. Generally there are few restrictions in 10-day World Team Championships, and very many in 3 hours novice match-point games.

The section on Carding on each chart of current ACBL Convention Charts explains the defensive carding systems allowed or disallowed for the corresponding class of competitions held under the aegis of the American Contract Bridge League.

Update #2 - Partnership Agreements:

Update #3: A sample Convention Card (pdf) as approved for ACBL sanctioned events.

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I have never heard the "explained to the opponents" requirement for bidding, or other, systems. Are there any resources on this rule, or other Stackexchange questions on the subject? –  Sparr Dec 14 '13 at 20:44
    
@Sparr: Please see Update #2 above. –  Pieter Geerkens Dec 14 '13 at 20:58
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Wow, thanks! That actually makes me a lot less wary of the sketchiness of bridge bidding systems in general. –  Sparr Dec 14 '13 at 21:04
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In addition there is PRISM signals which with some bidding understanding can give the shape of your partner's hand from his plays. Its somewhat complicated.

http://prismsignals.com/PrismSignals.pdf

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Bridge is after all a timed game. A neat little system that, but can anyone play it and understand it in tempo. If not, it remains a wholly theoretical construct. –  Pieter Geerkens Dec 14 '13 at 15:26
    
@PieterGeerkens It seems simple enough to give in tempo and to note what the signal was in tempo--in this respect, it's superior to e.g. odd-even or Lavinthal discards. At the point of time that you have a problem (i.e. when you need to decide which lead to make), you're allowed to pause to solve your problem, and in fact your pause in this situation gives no unauthorized information to partner (again, as opposed to the pause taken when deciding which discard to make when using Lavinthal or odd-even discards). –  ruds Dec 15 '13 at 5:46
    
@ruds: Surely you jest! One cannot pause to make an odd-even or Lavinthal discard, one must make the play in the same tempo as for a meaningless or standard-usage discard. Besides which making the play is the easy part - reading it is the harder half. –  Pieter Geerkens Dec 15 '13 at 5:49
    
@PieterGeerkens I agree, yet many do pause before making a discard. In fact, I am aware of players who consider these discarding agreements unethical by design, because they practically beg for the discarder to pause to consider a discard. –  ruds Dec 15 '13 at 5:51
    
@ruds: I can play and read odd-even in tempo, but I do not care to attempt anything fancier. I want my partner enabled to take a view when the opponents show a tell, not hamstrung because I hesitated. –  Pieter Geerkens Dec 15 '13 at 5:53
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Cards played constitute signals, and there are several basic types. For the partner of the leader, they include the following.

Attitude signals refer to playing a high spot card on a lead to show that you like the suit.

Count signals were better discussed in Pieter's post. Briefly, one example is playing high-low in a no trump contract to show an even number of cards, and low-high to show an odd number.

Suit preference signals are made when leading back a suit that is not a trump suit. Besides the main suit and the trump suit, there are two side suits. A high preference lead means "I have an entry in the higher side suit." A low lead for preference means, "I have an entry in the lower side suit." One expert suggested using an intermediate card to signal neither a preference in the high or low side suit, meaning that trumps should be led.

For the leader, there are several "conventions." The most common ones are "top of a sequence" if you have a sequence of at least three, or three out of four, and "fourth best," from a long suit in which you have no sequence. "Top of nothing" is a common "passive" lead when the leader is "playing not to lose" (tricks).

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