Mathematical Tables

Mathematical Probabilities Percentage

The numerous combinations of 52 cards and their probabilites and/or percentages of distribution and/or pattern and/or occurence have been studied by many mathematicians, arithmeticians, probability theorists, and mathematical statisticians. The source of the tables below are from The Official Encyclopedia of Bridge, published by the American Contract Bridge League in the year 1984.

Note to all readers: Some or several of theses percentages and probabilities may have changed as a result of newer studies. Many universities and colleges and other educational organizations continue to employ the 52 cards used in the game of bridge as the foundation of their doctorate or academic degree. Such studies may have resulted in more accurate formulae and results than those presented on this web page. Any reference to updated and possibly more accurate results will be greatly appreciated.

The following mathematical tables may/can/are used to determine the percentages of various distribution patterns, both for hand patterns and suit patterns. The numbers are expressed in percentage of hands. The percentage expectation of a particular pattern with the suits identified is expressed in the last column.

Pattern				Total				Specific
4-4-3-2				21.5512				1.796
4-3-3-3				10.5361				2.634
4-4-4-1				2.9932				0.748
5-3-3-2				15.5168				1.293
5-4-3-2				12.9307				0.539
5-4-2-2				10.5797				0.882
5-5-2-1				3.1739				0.264
5-4-4-0				1.2433				0.104
5-5-3-0				0.8952				0.075
6-3-2-2				5.6425				0.470
6-4-2-1				4.7021				0.196
6-3-3-1				3.4482				0.287
6-4-3-0				1.3262				0.055
6-5-1-1				0.7053				0.059
6-5-2-0				0.6511				0.027
6-6-1-0				0.0723				0.006
7-3-2-1				1.8808				0.078
7-2-2-2				0.5129				0.128
7-4-1-1				0.3918				0.033
7-4-2-0				0.3617				0.015
7-3-3-0				0.2652				0.022
7-5-1-0				0.1085				0.005
7-6-0-0				0.0056				0.0005
8-2-2-1				0.1924				0.016
8-3-1-1				0.1176				0.010
8-3-2-0				0.1085				0.005
8-4-1-0				0.052				0.002
8-5-0-0				0.0031				0.0003
9-2-1-1				0.0178				0.001
9-3-1-0				0.0100				0.0004
9-2-2-0				0.0082				0.0007
9-4-0-0				0.0010				0.00008
10-2-1-0				0.0011				0.00004
10-1-1-1				0.0004				0.0001
10-3-0-0				0.00015				0.00001
11-1-1-0				0.00002				0.000002
11-2-0-0				0.00001				0.000001
12-1-0-0				0.0000003				0.00000003
13-0-0-0				0.0000000006				0.0000000002

Probable Percentage Frequency of Distribution Patterns

The following table presents the expectation of holding specific point counts, using the 4-3-2-1 count.

Probable Frequency of High Card Content

Point Count				Percentage				Point Count				Percentage
0				.3639				16				3.3109
1				.7884				17				2.3617
2				1.3561				18				1.6051
3				2.4624				19				1.0362
4				3.8454				20				.6435
5				5.1862				21				.3779
6				6.5541				22				.2100
7				8.0281				23				.1119
8				8.8922				24				.0559
9				9.3562				25				.0264
10				9.4051				26				.0117
11				8.9447				27				.0049
12				8.0269				28				.0019
13				6.9143				29				.0007
14				5.6933				30				.0002
15				4.4237				31-37				.0001

 

The following table presents the probability, even before dealing the cards, of holding an exact number of cards in a specified suit. It must be noted that the number of times the specified number of cards can be expected in any suit during the course of 100 deals is four times as great.

Number of Cards				Percentage
0				1.279
1				8.006
2				20.587
3				28.633
4				23.861
5				12.469
6				4.156
7				0.882
8				0.117
9				0.009
10				0.0004
11				0.000009
12				0.00000008
13				0.00000000016

Probability of Holding an Exact Number of Cards in a Specified Suit

The following table present the probability of distribution of the remaining cards in a suit for:
A. a one-hand holding in column (1)
B. among the other three hands in column (2)
C. and expressed as a percentage in column (3)

Probability of Distribution of Cards in Three Hidden Hands

(1)		(2)				(3)													(1)		(2)				(3)
0		6-4-3				25.921													4		3-3-3				11.039
		5-4-4				24-301															4-4-1				9.408
		5-5-3				17.497															6-2-1				4.927
		6-5-2				12.725															5-4-0				2.605
		7-4-2				7.069															6-3-0				1.390
		7-3-3				5.184													5		3-3-2				31.110
		8-3-2				2.121															4-3-1				25.925
		7-5-1				2.121															4-2-2				21.212
		6-6-1				1.414															5-2-1				12.727
		8.4.1				0.884															5-3-0				3.590
1		5-4-3				40.377															4-4-0				2.493
		6-4-2				14.683															6-1-1				1.414
		6-3-3				10.767															6-2-0				1.305
		5-5-2				9.911													6		3-2-2				33.939
		4-4-4				9.347															4-2-1				28.282
		7-3-2				5.873															3-3-1				20.740
		6-5-1				4.405															4-3-0				7.977
		7-4-1				2.447															5-1-1				4.242
		8-3-1				0.734															5-2-0				3.916
		8-2-2				0.601															6-1-0				0.870
2		4-4-3				26.170													7		3-2-1				53.333
		5-4-2				25.695															2-2-2				14.545
		5-3-3				18.843															4-1-1				11.111
		6-3-2				13.704															4-2-0				10.256
		6-4-1				5.710															3-3-0				7.521
		5-5-1				3.854															5-1-0				3.077
		7-3-1				2.284													8		2-2-1				41.211
		7-2-2				1.869															3-1-1				25.185
		6-5-0				0.791															3-2-0				23.247
3		4-3-3				27.598															4.1.0				9.686
		5-3-2				27.096															5-0-0				0.671
		4-4-2				18.817													9		2-1-1				48.080
		5-4-1				11.290															3-1-0				27.122
		6-3-1				6.021															2-2-0				22.191
		6-2-2				4.927															4-0-0				2.608
		7-2-1				1.642													10		2-1-0				66.572
		6-4-0				1.158															1-1-1				24.040
		5-5-0				0.782															3-0-0				9.388
4		4-3-2				45.160													11		1-1-0				68.421
		5-3-1				13.548															2-0-0				31.579
		5-2-2				11.085

The following table presents the probability of distribution of cards in two given hands.

A. (1) shows the number of cards in the two known hands.

B. (2) shows the number of outstanding cards in the two hidden hands.

C. (3) shows the ways in which these cards may be divided.

D. (4) shows the percentage of cases in which the distribution in column (3) occurs.

E. (5) shows the number of cases applicable.

F. (6) is the result of dividing the percentage (4) by (5), and indicates the probability
that one opponent will hold particular specified cards.

 

(1)				(2)				(3)				(4)				(5)				(6)
11				2				1-1				52.00				2				26.0000
								2-0				48.00				2				26.0000
10				3				2-1				78.00				6				13.0000
								3-0				22.00				2				11.000
9				4				3-1				49.74				8				6.2175
								2-2				40.70				6				6.7833
								4-0				9.57				2				4.7850
8				5				3-2				67.83				20				3.392
								4-1				28.26				10				2.826
								5-0				3.91				2				1.9550
7				6				4-2				48.45				30				1.6150
								3-3				35.53				20				1.7765
								5-1				14.53				12				1.2108
								6-0				1.49				2				.7450
6				7				4-3				62.17				70				1.0362
								5-2				30.52				42				7.2667
								6-1				6.78				14				.4843
								7-0				0.52				2				.2600
5				8				5-3				47.12				112				.4207
								4-4				32.72				70				.4674
								6-2				17.14				56				.3061
								7-1				2.86				16				.1788
								8-0				0.16				2				.0800
4				9				5-4				58.90				252				.2337
								6-3				31.41				168				.1870
								7-2				8.57				72				.1190
								8-1				1.07				18				.0595
								9-0				0.05				2				.0250
3				10				6-4				46.20				420				.1100
								5-5				31.18				252				.1237
								7-3				18.48				240				.0770
								8-2				3.78				90				.0420
								9-1				0.35				20				.0175
								10-0				0.01				2				.0050
2				11				6-5				57.17				924				.0619
								7-4				31.76				660				.0481
								8-3				9.53				330				.0289
								9-2				1.44				110				.0131
								10-1				0.10				22				.0400
								11-0				0.002				2				.0010
1				12				7-5				45.74				1584				.02889
								6-6				30.49				924				.0330
								8-4				19.06				990				.0193
								9-3				4.23				440				.0096
								10-2				0.46				132				.0034
								11-1				.02				24				.0008
								12-0				0.0003				2				.0002
0				13				7-6				56.62				3432				.0165
								8-5				31.85				2574				.0124
								9-4				9.83				1430				.0061
								10.3				1.57				572				.0028
								11-2				0.12				156				.0007
								12-1				0.003				26				.0001
								13-0				0.00002				2				.00001

Probability of Distribution of Cards in Two Hidden Hands

A residue is said to be favorably divided when it is divided as evenly as possible. In the following table:
A. column (1) shows the number of cards outstanding in each of the two suits in the two hidden hands.
B. column (2) shows the percentage of cases in which both residues will divide as evenly as possible.
C. column (3) shows the percentage of cases in which at least one residue will divide favorably.

