Relay Structure

Relay Structure Table of Contents

Responder's Hand Valuation
Positive shape-showing relays
Balanced hands
One-suited hands
Two-suited hands
Three-suited hands
Control Asking
Zooming
Exceptions for Level-adjusted Relays
King Parity
Denial Cue-Bidding
Key Card Asking
Ending Relay Auctions

General Notes

Relayer (referred to hereafter as "R") will normally make the next highest bid ("Step 1") to ask responder (hereafter referred to as "RR") to continue describing the hand. The exception to this is 3NT which is never a relay. Other non-relay bids by R below game are natural and may be invitational or forcing in context. 2NT is almost never a contract after a second relay.

Responder's hand valuation after a strong opening.

After an opening 1C, responder normally gives a positive response with a hand with 9+ HCP balanced or 8+HCP unbalanced, unless that hand has substantially fewer than the number of controls normally held by a hand of that shape. R will eventually be able to ask for controls with A=2 & K=1 or A=3, K=2 & Q=1, of which there are at most 12 and 24 in a deck of cards with 40HCP. The ratio of AK and AKQ points to HCP is 0.3 and 0.6 respectively. RR's minimum number of AK or AKQ controls (RR's "base") can be deduced by multiplying the minimum HCP by the appropriate ratio (0.3 or 0.6) and always rounding down to the nearest integer. With a hand on or near the HCP minimum with a large amount of the HCP contributed by queens and jacks, RR may have fewer than the putative base number of controls. In such cases RR may exercise his judgement, however it would be exceptionally rare to describe a hand with a positive response that was two AKQ controls below base.

With a hand with 5-7 HCP, or too few controls in a stronger hand, RR describes a semi-positive hand. With a weaker hand yet, RR describes a full negative hand. Note that again, a hand that meets the semi-positive criteria but has too few controls can be described as a full negative hand. The agreements in auctions after a negative response may be found here.

Positive shape-showing relays

First response

The responding scheme with an unbalanced positive hand is almost "up-the-line"; RR makes the lowest bid that describes the hand held.

1H	Unbalanced, 4+S
1S	Unbalanced, 4+H, 0-3S
1NT	Unbalanced, 4+D, 0-3S, 0-3H
2C	Balanced, including a four- or five-card major
2D	Balanced, 2-3H, 2-3S
2H	Three-suited with a major suit shortage
2S	6+C, 0-2S (High shortage)
2NT	6+C, 0-1H (Middle shortage)
3C	3226 or 2227 (Even shortage)
3D	3316 (Low shortage)
3H	3217
3S	2317
3NT	3307
The only exception to the "up-the-line" rule is the 2H response, which takes priority over the 1H and 1S responses.

Balanced hands

With a balanced hand, RR selects whichever of 2C or 2D is appropriate.

2C							Balanced, including a four- or five-card major
	2D						Game-forcing relay
		2H					Any 4432 with 4S
			2S				Game-forcing relay
				2NT			4432 or 4423
					3C		Game-forcing relay
						3D	4423
						3D	4432 (with zoom)
				3C			4243
				3D			4342
				3H			4234
				3S			4324 (with zoom)
		2S					Any 4432 with 4H and not 4S
			2NT				Game-forcing relay
				3C			2443
				3D			3442
				3H			2434
				3S			3424 (with zoom)
		2NT					Any 5332 with 5S
			3C				Game-forcing relay
				3D			5233
				3H			5323
				3S			5332 (with zoom)
		3C					4333 or 3433
			3D				Game-forcing relay
				3H			4333
				3S			3433 (with zoom)
		3D					2533
		3H					3523
		3S					3532 (with zoom)
		This relay structure avoids RR bidding a four-card major that they hold and are symmetric in the 5-card major holdings.
2D							Balanced, 2-3H, 2-3S
	2H						Game-forcing relay
		2S					Any 5332 with 5D
			2NT				Game-forcing relay
				3C			2353
				3D			3253
				3H			3352 (with zoom)
		2NT					Any 5332 with 5C
			3C				Game-forcing relay
				3D			2335
				3H			3235
				3S			3325 (with zoom)
		3C					2344
		3D					3244
		3H					3343
		3S					3334 (with zoom)

One-suited hands

With a one-suited hand of at least six cards, RR shows that suit and then rebids at 2S or higher to describe the residual short suits.

2S					0-2 in the highest-ranking other suit
	2NT				Game-forcing relay
		3C			"Even shortage"
			3D		Game-forcing relay
				3H	6223
				3S	6232
2NT					0-1 in the middle-ranking other suit
3C					"Even shortage"
	3D				Game-forcing relay
		3H			6322
		3S			7222
3D					6331 with low-ranking shortage
3H					7321 or 7231 with low-ranking shortage (no resolution of 3-2 fragments)
3S					7330 with low-ranking shortage and at least base+2 AKQ controls
3NT					7330 with low-ranking shortage and base or base+1 AKQ controls
4C					8+card suit, low-ranking singleton
4D					8+card suit, low-ranking void, base or base+1 AKQ controls
4H+					8+card suit, low-ranking void, base+2 or more AKQ controls
The shapes not explicitly shown in the structure can be constructed through "symmetry" - for example, all hands of 6331 pattern include a 3D bid, possibly after 2S or 2NT to specify the suit of the singleton. Other hand patterns are resolved similarly.

Two-suited hands

With a two-suited hand, RR shows his first suit up-the-line as listed in the positive responses. RR then shows the second suit and resolves their relative length. A bid of 2D always shows at least four cards in the lower-ranking suit (always clubs, in fact) and at least five cards in the higher-ranking suit. However a bid of 2H shows precisely four cards in the higher-ranking suit and at least five in the lower-ranking suit. Hands with two suits of at least five cards always start with two bids at or below 2D, and then a bid of 2S.
With bothThe 1NT opening bid shows a balanced hand, but denies a major suit unless a 4333 shape is held. The 1NT opening bid shows a balanced hand, but denies a major suit unless a 4333 shape is held. majors, RR continues with 1NT over the 1S relay to the first response. With a major and diamonds, RR continues with 2C (transferring to diamonds!). With any suit and clubs, RR shows the first suit and then bids according to the above scheme - 2D with exactly four clubs or both suits of at least five cards, or 2H with at least five clubs and exactly four of the other suit.
Thus the structure below applies after showing a second suit with 1NT, 2C, 2D or 2H.

2D		Three-suited with both majors
2H		5+ in the lower-ranking suit, 4 in the higher-ranking suit (a "reverser" bid)
2S		5+ 5+ in the two suits (step in)
2NT		0-1 in the higher-ranking other suit
3C		A 5422 pattern
3D		5413 with lower-ranking shortage
3H		6412 with lower-ranking shortage
3S		6403 with lower-ranking shortage with at least base+2 AKQ controls
3NT		6403 with lower-ranking shortage with base or base+1 AKQ controls
4C		7411
4D		7402 with lower-ranking shortage with base through base+2 AKQ controls
4H+		7402 with lower-ranking shortage with at least base+3 AKQ controls

Again the the structure is "symmetric" - all 6421 shapes will include a 3H bid, after clarifying the relative length of the suits and the shortages with previous actions. The 5-5 substructure is also symmetric internally. Note that the 7411 shape is shown "asymmetrically". The only reasonable alternative is to treat it with 5422 as "even shortage", which is grossly inefficient because it costs a step on the greatly more frequent 5422 shapes.

Showing 5+ 5+ hands

(step out) Game-forcing relay after showing 5+ 5+ in the two suits

3C		0-1 in the higher-ranking other suit
3D		A (65)11 pattern (even shortage)
3H		5512 with lower-ranking shortage
3S		5503 with lower-ranking shortage
3NT		(65)02 with lower-ranking shortage

The relative length of the 65 suits is resolved next in the normal way; 56xx is shown first, then 65xx

Three-suited hands

With a three-suited hand with a minor shortage, RR simply shows both major suits and then uses the "empty" 2D bid to describe his holdings. With a major shortage, RR simply responds 2H. Then after the subsequent relay, RR bids as described.