 

Probability of Distribution of Two Residues Between Two Hidden Hands

(1)				(2)				(3)
8-8				11.87				53.57
8-7				21.77				73.13
8-6				12.44				55.81
8.5				23.10				77.45
8-4				13.86				59.56
7-7				40.42				83.93
7-6				23.10				74.60
7-5				43.31				86.69
7-4				25.99				76.88
6-6				13.20				57.86
6-5				24.75				78.61
6-4				14.85				61.37
5-5				46.75				88.90
5-4				28.05				80.47
5-3				53.29				92.53

 

Odds and Odds

The odds in the game of bridge has been a fascinating subject for many bridge players throughout the years. Mathematicians have devoted much time to finding formulas for calculating these odds. After their calculations, we present perhaps just a sampling of the different possibilities in the constellation of the cards.

The longest possible bridge auction in the game of bridge is presented on this web page.

The number of possible deals: 53,644,737,765,488,792,839,237,440,000.

The possible number of bridge auctions, as has been mathematically calculated, is: 128,745,650,347,030,683,120,231,926,111,609,371,363,122,697,557.

The number of possible different hands that a named player can receive: 635,013,559,600.

The number of possible auctions by North, if East/West passes: 68,719,476,735.

The number of possible auctions by North, if East/West do not pass: 128,745,650,347,030,683,120,231,926,111,609,371,363,122,697,557.

The odds against each player having a complete suit: 2,235,197,406,895,366,368,301,559,999 to 1.

The odds against one player holding a Yarborough: 1,827 to 1. The odds against two players holding a Yarborough: 546,000,000 to 1.

There are many ways to indicate, show, promise and inform a partner by the lead of a certain card or via a discard of a specific card the expectation of the ensuing play. These defense signals have a definite meaning and belong in every partnership agreement. These different leads and/or discards have been posted separately on this site and should be reviewed.

Summary Intent

The purpose of this web page is to give the reader a short summary of the different approaches, which a partnership may employ. This summary does not include every possible lead, defensive signal, and/or discard method, rather only those which frequency is higher than usual for the general partnership.

General Rules of Defensive Signals

1. When following to a suit or when discarding in a suit, the relative spot of a card is used to send signals.
2. Signals are usually given with cards from the Two spot to the Nine spot.
3. A signal can be, with a high frequency, interpreted:
A. From the bidding.
B. From the cards visible in the dummy.
C. From the cards held in your hand.
4. It is sometimes necessary, if not prudent, to wait until partner plays to the second round in a suit to fully understand a signal.
5. It is not always appropriate to signal, especially with a strong defensive hand.
6. It is not mandatory to follow your partner’s signals when it is deemed not suitable given the context of a hand.
7. It is generally profitable to signal as much as possible against less experienced players.
8. It is strongly recommended to always signal on the opening lead.

Attitude Signal

The attitude signal indicates the level of interest toward the suit, in which the signal is given. Common practice include positive and negative attitude signals.

1. A relatively high card shows positive attitude toward the suit being led.
2. Or a relatively low card shows negative attitude toward the suit being led.
3. An echo is a positive attitude signal consisting in a high card followed as soon as possible with a lower card.

Coded Nines and Tens

1. Coded Nines and Tens leads are used against No Trump contracts.
2. The lead of a Ten promises the Jack plus another non-consecutive higher-ranking honor or shows top of a sequence without a higher-ranking honor.
3. The lead of a Nine promises the Ten plus another non-consecutive higher-ranking honor or shows top of a sequence without a higher-ranking honor.

Count Signal

The count signal is used to show the number of cards held in a suit being led.
1. A relatively high card shows an even number of cards in a suit being led.
2. A relatively low card shows an odd number of cards in a suit being led.

Count is given by playing:
1. High-Low from two cards.
2. Low from three or five cards.
3. Second-high followed with Third-high from four cards.

Journalist or Lead of an Honor Against No Trump

Each lead of an honor has a special meaning:
A. The lead of a Jack denies a higher-ranking honor.
B. The lead of a Ten promises the Ace, the King or the Queen.
C. The lead of a Nine promises the Ten or no higher-ranking honor or a doubleton. For example: lead the Eight from 987.
D. The lead of an Ace shows AKJxx or AKQ10x or AK109x.
E. The lead of a King shows Ace-King or King-Queen.
F. The lead of a Queen shows QJ10 or KQ109 and requests unblocking the Jack when held.
Advantages: Journalist leads eliminate the ambiguity of leading from the top of inner sequences. For example: lead of the Jack from KJ109.

Lavinthal Discards

1. A relatively low card shows a preference for the suit ranking immediately below the suit being discarded. For example: Clubs ask for Spades.
2. A relatively high card shows a preference for the suit ranking immediately above the suit being discarded. For example: Spades ask for Clubs.
Advantages:
1. Allows suggesting a shift to a given suit from two other suits.
2. Avoids wasting a high card in a suit you wish your partner to shift.
3. Reduces the possibility of false carding by declarer.

MUD Leads

MUD means Middle-Up-Down when leading from xxx and xxxx, with or without a useful honor card. MUD Leads do not apply to suits bid by your partner during the auction.

This method is a lead convention in which the original lead from three small cards is the middle one, followed by the higher card. This particular lead applies to all suits, but possibly more so if the suit of partner is a Major suit.

Reverse Signals or UDCA

The designation is an abbreviation of the actual action referenced by the card played: Upside Down Count and Attitude

1. A relatively low card encourages the continuation of a suit being led
2. A relatively high card discourages the continuation of a suit being led.
Advantages:
1. Avoids wasting a high card to signal positive attitude in a suit.
2. Reduces the possibility of false carding by declarer.

Roman Discards – Odd / Even

1. An odd discard encourages continuation of a suit being led.
2. An even discard discourages continuation of a suit being led.
3. A relatively high even-card suggests a shift to the higher-ranking suit other than the trump suit.
4. A relatively low even-card suggests a shift to the lower-ranking suit other than the trump suit.
Advantages: When wishing the continuation of a suit, but lacking an odd card to encourage, the attempt to give a preference signal would appear inconsistent.

Rusinow Leads or Journalist Leads

Lead the second higher-ranking honor from a sequence of two or more honors. Applies only against suit contracts in suits not declared by your partner during the auction. Leads other than the opening lead are standard.
Advantages: Reduces the ambiguity of leads from Ace-King or King-Queen.

Scanian Signals

Definition contributed by Mr. Stephen Tu. A defense signal mechanism devised by Mr. Anders Wirgren, and which uses standard or upside-down attitude signals depending on the situation, in an attempt to retain the advantages of each while not taking on the disadvantages.

Standard signals fail when a clear signal might waste a critical spot card. Upside-Down signals fail when a clear signal might block a suit. The basic principle of Scanian signals is to use Upside-Down signals when the dummy contains a card which can be finessed, or when it is presumed that the signaling player is long in the suit and declarer short, or when discarding. Standard signals are used otherwise. Several examples are illustrated below.

Hearts J742
Hearts AK105 Hearts Q83
Hearts 96
The object is to use normal signals unless the dummy contains a card, which can be finessed. Once the Ace or King is lead, East signals “upside-down” with the Hearts3. West will then lead the Hearts10.
Hearts AJ
Hearts 873 Hearts KQ104
Hearts 9652
Lead is the Hearts8, or top of nothing, and the dummy plays Hearts Ace. To signal encouragingly in third seat, the play of the Hearts4 is necessary.
Hearts 6
Hearts KQ954 Hearts A102
Hearts J873
The contract is No Trump and the lead is Hearts King. The Scanian signals in this example are standard and the Hearts10 is played, which simultaneously encourages and unblocks. If the upside-down carding were used, then either the suit would be blocked or the Hearts10 may be interpreted as discouraging.

Signaling with Touching Honors

Contributed by Cornelia Yoder.

Whenever you have two or more touching honors, they are equal in value, so either can be used to signal.
a. When you are winning the trick, play the lowest of touching honors.
b. When you are following to a trick that you cannot win, play the highest of touching honors.

The play of an honor when not winning the trick has special meaning.
a. It denies the card above it.
b. It shows the card below it (unless it is a singleton or clear unblocking play).

For example, holding the QJ10 and partner leads low:
a. If dummy wins the Ace, play the Queen, denying the King and showing the Jack.
b. If dummy plays low, play the 10, denying the 9.

Smith Echo Signal

A card signal, showing attitude, at the first opportunity by the partner of the opening leader against a No Trump contract indicating the attitude for the opening leader’s suit. This signaling feature is attributed to Mr. T. R. H. Lyons of England, although Mr. I. G. Smith of England suggested the same principle in the British Bridge World magazine in December 1963 issue.

 

Preference Signal

The preference signal is used to show a preference for one of the two suits outside the trump suit and the suit being led.
1. A relatively high card shows a preference for the higher-ranking suit outside the trump suit and the suit being led.
2. A relatively low card shows a preference for the lower-ranking suit outside the trump suit and the suit being led.

Precedence When Signaling

1. When following to a suit led by your partner:
A. Signal attitude with the first card.
B. Signal preference with the second card.
2. When following to a suit led by the declarer:
A. Signal count with the first card.
B. Signal preference with the second card.
3. When discarding in an suit not yet led:
A. Signal attitude with the first card.
B. Signal present count with the second card.
4. When discarding in a suit already led:
A. Signal present count.

Trump Suit Preference

This is a signal by the defenders employed when the declarer first plays the trump suit. If the player plays a high trump, then this signal shows interest in the higher-ranking non-trump suit. If the player plays a low trump, then this signal shows interest in the lower-ranking non-trump suit.

For example, if Diamonds constitute the trump suit, then when declarer plays the first trump card, then from a holding of 952 the play of the 9 is asking for a switch to the next higher-ranking non-trump suit, or Hearts. If the 2 is played, then this signal is requesting a switch to the next lower-ranking non-trump suit, or Clubs. In the case that the trump suit is Spades, then the next higher-ranking non-trump suit is Clubs and the next lower-ranking non-trump suit is Hearts.

Such a signal is not confined to the declarer playing the first card of the trump suit according to the publication Easy Guide to Defensive Signals by Mr. Julian Pottage. In this publication he states that the partnership is free to apply this trump suit preference signal when the player on lead also leads the trump suit. The conclusion is that the partnership must decide and mutually agree.

The development of the Gerber convention is accredited to Mr. John Gerber, born in the year 1906 in Houston, Texas, United States, and died January 28, 1981, who devised the method in 1938. This convention is sometimes referred to as the Four Clubs Blackwood. The concept and fundamental idea was devised independently by Dr. William Konigsberger and Mr. Wim Nye, both of Geneva, Switzerland, and was also published by them in Europe in 1936.

Note: As is often the case in providing historical information of the 1930s several sources maintain that Mr. John Gerber first published the concept, promoted the concept to the bridge community, and contributed immensely to its acceptance by the bridge community beginning in the year 1936, and it is for these reasons that the conventional method is named for him.

Definition of the Concept

The Gerber convention uses the bid of 4 Clubs to ask partner to communicate by a bid the number of held Aces, and subsequently how many Kings.

According to the concept, as soon as a suit or No Trump has been agree upon, preferably No Trump, the responder will bid 4 Clubs to ask for Aces. In No Trump auctions, it is almost always the responder who will ask for Aces and Kings, since the opener has conclusively limited his holdings. The Gerber convention was devised in order to ask for Aces and Kings one level lower than with the Blackwood convention. In this manner, the two partners can stop the auction, if it proves necessary, on a lower level.

Responses to a 4 Clubs Ace Ask

4 : Shows no Ace or 4 Aces
4 : Shows 1 Ace
4 : Shows 2 Aces
4 NT: Shows 3 Aces

Responses to a 5 Clubs King Ask

5 : Shows no King or 4 Kings
5 : Shows 1 King
5 : Shows 2 Kings
5 NT: Shows 3 Kings

The Gerber conventional method of inquiring about the number of held Aces and Kings is simplistic in form and execution. A partnership must deal individually with any competition from the opposing side.

Sliding Gerber or Rolling Gerber

Note: In the original concept of the Gerber convention, the auction was a little different. The original version is known as Rolling Gerber or Sliding Gerber. Some partnerships still apply this method.

The responses of the opener to a 4 Clubs bid by his partner, after agreeing that No Trump is the contract, and who is asking for Aces are:

4 : Shows no Ace.
4 : Shows 1 Ace.
4 : Shows 2 Aces.
4 NT: Shows 3 Aces.
5 : Shows 4 Aces.

The responses of the opener to a 4 Clubs bid by his partner, after agreeing that the contract is definitely a suit contract, and who is asking for the number of held Aces are:

Agreed trump suit is Hearts

Responder Opener Meaning
4 Gerber inquiry asking for the number of held Aces.
4 Shows 1 Ace.
4 King inquiry.

Responder asks for Kings by bidding the next higher ranking suit:

Responses
4 NT Shows no King.
5 Shows 1 King.
5 Shows 2 Kings.
5 Shows 3 Kings.
5 Shows 4 Kings.

Note: The responder may not bid the agreed Trump suit to ask for Kings. This action would signal a sign-off.

The Rolling Gerber, or Sliding Gerber, has proven to be ineffective in some auctions due to the ambiguity of the bidding, especially if the contract is Clubs. The difficulty in distinguishing between a conventional and a natural 4 Clubs bid in such cases caused many bridge players to adopt the more effective method mentioned above.

Another factor is the procedure with a void, and still another factor is an intervening call. The Rolling Gerber, or Sliding Gerber, did not provide for such instances.

Bridge partnerships have agreed to use the Gerber convention in suit contracts. The following two auctions should clarify this partnership agreement.

Opener Responder Meaning

1 3
4 The 4 Clubs bid by the opener is the Gerber convention.

Opener Responder Meaning
1 Promises opening values.
3 Limit Raise
3 Splinter bid showing a singleton or void in Spades.
4 The 4 Clubs bid by the opener is the Gerber convention.

Points of Consideration

It must be noted, however, that many bridge partnerships have decided that they are unwilling to surrender the 4 Clubs bid as a natural bid or as a cuebid. These bridge partnerships have decided to employ the Gerber convention only after a No Trump opening.

Using the Gerber convention after a 2 No Trump Opening can cause partnerships some amount of ambiguity. Using the Gerber convention after a 3 No Trump Opening can cause some partnerships several tactical difficulties. Even using the Gerber convention after a strong, artificial Two Club Opening with a Two or Three No Trump rebid could cause the partnership some troublesome disagreement.

The following example should illustrate these difficulties, and possible ambiguities.

It is evident that a possible slam in a Club contract is in the making, but the question pertains to the best possible method of ascertaining this goal. A bid by the responder of 3 Clubs is normally used as the Stayman convention, asking for a 4-card Major suit. Some partnerships have decided to use the immediate jump bid to 4 Clubs as the Gerber convention. Still other partnerships have agreed to use the 3 Clubs bid, followed by a 4 Clubs rebid as the Gerber convention. Whatever the partnership agreement may be, these partnerships have no way to bid Clubs naturally.

If the responder bids 4 Clubs, the opener will have some difficulty in deciding whether this bid is natural, or the introduction of the Gerber convention. Several partnerships have solved this problem by reserving the 4 Clubs bid by the responder as the Stayman convention, and a 4 Diamonds bid by the responder as the introduction of the Gerber convention.

The meaning of these two bids can, however, be reversed by other partnerships. It seems, however, more logical, in the view of many, to use the 4 Diamonds bid as the Stayman convention, reserving the 4 Clubs for the Gerber convention. There are also some partnerships who employ 4 Clubs as the Stayman convention, and 5 Clubs as the Gerber convention, thereby taking the opener one level higher than Mr. John Gerber intended.

Note: The bridge columnist for The New York Times published his bridge column on July 23, 1988, wrote about the Gerber convention being such a contribution to the game of bridge and to the bridge community in general, that the convention had to be invented in two places. This article has only been preserved and archived on this site in .pdf file format for future reference.

Note: The bridge columnist for The New York Times published his bridge column on January 29, 1981, and described how Mr. John Gerber employed unusual play techniques and strategy at the bridge table. This article has only been preserved and archived on this site in .pdf file format for future reference.

Note: The bridge columnist for The New York Times published the obituary on January 29, 1981, for Mr. John Gerber. This article has only been preserved and archived on this site in .pdf file format for future reference.

Delayed Canapé

This is a developing concept originating with Mr. Kenneth Rexford (aka Ken), of Lima, Ohio, United States, blogger, and Mr. Kenneth Eichenbaum (aka Ken), of Columbus, Ohio, United States. The source is archived information on his Internet blog called Cuebidding At Bridge. Mr. Keneth Rexford is the author of Cuebidding At Bridge, published in 2007 by Master Point Press, ISBN-10: 1897106173 / ISBN-13: 978-1897106174.

The first introduction of a possible concept designated perhaps improvisationally as delayed canapé occurs on the pages of the blog, more precisely in the presently archived section (link), operated by Mr. Kenneth Rexbord on Friday, June 11, 2010. The identical article appeared again on the blog at this link.