Step 1	High shortage (0-1)
Step 2	4441 (low shortage)
Step 3	5440 (low shortage)
Step 4	4540 (low shortage)
Step 5	4450 (low shortage)
After showing a high-ranking shortage, RR shows his exact shape by using the step responses as above, beginning at 4441.

Control asking relays

After the shape is shown, the next relay asks for controls. R has a choice of three asks: Step 1 asks for AKQ controls, Step 2 asks for AK controls and Step 3 asks for aces (Gerber!) subject to the usual stricture that 3NT and game-level bids above Step 1 are never relay asks. Also, the use of 4D as an end signal supersedes the use of that bid as an AK control ask or ace ask.

AKQ and AK controls are evaluated as simple sums. With AKQ controls, an ace counts three, a king two and a queen one. With AK controls, an ace counts two and a king one. When holding a singleton honour:

a singleton ace is counted normally in the hand's controls,
a singleton king counts one AK control for an AK control ask and one AKQ control for an AKQ control ask, and
a singleton queen or lower is not counted at all.

As described in the section above on hand valuation, both players can deduce RR's minimum HCP holding and thus the control base. The manner in which the number of controls is shown depends on the level of the asking bid. Asking bids of 3H and higher (obviously not 3NT) receive step responses such that Step 1 by RR shows they have a number of controls that is at most equal to the base. Step 2, 3, 4, etc. show one, two, three, etc. extra control(s) over that required for the base. When the asking bid is below 3H then the scheme "inverts" to improve efficiency. Bids of 3NT and 3S show the base and base+1 controls respectively. Bids below that show increasing numbers of controls, with bids of 4C and higher showing at least base+4 and more controls. Thus when only 3H is available it shows base+2 or base+3 controls. A further relay then requires 3NT with base+2 or a higher response with base+3 (see below). When both 3H and 3D are available then they show base+2 and base+3 controls respectively. Should 3C also be available, then it shows base+4 controls and in this case only, 4C and higher will show base+5 and more controls. Should any lower bids be available, then the scheme expands similarly.

The onus lies on R to ask for controls only when there are no replies that are reasonably likely to be awkward, since their next Step 1 is also a relay. An ace ask always begins at zero.

In one case above a response is made that shows a specific range of controls. When R bids Step 1, RR zooms to Denial Cue Bidding (see below) when holding the highest number of controls. R should be prepared for this zoom by a maximum RR. This principle holds in other situations where a range of controls is known, including where a maximum can be inferred from a known HCP maximum. Such a maximum is realised when holding the maximum number of aces with the remaining HCP contributed by as many kings as possible, etc.

Zooming

When RR holds the shape that is the highest call defined in the response structure it is efficient that that response follow on to the number of controls held without requiring R to waste two steps in making a subsequent ask. The scheme for zooming is to always show AKQ controls according to the above scheme, which depends on the level of the zoom. Should that zoom occur at or below 3H, then the "inverted" scheme described above applies in the same way.

There is one case in non-level-adjusted relay auctions where shape is shown above 3NT. This occurs when a 7411 pattern is shown with 4C. In this case, bids at or above 4D show the shape that was shown with 3NT (7420) with at least base+4 AKQ controls in the normal manner described above.

Exceptions for Level-adjusted Relays

In a variety of situations the relay structure can be shifted up or down a number of steps such that shape is shown with bids above 3NT (see Relay Interference). A balanced RR may never show shape past 3NT if the ask was at most 3C. An ask of 3D or higher requests normal responses. If truncation occurs with a 3NT bid, R may relay with 4C to complete the shape description, with a zoom with base+4 for the highest-ranking shape. An unbalanced RR does show shape above 3NT. In these cases, a 3NT bid shows the shape that would be shown at 3NT, but with at most base+3 AKQ controls. Higher bids show the appropriate shape, however the bid above the highest-ranking shape shows the shape that would have been described by a 3NT bid, but with at least base+4 AKQ controls. By limiting the strength held for a 3NT bid, R will continue to ask past 3NT when that is the last makeable contract less often.