The fundamental concept behind delayed canapé is the fact that the player can show a particular and precise distribution by employing the concept of the canapé principle on the second rebid. The range of the values of the holding can also be more precisely inferred by what the player does not bid. The following three examples should illustrate the cornerstones and parameters of this concept, and which are conceptually expressed in the written cogitations, intellectual deliberations, and brain-storming sessions of Mr. Kenneth Rexford and Mr. Kenneth Eichenbaum.

Illustrative Examples

The necessity arose owing to those particular combinations of cards, by which there was no accurate rebid by the opener when agreeing to play the two-over-one approach. The following example illustrates the difficulty in finding the more correct contract by introducing the concept of the delayed canapé agreement.

Note: The generally accepted lower limit for a reverse bid is considered to be 16/17 points.

Note: The Impossible 2 Spades bid is employed only in this bidding sequence and only within these partnership parameters.

Note: The support rebid of 2 Diamonds can be interpreted by the partnership as showing minimum values or encouraging values. This rebid remains undefined.

Weak Jump Shift Response

During the evolution of the game of bridge the introduction and employment of the immediate Strong Jump Shift response by the responder, signifying a minimum of 15-16 high card points plus and a 6-card suit, became standard. This action was forcing and many bridge players and bridge authorities considered it forcing to game. However, it soon became evident that the frequency of such a holding held by the responder was very low and restricted the frequency of employing a Jump Shift first response.

It soon, in the evolution of the game of bridge, became evident that even a normal response had the same effect of being forcing, since any response by the responder continues to be forcing for one round. Therefore, another interpretation of the immediate Jump Shift response became a necessity and essential.

Instead of being strong, the immediate Jump Shift became weak, just the opposite of its original conception. It informed the partner, generally also the defenders, that the holding was weak in values. The holding could indeed have fewer than the generally required 5/6 points for a normal response. The length of the suit is limited to a minimum of 6 cards, but the suit may contain more than only six cards. The partnership agreement is that the weak jump shift first response is preemptive.

When the bridge player considers the frequency, with which the Weak Jump Shift may be employed, then it becomes obvious and logical that this definition is preferable. The bridge player can also calculate that the employment of a Weak Jump Shift can be employed twelve times only. When the partner bids 1 Club, then the responder has only three possibilities to make a Weak Jump Shift, which is also true by an opening of 1 Diamond, and 1 Heart, and 1 Spade.

With one response via the employment of a weak jump shift, the responder can adequately describe the holding and the minimum range of held values, namely zero points to about 5 high card points. However, many bridge players have not favored the Weak Jump Shift when the responder holds zero to a Queen, or two high card points. This becomes a matter of partnership agreement.

This jump shift by the responder also denies any support for the suit of partner.

The examples below should clarify this concept of the weak jump shift by responder. The bridge player should be aware of the fact that the Weak Jump Shift is preemptive in nature. If the opponents wish to enter the auction, then the opponents must do so on or above the level of the preemptive weak jump shift.

It is also the obligation and decision of the responder whether to compete if the immediate opponent, following the opening bid, also competes by bidding a suit. This bidding sequence creates a different situation, to which the responder must adapt and decide whether it would be more favorable to compete or to pass, awaiting any further and possible action by partner.

 

In the above example, South has very few values, insufficient to make even a 1 No Trump response. In the fortunate situation that East passes, South has the opportunity to employ a Weak Jump Shift of 3 Hearts. Although East and West may have the majority of the high card points, it will prove difficult for East and West to compete at the four level and perhaps find their fit in Clubs.

 

In the second example, South again has very few values, insufficient to make even a 1 No Trump response. In the fortunate situation that East passes, South has the opportunity to employ a Weak Jump Shift of 2 Hearts. East and West, if they wish to enter the auction, are forced to enter the bidding process on the two level or higher.

 

By this bidding sequence, whereby the immediate opponent enters the auction with 1 Diamond, then the effectiveness of the Weak Jump Shift still retains its preemptive nature. Compare with the following auction:

 

By this bidding sequence the immediate opponent, East, has removed the possibility of employing a Weak Jump Shift. If South still wishes to employ the Weak Jump Shift, then South must preempt on the three level. Depending on the vulnerability and other factors this may not be the most preferred action. South must make the decision as to whether to bid on the three level or to pass, awaiting any possible action by partner.

 

In the third example, the situation is the same. South again has very few values, insufficient to make even a 1 No Trump response. In the fortunate situation that East passes, South has the opportunity to employ a Weak Jump Shift of 2 Spades. East and West, if they wish to enter the auction, are forced to enter the bidding process on the three level.

The concept behind the Weak Jump Shift is to inform the partner immediately of the fact that there is no support for the suit bid or intended to bid, except the suit preempted by the responder, and that the values are not present for a normal response. The values for a Weak Jump Shift are normally less than the values required for a Weak Two opening, generally a King-Jack or less.

The auction does not necessarily cease once the responder has made a Weak Jump Shift in his suit. The opener may have more values and will continue to bid, requesting further and additional descriptive information from the responder. Any rebid by the opener is forcing for one round.

The general approach is explained below:

Rebids by the opener:

1. 2 No Trump is forcing and shows a 2-card support for the suit of the responder. The responder must bid three of his suit with minimum values.

2. A rebid on the three level by the opener of the suit preempted by his partner is also considered preemptive, which serves to continue to hinder the opponents from finding a fit.

3. Any new suit or rebid of the suit of the first bid suit by the opener is considered natural and non-forcing.

4. Any jump bid by the opener is considered to be natural and invitational, and in certain bidding sequences asking suit preference.

5. Any rebid on the four level by the opener of the suit preempt by his partner is invitational and considered competitive, mainly in tournaments, especially after an immediate overcall.

6. Any game bid is to play and is a sign-off.

This conventional defense method was devised and developed by Mr. Gerald W. Helms , also known Jerry Helms, of North Carolina, United States. The defense method is derived from the surnames of Mr. Jerry Helms and his bridge partner and co-contributor Mr. Bill Lohman. This defense method was developed as an improvement of the Cappelletti conventional defense method, of which Mr. Jerry Helms was a co-developer.

The concept can be employed in many different situations and auctions such as:

• Exclusion Bids: In the case that the responder of the No Trump bidder makes a call or bid, then this conventional method can enable the partner of the overcaller to take some action.
• Balancing: This concept is also available to the player in the fourth seat to either balance or respond to the action taken by partner after the opponents open the auction with No Trump.
• After Strong 1 Club and 2 Clubs Openings: This concept can also be applied in these situations when the opponents are employing a Strong 1 Club system or after a strong, artificial 2 Clubs opening.
• After NT Rebids by Opponents: This concept may also be employed after an opponent has rebid No Trump.
• After NT Overcalls by Opponent: When the partner opens the bidding and an opponent overcalls with No Trump, then the concept may also be employed.

Opponents Open 1 No Trump

After an opponent has opened the auction with 1 No Trump, then the Hello bidder can inform his partner about the shape and distribution and also about the values held, as shown in the following schematic:

• Double: This Hello double conveys to partner that similar No Trump values are held and that the double is natural and penalty-oriented or that the Hello doubler has a long, unspecified suit which could run against a final No Trump contract by the opponents.
• 2 : This is an artificial overcall and informs partner that the intervenor holds either a one-suiter in Diamonds, or a two-suited holding with a Major suit and a Minor suit, both unspecified.
• 2 : This is a transfer bid to Hearts. The values may be either strong or weak. If weak, then the suit should be at least a 6-card suit.
• 2 : Promises both Major suits. The strength can be either weak or intermediate. The guideline is that in direct seat both suits should be a 5-5 distribution and in the balancing seat a distribution of at least 5-4.
• 2 : Promises a long Spade suit. If weak, then the suit should be at least a 6-card suit. If strong, then a 5-card suit is acceptable.
• 2 NT: This is a transfer bid to Clubs.
• 3 : Promises both Minor suits.
• 3 : Promises both Major suits and generally 16 plus high card points.
• 3 : Preemptive in nature and promises a 7-card plus Heart suit. Weak in point count.
• 3 : Preemptive in nature and promises a 7-card plus Spade suit. Weak in point count.

Note: The concept presented on this web page is as Mr. Jerry Helms presents it originally. Emphasis is placed on the fact that the overcalls, rebids and responses should be decided depending on the state of vulnerability and that the bridge players should be aware of this fact at all times before making a call or bid.

Note: The concept of the Hello conventional defense method is somewhat dependent on the partnership agreement employed and can be altered or varied to meet the requirements of the particular partnership in values and strength as well as length.

Note: Some partnerships have agreed that the distribution of the holding, when overcalling could / may be reduced to 4-4 in both specified or unspecified suits regardless of the state of vulnerability. This is entirely a partnership agreement in all employed variations of the concept.

Responses

Partner: Responder

Double: The responder is required to bid or pass. If the responder passes, then the intention is to play for penalties and the responder should have about 7/8+ high card points. If the responder recognizes a chance at a possible game and/or partscore, resulting in a better score, then the responder should preferably bid, paying attention to the state of vulnerability. Whether systems are “on” or “off” is a matter of partnership agreement.

To complete the relay, the responder should bid 2, which is artificial. If the partner has Diamonds, then the partner may pass or raise to the next level. Otherwise the Hello bidder bids the Major suit on either the two or three level, depending on values. A jump to the three level is invitational.

Alternatively, the responder may pass the 2 only if the responder has a good Club suit with added length and is of the opinion that a play is possible even opposite a void in the hand of the Hello overcaller.

The responder generally accepts the Transfer bid to 2. Otherwise, if the responder has a good holding in Hearts, then the responder can “re-transfer” with 3 indicating invitational values and 4 with game values.

Holding good values the responder can also imply the “Heavy 2 NT” response indicating a possible game in Hearts. The Hello bidder can accept game and bid 4 or reject game and bid 3.

Alternatively, the responder may pass the 2 overcall only if the responder has a good Diamond suit with added length, no tolerance for Hearts, and is willing to play even opposite a Diamond void in the hand of the Hello overcaller.

Since this Hello overcall promises both Major suits, the responder can either pass with good Heart tolerance or bid Spades if the Spade is preferable. With equal tolerance in both Major suits and invitational values, the responder can employ the “Heavy 2 NT” bid and allow the Hello overcaller accept game by bidding 4 (Note: the responder can correct to 4) or reject game by bidding 3 (Note: the responder can correct to 3).

The responder can pass showing tolerance for Spades and weak values. The responder can also invite by raising one level. Any and all cuebids on the three level are forcing for one round and shows more than minimal values. Any first response on the four level is a Splinter bid showing a singleton and/or void and game values.

2NT: As a Transfer bid to Clubs, a non-jump bid of the Clubs suit shows weak values; a jump bid in the Clubs suit indicates an invitational holding with values; a game bid can show either game values or be preemptive in nature. Any bid other than Clubs after the Transfer bid promises an independent suit and is non-forcing.

Pass shows minimum values in Clubs and preferred Minor suit. A raise to 4 is invitational and 5 can show game values or be preemptive in nature. A response of 3 shows only preference, whereas a response of 4 is invitational and a 5 response can show game values or be preemptive in nature.

The general guideline is to make a preference response with a range of 0-6 points. With higher values the responder should bid game in one of the Major suits.

The responder should pass if also weak and little support or preempt on the four level with Heart length as support. Any cuebid of an unbid suit is game-forcing and the desire to double any suit, in which the opponents bid game other than the cuebid suit.

The responder should pass if also weak and little support or preempt on the four level with Spade length as support. Any cuebid of an unbid suit is game-forcing and the desire to double any suit, in which the opponents bid game other than the cuebid suit.

Hello Defense Method

When the partner of the No Trump bidder enters the auction after a Hello conventional bid has been made, the partnership requires a means of additional communication. This is illustrated below in the guidelines. Assume the following auction:

South West North East
1 NT 2 2// Double
Any double by East, the Advancer, communicates the information to West, the Hello bidder, of any suit bid by North, the partner of the No Trump bidder, is employed to initiate additional competition by promising a suitable fit and support for the shape of holding held by the Hello bidder. Therefore, the advancer should have at least a 3-card support in Diamonds, Hearts and Spades. This guideline is employed generally up to and including a 3 bid.

Further rebids are shown below with the corresponding meanings.

South West North East
1 NT 2 2// Double
Pass
As soon as the auction returns, in this sequence, to West or the Hello bidder, then the following guidelines are recommended:

• This rebid confirms a one-suited Diamond overcall.
• This rebid confirms Hearts and an unspecified Minor suit.
• This rebid confirms Spades and an unspecified Minor suit.
• Pass: A Pass confirms that the partner of the No Trump bidder has advanced with a bid of one of your suits.

In the following auction, the following guidelines are the general recommendations for the Advancer of the Hello bidder:

South West North East
1 NT 2 Double
Redouble: The Advancer, in this example East, should have at least a 3-card support in Diamonds, Hearts and Spades.
Pass: A pass indicates no support in the suits of the Hello bidder and shows a rather neutral holding.
New Suit: Any bid by the Advancer in a new suit promises an independent suit which also includes at least a 3-card Diamond support.

Balancing Seat

This concept is also available to the player in the fourth seat to either balance or respond to the action taken by partner after the opponents open the auction with No Trump. The concept behind this action is the reasoning that a penalty double in fourth seat asking for an inspired and/or unusual lead becomes a guessing game. An alternative is that the call of double forces the partner to bid: 2. The rebids of the Hello Doubler take on other meanings than those of the Hello Doubler in the immediate seat. The following auctions and guidelines illustrate this principle. Note the change of dealers in the two auctions. One is a passed hand.

South West North East
1 NT Pass Pass Double
Pass 2 Pass ?

West North East South
Pass 1 NT Pass Pass
Double Pass 2 Pass
?
Pass: The 2 overcall is natural and promises a semi-solid 5-card Club suit or a broken 6-card Club suit. Note: the Hello bidder must be aware of the distinction between a Pass and a “heavy” 2 NT overcall.
2 : This rebid promises Diamonds and an unspecified Major suit.
2 : This rebid implies at least a 4-card Heart suit but guarantees a 5-card plus Club suit.
2 : This rebid implies at least a 4-card Spade suit but guarantees a 5-card plus Club suit.
Other: Owing to the fact that most overcalls are able to show shape and length, any other overcall implies strongly a holding with less shape and/or values or playing defensive strength.
The suggested responses by the Advancer follow:

2 : A pass by the Advancer indicates a preference to Diamonds. To ask for the unspecified Major suit, the Advancer bids: 2. If this is the Major suit of the Hello bidder, then the Hello bidder could initiate an invitation and/or the Advancer could jump one level to show maximum values and shape.
2 : A pass by the Advancer indicates a preference to Hearts and minimum values. The Advancer bids 3 with Club support. The Advancer may also employ the “heavy” 2 No Trump response.
2 : A pass by the Advancer indicates a preference to Spades and minimum values. The Advancer bids 3 with Club support. The Advancer may also employ the “heavy” 2 No Trump response.
Other: Owing to the fact that most calls of the Advancer are able to show shape and length or preference, any other overcall implies strongly a holding with less shape and/or values or playing defensive strength.

Following Strong 1 Club and 2 Clubs Opening Bids

The Hello conventional method can also be employed after a Strong 1 Club and 2 Clubs openings. This concept can also be applied in these situations by employing the double as the original 2 bid after a No Trump opening. The student of this concept will recognize that the the responses remain the same as does the significance of the bid. Depending on the level of bidding the responses also remain the same.

This method requires a solid partnership understanding and an awareness of the situation, the action of the opponents, and the state of vulnerability in addition to any defense mechanism in the case the partner of the opener enters the auction to interrupt the line of communication.

Following No Trump Overcalls by an Opponent

The Hello conventional method can also be employed once the auction has been opened on the one level and the immediate opponent overcalls with No Trump as shown in the following example:

After South has opened the auction and an immediate No Trump overcall has been made, then the advancer, in this example North, has several options as outlined below. These guidelines may differ from those where the auction is opened with a Major suit. The student should be aware that the guidelines recommended may be the same for either a Minor suit or Major suit opening, but they may also differ according to the partnership understanding. Included are both.

Pass: A pass indicates a holding which is not capable of either doubling or making a bid. The holding is more destined to defend than compete. The maximum number of values should be 10 or less.
Double: A double promises 10 plus points and may be converted to Penalty.
2 : This is a relay to 2 and either shows Diamonds and Spades OR Spades and an unspecified Minor suit. A continuation to 2 may be followed by 2 No Trump by the opener to ask for the unspecified Minor suit and should be employed when holding no Spade tolerance.
2 : This bid is a transfer bid to Hearts.
2 : This bid promises both Major suits.
2 : This bid promises a longer Spade suit. It is natural and non-forcing. A jump to 3 is invitational.
3 : This jump bid promises both Minor suits. The state of vulnerability may be the deciding factor in the length required or recommended.

If the auction begins with an opening of a Major suit, specifically Hearts, then the partnership understanding may differ according to agreement. A differing set of guidelines has been suggested by Mr. Jerry Helms, which are listed below with the corresponding auction.

Pass: A pass indicates a holding which is not capable of either doubling or making a bid. The holding is more destined to defend than compete. The maximum number of values should be 10 or less.
Double: A double promises 10 plus points and may be converted to Penalty.
2 : This first response is a relay to Diamonds and promises a semi-solid 5-card Diamond suit; otherwise it should be a 6-card Diamond suit.
2 : This response is a limited Heart raise. Per partnership agreement, this may be a jump response to show additional values and excellent support for Hearts.
2 : This bid promises both Major suits. The holding should be at least a 3-card Heart suit and a 5-card plus Spade suit.
2 : This bid promises a 6-card or longer Spade suit. (Optional agreement)
2 NT: This is a relay to 3 and promises a 7-card semi-solid Club suit headed by Queen-Jack at least.
3 : This first response promises both Minor suits and should be 4-5 or 5-5 depending on the state of vulnerability.