Further, when resolving the shape of a hand known to be balanced, the structure will be similar to that used in non-level-adjusted relays, but with relevant bids swapped so that a major suit is not shown by a bid of that suit. Symmetry will be preserved, however.

King Parity

After shape has been resolved and an AKQ control number has been given (in response to a direct ask or a zoom), the next relay asks for "king parity". Note that a singleton king is not counted as a king here, consistent with the fact that it counted only one in the AKQ control number.

RR bids Step 1 or higher according to the following scheme:

King Parity	AKQ controls	Action
Even	2, 3, 6, 9, 12, 15, ...	Bid Step 1
Even	4, 5, 7, 8, 10, 11, 13, 14, ...	Zoom to Step 2 or higher
Odd	2, 3, 6, 9, 12, 15, ...	Zoom to Step 2 or higher
Odd	4, 5, 7, 8, 10, 11, 13, 14, ...	Bid Step 1

As can be seen by inspection, RR stops with odd number of AK controls unless they hold either 2 or a multiple of 3 AKQ controls. RR behaves in the opposite manner when holding an even number of AK controls. The rationales are that

with 2 AKQ controls RR should bid Step 1 with QQ and zoom with K because that is more effective for the subsequent DCB,
with a multiple of 3 AKQ controls, frequency analysis shows that around two hands with odd AK controls are held for every hand with even AK controls, and zooming should occur with the more frequent hand types, and
with other numbers of AKQ controls, there is either no significant difference in the ratio of odd:even AK controls, or a distribution with more hands with even AK controls.

One mnemonic is that RR with "odd" kings bids Step 1 with AKQ controls that are (approximately) "prime" with respect to 3.

Note that this criterion is somewhat arbitrary. The objective of maximising human slam-bidding efficacy is difficult to codify. Merely ensuring a Fibonacci-like distribution of step frequencies is a fair attempt, but there exist many distributions of hands to steps that satisfy this constraint but which do not permit effective bidding. Moreover, some distribution that could be demonstrated to be the most effective for bidding in the abstract might well be impractical for use by a human at the table. Additional work in this area would be of interest, but of little practical value. Using some king parity style is probably more effective than not using one, and even a simple style of bidding Step 1 arbitrarily with even AK controls is probably acceptable.

Denial Cue-Bidding

(Also known as "spiral scan".)

After controls (AKQ, AK or A) and possibly king parity have been shown, "denial cue-bidding" commences. In denial cue-bidding the suits are assigned an order of priority - firstly by order of length, but if two or more lengths are equal (or have lengths that are unknown), then the higher-ranking suit is scanned first. On the first ask ("scan"), the RR is asked to look for an ace, king or queen in the suit of highest priority. If neither of these is held then RR bids Step 1 to show this. Otherwise, RR then scans the suit of second priority, also for any of the top three honours, bidding Step 2 to deny one. This process continues through all the suits, and eventually may return to the suit of highest priority (i.e. "spiralling"). When this occurs, RR is expected to look for a second top honour in the suit if one was previously shown). This process continues. In principle, jacks could be investigated, but such auctions are usually too high for such an ask to be useful.

Editing needed A suit of a given length can only be scanned that given number of times - a singleton may only be scanned once, a doubleton twice, etc. The highest possible relay ask is 6C. If a response is made at 6C or higher, then R must be prepared to place the final contract. No relay response higher than 7C may be given. The onus is clearly on R not to make an ask when there is reasonable chance of unfortunate consequences. It is occasionally necessary to finesse a card during the bidding! (Don't tell your teammates, it spoils your image.)