Optional Treatments and Variations

If the auction begins with a specific opening of the Diamond suit, then the partnership understanding may differ according to agreement. The following meanings of the first response may / can differ according to individual partnership agreements. Mr. Jerry Helms has not addressed this possibility. For example, if the auction proceeds:

In this particular auction the first bids of the responder may take on other meanings as outlined below:

Pass: A pass indicates a holding which is not capable of either doubling or making a bid. The holding is more destined to defend than compete. The maximum number of values should be 10 or less.
Double: A double promises 10 plus points and may be converted to penalty.
2 : This first response promises Spades and an unspecified Minor suit. A rebid of 2 NT by the opener asks for the Minor suit.
2 : This first response is a transfer bid to Hearts. The length should be at least a 5-card plus Heart suit.
2 : This first response promises both Major suits and equal length or working values in both Major suits.
2 : This bid promises a 6-card or longer Spade suit. (Optional agreement)
2 NT: This is a relay to 3 and promises a 7-card semi-solid Club suit headed by Queen-Jack at least.
3 : This first response promises both Minor suits and should be 4-5 or 5-5 depending on the state of vulnerability.

If the auction begins with a specific opening of the Spade suit, then the partnership understanding may differ according to agreement. The following meanings of the first response may / can differ according to individual partnership agreements. Mr. Jerry Helms has not addressed this possibility. For example, if the auction proceeds:

In this particular auction the first bids of the responder may take on other meanings as outlined below:

Pass: A pass indicates a holding which is not capable of either doubling or making a bid. The holding is more destined to defend than compete. The maximum number of values should be 10 or less.
Double: A double promises 10 plus points and may be converted to Penalty.
2 : This first response is a relay to 2 and promises at least a semi-solid 5-card Diamond suit or a broken 6-card Diamond suit.
2 : This first response is a Transfer bid to Hearts. The length should be at least a 5-card plus Heart suit.
2 : This first response promises a one-level raise of Spades with corresponding support.
2 : This first response promises at least 3-card Spade support and at least a 5-card plus Heart suit.
2 NT: This is a relay to 3 and promises a 7-card semi-solid Club suit headed by Queen-Jack at least.
3 : This first response promises both Minor suits and should be 4-5 or 5-5 depending on the state of vulnerability.

Against Strong, Artificial 1 Club Openings

The concept of the Hello conventional method can be combined with the Mathe system of conventionally defined doubles as authored and developed by Mr. Lew Mathe. This combined conventional method is employed mainly against strong, artificial 1 Club openings by the opponents. A certain immediate disadvantage of the strong, artificial 1 Club opening is that the bid communicates a definitely held high card point range, but does not specify on the opening any suit or distribution. The guidelines are outlined below:

Pass: A pass indicates either no particular suit OR promises a strong balanced to semi-balanced holding. Whether this pass is regarded as a Forcing Pass is partnership agreement.
Double: Promises both Major suits. If weak, then the distribution must be 5-5, otherwise distribution can be 5-4 based on partnership agreement.
1 : This overcall is natural promising at least a 5-card plus Diamond suit and may be lead-directing.
1 : This overcall is natural promising at least a 5-card plus Heart suit and may be lead-directing.
1 : This overcall is natural promising at least a 5-card plus Spade suit and may be lead-directing.
2 : This overcall is a transfer bid to Diamonds and is preemptive / obstructive in nature.
2 : This overcall is a transfer bid to Hearts and is preemptive / obstructive in nature.
2 : This overcall promises both Major suits and at least a distribution of 5-5, which may depend on the state of vulnerability.
2 : This overcall promises the equivalent of a Weak Two bid in Spades.
2 NT: This overcall is a Transfer bid to Clubs and is preemptive / obstructive in nature.
3 : This overcall promises both Minor suits and at least a distribution of 5-5, which may depend on the state of vulnerability.

Against a Strong, Artificial 2 Clubs Opening

The concept of the Hello conventional method can also be employed after a strong, artificial 2 Clubs opening by the opponents. The guidelines are outlined below for an immediate overcall:

Double: This is a transfer bid to a long Diamond suit. The holding may not be two-suited in shape.
2 : This is a transfer bid to a long Heart suit. The holding may not be two-suited in shape.
2 : This promises both Major suits with at least a 5-5 distribution by all states of vulnerability.
2 : This bid is natural and promises a long Spade suit with corresponding trick-taking ability.
2 NT: This is a Transfer bid to Clubs and promises at least a semi-solid 5-card Club suit or otherwise a 6-card plus Club suit.
3 : Promises both Minor suits and should be 5-5 in shape.

The concept of the Hello conventional defense method can also be employed after a strong, artificial 2 Clubs opening by the opponents. The guidelines are outlined below for an fourth seat overcall:

Double: Promises both Major suits.
2 NT: Promises both Minor suits.
2 : This is a natural bid and promises a one-suited holding.
2 : This is a natural bid and promises a one-suited holding.
3 : This is a natural bid showing long Clubs and trick-taking values.
3 : This is a natural bid showing long Diamonds and trick-taking values.

Against a Strong 2 No Trump Opening

The concept of the Hello conventional method can also be employed after a strong 2 No Trump opening by the opponents. The overcaller may be sacrificing for a better score or may have a natural overcall with a strong one-suited, possibly two-suited holding with trick-taking capabilities. The following guidelines are outlined below:

Double: This is a transfer bid to a long Club suit.
3 : This is a transfer bid to a long Diamond suit.
3 : This is a Transfer bid to a long Heart suit.
3 : This overcall promises a two-suited holding in both Major suits. Possible void.
3 : This is a natural bid showing long Spades and trick-taking values.
3 NT: This overcall promises a two-suited holding in both Minor suits.

Since the official designation, which is Two No Trump Response Over Opponent’s Takeout Double, is too long, this convention has simply been called Truscott Two No Trump, Jordan Two No Trump and Dormer Two No Trump. This conventional method was devised by Mr. Alan Truscott and described by him in The Bridge World magazine, issue November 1954.

However, the second designation for this conventional method is named after Mr. Robert F. Jordan, of Cincinnati, Ohio, United States, who was foremost in bringing the conventional method to the bridge community mainly in the United States, which adopted the concept and where it became popular, and where the bridge community began calling the concept the Jordan Two No Trump.

Mr. Albert Dormer from England assisted in making the conventional method popular in England and Europe and, by the nature of things, became designated with his surname, thus Dormer Two No Trump.

A bidding example should show the meaning:

The 2 No Trump bid by North is completely artificial. The conventional method is employed once an opponent makes a Takeout Double after partner opens a Major suit. The 2 No Trump response shows a minimum of 4-card Heart support, 9/10-12 points.

Note: Some partnerships define this bid as having 1.5 defensive tricks outside the trump suit.

Note: In the original version the 2 No Trump bid by North after the intervening double shows a Limit Raise in the bid Major suit of the opener. The meaning of this response is that a 2 No Trump bid by the responder shows a 4-card support in the bid Major suit, and a point range, including distribution, of 9 to 11 support points.

Note: Some partnerships have the agreement to reduce the support length to a good 3-card suit.

Note: The Truscott / Jordan / Dormer conventional method can and may be employed in bidding sequences when the opener is in a position to rebid when the new suit of the partner is doubled by the third hand opponent, as in the following auction.

Examples

In order to make the Jordan Two No Trump convention clearer to the bridge player, the following examples serve to demonstrate the strategy behind it. They should illustrate the effectiveness of the convention in connection with other bids. Distinguishing between the different bids after an overcall or a double is essential in understanding the mechanism of this convention. The meaning given to each of the different possible bids is important to remember and essential in the partnership agreement.

In the bidding example:

North would normally have 10 support points or more, but North would also normally have only a 3-card support in Hearts. The redouble is generally considered to be a forcing action and demands partner to either bid and establish the final contract in Hearts or to double the contract of the opponents if the opponents declare. The disadvantage of this action would be that East has the opportunity to enter the auction on the one level, and once in the auction, it will be very difficult to prevent the opponents from exchanging vital information about their holdings.

In the bidding example:

Playing Limit Raises, it would be more advisable if North, having a 3-card support in Hearts, would jump to 3 Hearts, and this bid would show 10-12 support points. Not enough for game, but the bid makes it more difficult for East to arrive at a bid, and South has all the information he needs to make the right decision. If North were to respond with 3 No Trump, this would signify at least a 3-card support in Hearts, and a point range, including distribution, of 12 to 15 support points.

In the bidding example:

If the bridge player were to adopt the Jordan Two No Trump convention, then the above example would show a Preemptive Raise, a 4-card length in Hearts, and less than 9 Support Points.

North would have something like:

The use of the Preemptive Raise in accordance with the Jordan Two No Trump convention makes it more difficult for the opponents to compete, and that is essential in the auction. North and South, per their partnership agreement, will not bid too high, but make it very difficult for the opponents to enter the auction, and if doubled, the penalty will not be that great.

For clarification purposes, following is a short summary:

Note: Some partnerships have extended this convention to include the Minor Suits. Beware, however, that some partnerships, if the opening is in a Minor suit, have reversed the significance of the 2 No Trump bid and the Jump Raise.

Variation

Some partnerships have agreed to reverse the meanings of the following responses after the double, and this variation has become known as Flip Flop.

The partnerships playing in this manner maintain that the advantage lies in the fact that when the opener, who holds the stronger values, wishes to play in No Trump rather in a known suit contract, then the opener becomes the declarer and the lead is up to the stronger of the two holdings, which can result in an additional trick.

The concept is attributed to Mr. Mark David Feldman, a bidding player and bridge theorist. He was born in the year 1951 and is of New York City, New York, United States. He is also the originator of a defense methiod to a strong Club opening, devised in the year 1971 at the age of twenty years old known as SCREW.

This defense method later became more popularly known as CRASH. In the year 1975 he developed the treatment of a jump fo four of a Minor suit over an opposing Major suit Weak Two bid to show the bid Minor suit and the other Major suit.

This is a method whereby the player makes a jump to four of a Minor suit over an opposing Major suit Weak Two bid, and sometimes preempts on the three level, to show a two-suiter, generally a 5-5 distribution, in the suit bid and the unbid Major suit and/or one still unknown and unspecified Major suit, depending on whether the Weak Two bid and/or Preempt is a Minor or Major suit.

However, if the two suits are different in length, then the assumed longer suit is the Minor suit as in a 5-6 distribution. The so-called leap is not forcing so one would expect opening bid strength, but rather distributional features. Not to be confused with Super Michaels. As a defense against a preempt on the three level, the following example is offered from the Bermuda Bowl 2000 tournament.

East, Mr. Wilkosz, opens the auction with: 3 Clubs. Mrs. Sandy Low overcalls with: 4 Diamonds explained as showing at least a 5-card Diamond suit and an unspecified Major suit, also of 5-card length. Leaping Michaels. West passes and North raises to 6 Diamonds. The result was down one, but review showed that had Mrs. Sandy Low played for the singleton King of Diamonds, she would have taken all thirteen tricks.

Overcall Method Summary

The following is an outline of the possible overcalls and the definitions assigned to each overcall.

Opener Overcaller Meaning

•  2 4 Leaping Michaels: promises Spades and Hearts.
• 2 4 Leaping Michaels: promises Spades and Diamonds.
• 2 4 Leaping Michaels: promises Clubs and Hearts (the other Major suit)
• 3 4 Leaping Michaels: promises Spades and Hearts.
• 3 4 Leaping Michaels: promises Spades and Hearts.

Cuebids which are not Leaping Michaels:

• 1 3 Western Cuebid, asking partner to bid 3 No Trump with a Heart stopper (Note: the bid is not Leaping Michaels at the 3 level).
  2
• 3 Western Cuebid, asking partner to bid 3 No Trump with a Heart stopper (Note: the bid is not Leaping Michaels at the 3 level).
• 2 3 This overcall is a takeout of the Major suits. The overcall is not a game-forcing action and does not promise a two-suited holding.

The basics of the Goren Bidding System includes opening the longest suit first. Other features is opening the lower of 4-4 in the Minor suits, jumping to 2 No Trump or 3 of the opening suit, if the point count is 13 to 15 support points. The No Trump range is between 16 and 18 high card points, and all 2 Diamonds/Hearts/Spades opening are strong.

Mr. Charles Goren devised a Point Count Table to be used when opening, responding, and rebidding. The charts below present his Point Count Tables.

Ace: 4 points
King: 3 points
Queen: 2 points
Jack: 1 point

Added Points

All 4 Aces: add 1 point
Ace and King: 2 points
Ace and Queen: 1.5 points
King and Queen: 1 point
King and x: .5 points

Distributional Points are counted as follows:

For any opening bid:

Void: 3 points
Singleton: 2 points
Doubleton: 1 point
If the partner is able to raise the opening of his partner:

Void: 5 points
Singleton: 3 points
Doubleton: 1 point

The concept behind the Point Count is expanded by adding the Distributional Points to the Point Count of the responder when a fit has been determined, and the result is then added to the actual point count of the total honors. The thought behind this calculation is to increase or promote each honor in the bid suit of the partner by 1 point, unless the honors already exceed 4 points. On the other hand, 1 point is deducted from the total distributional values, if the holding only contains a 3-card support, and/or the complete distribution is 4-3-3-3.

Certain requirements are advised when opening one of a suit.

1. All holdings containing 14 high card points must be opened.
2. Any holding with 13 high card points may be opened, but there must be a reasonable, logical rebid available.
3. All openings are required to have 2 Quick Tricks.
4. Any 1 No Trump opening must contain between 16 and 18 high card points and must have a balanced distribution.
5. An opening in Third Seat is permitted, if the hand contains 11 high card points and the holding contains a good suit.

Certain requirements are advised when opening two of a suit. As the high card point range diminishes, the quality of the suit increases.

1. All holdings containing 14 high card points must be opened.
2. The opener must have 23 high card points and a good 6-card suit.
3. The opener must have 21 high card points and a good 7-card suit.

In his original book, Goren’s Bridge Complete, the Goren Opening Bids are shown below:

• 1 : 13-22 high card points Shows 3+ Clubs.
• 1 : 13-22 high card points Shows 4+ Diamonds.
• 1 : 13-22 high card points Shows 4+ Hearts.
• 1 : 13-22 high card points Shows 4+ Spades.
• 1 NT: 16-18 high card points Shows balanced shape.
• 2 : 23+ high card points Shows 5+ Clubs.
• 2 : 23+ high card points Shows 5+ Diamonds.
• 2 : 23+ high card points Shows 5+ Hearts.
• 2 : 23+ high card points Shows 5+ Spades.
• 2NT: 22-24 high card points Shows balanced shape.

Revised Opening Bids

This early version shows that the opening of a 4-card Major suit was allowed. The later, revised edition of the book Goren’s New Bridge Complete in 1985 showed a preference for opening a 5-card Major suit and allowed for an Minor suit opening of a 3-card suit. The point range for a 2 No Trump range was also revised. These revised opening bids are shown below.

• 1 : 13-22 high card points Shows 3+ Clubs.
• 1 : 13-22 high card points Shows 3+ Diamonds.
• 1 : 13-22 high card points Shows 5+ Hearts.
• 1 : 13-22 high card points Shows 5+ Spades.
• 1 NT: 16-18 high card points Shows balanced shape.
• 2 : 23+ high card points Shows any shape.
• 2 : 6-12 high card points Shows 6+ Diamonds.
• 2 : 6-12 high card points Shows 6+ Hearts.
• 2 : 6-12 high card points Shows 6+ Spades.
• 2NT: 21-22 high card points Shows balanced shape.

Certain circumstances are understood, if one partner decides to open with a preemptive bid on the Three Level. The partner should not open any suit on the three level with a holding containing 10 high card points or more. The partner, after a preemptive opening, should not raise the suit of the partner unless he holds at least 3 or 4 certain Quick Tricks.

If the opponents open the auction with a bid suit first, then a Takeout Double requires that the doubler must possess a holding which would normally be an opening, which signifies 13 high card points or more. If the Takeout Double is over a 1 No Trump opening, then the doubler is required to hold at least 10 high card points.

If the right hand opponent responds to the opening of his partner, then the responder of the Takeout Doubler is not required to bid. If the right hand opponent passes, then the responder of the Takeout Doubler is required to respond. According to the Goren Bidding System, the responder may then bid once with 0 to 6 high card points, the responder may rebid again with 9 high card points, and the responder may jump bid with 11 to 12 high card points.

As a defense against the Takeout Double, the responder to the opener should pass with less than 5 high card points, bid with any values between 6 and 9 high card points, and redouble when holding 10 high card points or more.

After the auction has officially been opened, any overcall must contain at least 10 high card points if the overcall is on the one level. On the two level, the overcaller must have 12 high card points or more and a good suit. To overcall with 1 No Trump, the point range must be between 16 and 18 high card points and the distribution must be balanced.

Note: In the Goren Bidding System, the responses are defined and should be adhered to as much as possible in order to communicate definite information to the partner.

If the partner opens with one of a suit, the responder will respond according to the following chart, if there is no immediate fit. The responses are based on a balanced distribution, not on a non-balanced distribution.

• 1 No Trump: 6-10 high card points
• 2 No Trump: 13-15 high card points
• 3 No Trump: 16-18 high card points

If the responder is holding any support for the suit bid by his partner, then the responses should follow the guidelines established below. These responses are based on the fact that the responder has an unbalanced distribution and can respond after an immediate fit.