Exceptions in Denial Cue-Bidding

When scanning a suit for the last card held (e.g. the first or second respectively for a singleton and doubleton, etc.), RR stops (i.e. bids the current step) when holding the relevant honour, and spirals if the honour is not held. This is much superior to the normal approach, because it is more probable that the relevant honour is not held. It suffers only a 1 step loss relative to a DCB style that never scans a singleton, losing 2 steps only where "unexpected" information is transferred, whereas scanning a singleton normally loses 2 steps most of the time. A case can be made for not scanning singletons at all when RR has shown AK controls, but that method is not used here.
When holding the AKQ of a suit, that suit is denied on the first scan. Thus a first-round denial of suit promises holding neither A, K or Q, or alternately holding all three of those cards. The 3 or 5 control discrepancy that is flagged by this denial is almost always apparent to R and recognisable - and it is assumed that R knows what holding RR has. Experience suggests that by the time this suit is scanned again no ambiguity remains, and both hands will know that AKQ has been shown. Thus on a second scan of this suit when holding at least four cards in the suit, the jack is investigated. There is no change of denial cue-bidding suit order in a case where a first-round denial has occured and the remaining honour locations are still ambiguous (e.g. the bidding sequences with AKQx Axx Kxx Qxx and xxxx AKx KQx AQx differ on the third response)
Additionally and analogously, the previous exception applies to a holding of exactly four cards to the AKQ; on the second round RR stops with AKQJ and spirals with AKQx. If a three-card suit contains AKQ then there is only one scan made of this suit.
When RR is known by both hands to have shown all possible aces, kings and queens, then the DCB skips directly to jacks in the first suit in the scan. This has been known to create amusing encrypted auctions when RR has 6 AKQ controls and a holding of AKQ in a suit is possible and R is missing at least 11 AKQ controls. Now after RR denies the suit in which AKQ might be held, R must ask until RR shows a card that R holds in one "version" of the auction, since the assumption that the control discrepancy will be recognisable is no longer as valid. Potential slams missing 5+ AKQ controls when R is missing at least 11 AKQ controls and has two "empty" suits are too rare for this to be damaging, however.

Ending relay auctions

R may end a relay auction at any time by passing a response (where appropriate!) or by bidding Step 2 or higher when that bid is at least at game level. The only exception to this is that 3NT is never a relay - even if the previous response was 3S. R must bid 4C to relay in this case.

If 4D is above Step 1, R has two ways to achieve a sign-off. A 4D "end signal" bid prefaces a sign-off opposite normal hands, and with a normal hand RR must bid 4H and pass any rebid by R. RR is not required to respect that intended signoff with a hand that is significantly better than that promised by the auction to this stage. Usually this would occur when holding extra controls, or an extreme shape that can only be approximately shown in the above relay structure (e.g. 8-card suits, 7-5 shapes). In the latter case, RR must use their judgement based on what they know partner knew for their signoff decision. The system permits an unlimited RR to bid past 4H (known as "kicking") when holding base + 4 AKQ controls. Successive bids above 4H show increasing numbers of AKQ controls. A limited RR who is kicking because of extreme shape can bid correctably - bidding the cheapest invitation that they would reject. An initial call by R higher than 4D is natural and invitational, and RR should evaluate his hand and particularly his trump suit. Since from the preceding, a direct 4NT by R is natural and invitational, a 4NT bid after a 4D end-signal is RKCB for RR's longest suit, or simple ace-asking if RR has shown no suit longer than four cards.

When RR has resolved or partially resolved their shape and R has selected a 3NT contract without establishing that RR has greater than minimum strength, RR should kick with base + 4 AKQ controls.

It is not mandatory to kick with a hand that meets the requirements - any of the following may indicate to RR that kicking is undesirable without substantial extra values : an early signoff before shape resolution, RR's poor shape, poor intermediates and the state of the match/event. R should be careful to sign off in tempo, particularly when slam requires substantial extras with RR, to avoid the transmission of unauthorised information.