Raise 1 Level: with 7-10 high card points
Raise 2 Levels: with 13-16 high card points
Jump to 4 Level: with 9 high card points or less and 5-card support
Jump Shift: with 19 high card points or more
If no immediate fit is discovered, then the following chart shows the possible responses.

Show a new suit at the 1 Level: with 6 high card points plus
Show a new suit at the 2 Level: with 10 high card points plus
Make 2 progressive bids
without forcing to game: with 11-12 high card points

Strong 2 Clubs / 2 Diamonds / 2 Spades

If the partner opens a strong 2 Clubs / Diamonds / Hearts / Spades, then the responder should communicate his holding to the partner in the following manner, by bidding:

• 2 No Trump: with 6 high card points or less
• Positive Response: with 7 high card points and 1 Quick Trick
• Positive Response: with 8 high card points and 0.5 Quick Tricks

1 No Trump Opening

An opening of 1 No Trump promises 16 to 18 high card points and a balanced distribution. The responder has several options to communicate to his partner a description of his holding by bidding the following, which would strongly indicate an unbalanced distribution.

• Bid 2 Clubs with 8 high card points or more and a 4-card Major suit.
• Bid 2 Diamonds, 2 Hearts or 2 Spades with less than 8 high card points and a 5-card suit.
• Bid 3 of any suit with 10 high card points and a good suit.
• Bid 4 of a long Major suit and less than 10 high card points.

An opening of 1 No Trump promises 16 to 18 high card points and a balanced distribution. The responder has several options to communicate to his partner a description of his holding by bidding the following, which would strongly indicate a balanced distribution.

• 2 No Trump: with 7 high card points and a 5-card suit.
• 2 No Trump: with 8-9 high card points.
• 3 No Trump: with 10-14 high card points.
• 4 No Trump: with 15-16 high card points.
• 6 No Trump: with 17-18 high card points.
• 7 No Trump: with 21 high card points.

2 No Trump Opening

If the opener opens the auction with 2 No Trump, promising 21 to 22 high card points, a balanced distribution, and all four suits protected, then the responder has the following options with a balanced distribution:

• 3 No Trump: with 4-8 high card points
• 4 No Trump: with 10 high card points
• 6 No Trump: with 11-12 high card points
• 7 No Trump: with 15 high card points

If the opener opens the auction with 2 No Trump, promising 21 to 22 high card points, a balanced distribution, and all four suits protected, then the responder has the following options with an unbalanced distribution:

• Responder bids a 5-card Major suit with 1 top honor and 4 high card points,
• Responder bids a 6-card suit except Clubs,
• Responder bids 3 Clubs with 4 high card points and a 4-card Major suit,

These are a few of the basics of the Goren Bidding System, but for a complete analysis of this bidding system, it is strongly recommended that the bridge players purchase the book Goren’s New Bridge Complete. This book covers all of the principles and features of this bidding system including:

• Opening Bids in a Suit
• Responses to Suit Openings
• No Trump Openings
• Rebids by Opener
• Rebids by Responder
• Four-Card Major suit Openings
• Slam Bidding
• Preemptive Openings
• Overcalls
• Takeout Doubles
• Penalty Doubles
• Weak No Trump Openings
• Drury Convention
• Landy Convention
• Texas Convention
• Flint Convention
• Flannery 2 Diamond Openings
• Splinter Bids
• The Blue Team Club
• The Neopolitan Club
• The Roman Club
• Schenken 1 Club
• Precision 1 Club
• Defensive Play
• Signals on Defense
• Deception
• Squeezes
• End Plays

Exclusion Keycard Blackwood is a continuation and extenuation of the Roman Key Card Blackwood convention. The concept behind this convention is to show a void while exploring for the possibility of a slam. The bidding process is quite easy to learn and will assist in reaching, through the exchange of information, the correct contract.

Many contributions to bridge theory were made by Mr. Robert Eugene Goldman, aka Bobby born November 10, 1938 and died May 15, 1999, and the idea behind Exclusion Keycard Blackwood is attributed to him. The Bridge World, issue May 1981 Volume 52, Number 8, has an article about the Exclusion Keycard Blackwood convention, written by Mr. Ron Gerard.

Note: The convention of Exclusion Keycard Blackwood is also referred to as Voidwood.

Note: The photograph of Mr. Robert (Bobby) Goldman is from the year 1982.

Basic Concept

In Exclusion Keycard Blackwood there are only four Keycards. The Ace of the void suit is not counted. Therefore, only the other 3 Aces and the King of the trump suit count as the four Keycards. This conventional method is initiated:

1. After establishing the trump suit.
2. By a jump bid higher than game level in an unbid suit or
3. In a suit bid by the opponents.

The suit of the jump bid is then excluded by partner from any response bids. The responses to the Keycard Asking bid is accomplished in the following manner:

1st Step: Shows 0 Keycards.
2nd Step: Shows 1 Keycard.
3rd Step: Shows 2 Keycards.
4th Step: Shows 3 Keycards.

The bidding process:

Opener Responder

It is agreed that Spades is the trump suit. Normally, the opener, who is looking for a possible slam contract, will generally employ the Roman Key Card Blackwood convention to discover the number of Key Cards held by the responder. However, the opener has a void, which makes the hand much more valuable. Exclusion Keycard Blackwood is a conventional method, which will assist the opener in showing his partner that he holds a void and in which suit the void is.

Opener Responder Meaning

5 Exclusion Keycard Blackwood – void in Clubs.
5 Exclusion Keycard Blackwood – void in Diamonds.
5 Exclusion Keycard Blackwood – void in Hearts.

By jumping to the five level, the opener is communicating to his partner that he has interest in a slam contract and that he has a void in the bid suit. The responder, realizing the location of the void, responds to the Exclusion Keycard Blackwood convention by counting his Key Cards except the Key Card in the suit, in which the opener is void.

The bid on the five level by the opener is treated the same as had the opener bid 4 No Trump, employing normal Roman Key Card Blackwood. Therefore, the responder would bid according to the following, showing his Key Cards.

Void in Clubs

5 Exclusion Keycard Blackwood – shows a void in Clubs.
5 Responder has 0 Key Cards – 1st Step.
5 Responder has 1 Key Card – 2nd Step.
5 Responder has 2 Key Cards – 3rd Step.
5 NT Responder has 3 Key Cards – 4th Step.

Void in Diamonds

5 Exclusion Keycard Blackwood – shows a void in Diamonds
5 Responder has 0 Key Cards – 1st Step.
5 Responder has 1 Key Card – 2nd Step.
5 NT Responder has 2 Key Cards – 3rd Step.
6 Responder has 3 Key Cards – 4th Step.

Void in Hearts

5 Exclusion Keycard Blackwood – shows a void in Hearts
5 Responder has 0 Key Cards – 1st Step.
5 NT Responder has 1 Key Card – 2nd Step.
6 Responder has 2 Key Cards – 3rd Step.
6 Responder has 3 Key Card – 4th Step.

In all bidding auctions, it is important to remember that the promised void suit Key Card is not counted as a Key Card when responding.

In all responses presented above it is necessary for the bridge student to notice that the Queen of the trump suit is not included in any of the responses. In order to discover whether or not the Queen of trump is held, any relay bid following the response bid, excluding the trump suit, is asking for the Queen of the trump suit.

Note: However, if one partner has to make a higher bid than the agreed trump suit on the five level, a repeat of the void suit becomes then the Queen-Asking bid.

Note: A 5 No Trump bid is never employed as a Queen-Asking Bid.

Competition

If the opponents, for any reason, decide to enter the auction once the Exclusion Keycard Blackwood conventional method has been initiated, then the partnership has two additional bids / calls at its disposal to exchange information. They are as follows:

Pass: Shows 0 Keycards.
Double: Shows 1 Keycard.
1st Step: Shows 2 Keycards.
2nd Step: If this response does not bypass the established trump suit, then this response shows 2 Keycards and the Queen of the trump suit.

One example of how this conventional method can be employed follows with the corresponding explanations:

• 1 A natural opening bid.
• 1 As always, a new suit is one-round forcing.
• 2 Shows limited support. Trump suit is established.
• 5 Exclusion Keycard Blackwood showing a void in Diamonds and asking for Keycards.
• 5NT 3rd Step showing two Keycards. The Diamond suit is not counted, so therefore the two Keycards, by inference, must be the King of Spades and the Ace of Clubs.
• 6 Remember, if one partner has to make a higher bid than the agreed trump suit on the five level, a repeat of the void suit becomes then the Queen-Asking bid.
• 6 Shows / promises the Queen of Spades.
• 7 Since there are no losers in trump, no losers in Hearts, no losers in the Diamond suit owing to the void, and partner has the Ace of Clubs, East bids the grand slam in Spades.