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Losing trick Count
The negative double
Five-Card Majors
Roman Key Card Blackwood
Bridge for Beginners
Quantitative Bidding


Losing Trick Count

This was a bidding system devised by an American writer, Dudly Courtenay. Its principal feature was a method of hand valuation based on a count of losers.
To assess the value of his hand in support of his partner's suit call (with less than 11 points), responder first counts his losers. Then he applies the “rule of eighteen".

Counting losers

There is a maximum of three losers in each suit, each missing top card (A, K, D) counting as one loser (except Qxx = 3 losers | but Qxxx = 2 losers). Losers in short suits are counted only up to the number of worthless cards held. Thus, in the following hand there are nine losers in support of spades *:
QJxx xxx KJxx xx
There are three losers in hearts and two losers in each of the other suits, nine losers in all.

Rule of Eighteen

The rule is: “Ascertain the total number of losers held by the partnership and deduct that total from eighteen. The answer gives the number of odd tricks that should be made.”
It is assumed that a sound minimum opening bid contains seven losers. Thus, if South held the hand given above and heard North opening one spade, South would add his partner’s assumed seven losers to his own nine losers. He would deduct the total from eighteen and the answer, two, would give the number of odd tricks (on top of 6) that should be made in a spade contract. South, therefore, would raise to two spades.


The negative double

This convention is especially useful over a minor suit opening bid by partner which is overcalled by opponent's major suit, but may be used over any opening bid/overcall sequence. A double by you shows:

1)    9 plus hcps, with likely interest in two suits other than the opening bid suit
2)    It is forcing for 1 round and alertable
3)    It is for take-out but may be left in for penalties
4)    It denies 4 card support for an opening major suit bid.
5)    It applies even up to an overcall of 2 spades by opponents.

Responses by partner:

1)    Bid a new suit, or no-trumps with 2 guards in the opponent's suit
2)    A new suit may occasionally be 3 cards
3)    Rebid the opening suit (shows 6 if a major or a very good 5 card suit headed by 2 honours; 5 or more if a minor)

Five-Card Majors bidding (source: Wikipedia)

The concept

Typically, when a bridge player makes a natural bid in a major suit (hearts or spades), he is promising at least four cards in that suit and asking partner if it will be an advantageous trump suit for the partnership. Because of the power of naming a trump suit with an eight-card fit, the responder with four or more cards of that suit will support his partners bid as if to say "we have found our eight-card fit."

If the opening bid promises five cards in the suit rather than just four, and responder holds three-card support, the 5-3 fit will be found immediately, rather than after opener's rebid. A 5-4 fit will also be found immediately, although a 4-4 fit will be found only after partner's first response. Since finding major suit fits is a high priority, making opening bids of 1 and 1 promise five cards rather than four is attractive.

Key advantages and disadvantages

Five-card major systems have the following advantages compared to four-card majors:

  • 5-3 fits are found immediately, rather than after opener's rebid.
  • If opponents overcall, responder knows definitely if there is a 5-3 major fit.
  • If responder holds four-card support, he knows at once that there is a nine-card fit rather than just eight cards. This can be helpful in slam bidding or competitive bidding.

However, they have the following disadvantages compared to four-card majors (particularly where, in hands with a four-card major and a four-card minor, the major is opened):

  • 4-4 major fits are not found immediately, though they will normally be found after responder's first bid.
  • If opponents overcall, a 4-4 major fit could be lost. Negative doubles are essential to combat this.
  • 4-4 major fits and some notrump contracts are more likely to be played "wrong-sided", by responder. This can be partly overcome by using Transfer Walsh responses over 1.
  • Opening bids in a minor suit will sometimes need to be on less than four cards.

Additional considerations

With 13 cards in each suit, an eight-card fit implies that only five trump cards can be held by the opponents. They will most likely be distributed 3-2 or 2-3 among the opponents, so playing trump for three rounds will probably draw all trump cards from the opponents and leave two additional trump to be used separately for offensive purposes. However, if the trump cards break 4-1 or 1-4, then drawing trump will result in no trumps left for offensive purposes.

The value of five-card majors can be understood then on two levels:

  • When partnerships have a 5-3 distribution in a major suit, the eight-card fit is easier for the player with the three cards to find. The strong preference to play duplicate bridge in the major suits at the game level makes the five-card major convention very attractive.
  • When the trump suit can be declared with a 5-3 fit, then often one extra trick can be taken due to the extra trump card in declarer's hand because
    • if the opponent's five trump cards are distributed 3-2 or 2-3, then declarer will have two remaining trump cards to use in continuing play.
    • if the opponent's five trump cards are distributed 4-1 or 1-4, then declarer can pull trump for four rounds and still have one trump card in declarer's hand for continuing play.

But five-card majors have several drawbacks:

  • Immediate 5-3 fits occur less frequently than immediate 4-4 fits (16.3% of the time versus 11.8%)[3] reducing the probability of auctions such as 1 – 3
  • Since playing 5-3 fits needs (at least) three turns to establish so there is often no trick gained by ruff in the short hand, while 4-4 fits can lend themselves to cross-ruff. In the 5-3 case, the two remaining established cards (assuming the opponents cards are 3-2 or 2-3) can also bring tricks in no trumps, if there is an entry to the hand which owns these cards.
  • Immediate discovering of 5-4 fits is possible on one way with five-card majors, and on two ways with four-card majors.
  • Hands with four-card majors and no five-card major are opened by one of a minor suit, which is less informative and more easily preempted by opponents than a four-card major opening.

To play five-card majors

Both partners must agree to follow the five-card major bidding treatment on their opening bid. Opener must have at least five cards in hearts or spades to start the bidding with that suit. Responder is expected to show support with three-card support, indicating an eight-card fit. With only four cards in a major suit, the opening bidder is expected to open one of a minor suit (which may show less than four cards in that suit) or 1NT if in the agreed points range. After the opening bid, the five-card limitation is no longer in effect and any other bid typically promises only four cards as before.

Bridge partnerships who use five-card majors need some kind of short club [4] opening bid. The most common practice is for 1 to promise at least a three-card club suit, indicating that opener has:

  • at least 13 points and interest in winning the contract,
  • no five-card major (else opener would have bid it, unless also holding a six-card or longer minor),
  • no four-card diamond suit (else opener would have bid 1).

In this case, a 1 bid may also be on three cards, to cope with a 4-4-3-2 shape. This method is used in Standard American bidding. The alternative is for 1 to promise at least four cards, in which case the 1 opening may have to be made on a two-card suit.

There is strong pressure upon responder to bid a four-card major even after an intervening bid, or to show it indirectly by a negative double. In some methods, 1 – (1NT) – 2 as first response may promise only four hearts. Opening bidder will not raise the 2 bid with only three hearts.

  • Most bidding systems use five-card majors in conjunction with a strong no-trump. However, it is also possible to play it with a weak no-trump, as practiced by some club and tournament players in the United Kingdom.

Roman Key Card Blackwood

Roman Key Card Blackwood (Key Card, RKC, RKCB, 0314, 1430) is a variation of the Blackwood convention. It is used when the partnership has agreed to a trump suit and is interested in slam. A 4NT bid asks partner how many "key cards" he holds. A key card is any ace or the trump suit king.

There are two versions of RKC: 0314 and 1430 ("Fourteen-Thirty"). We'll explain here only the 1430 version which refer to the step responses below.

Responses to 4NT

Playing 1430:

5 Shows 1 or 4 key cards.
5 Shows 0 or 3 key cards.
5 Shows 2 or 5 key cards without the trump queen.
5 Shows 2 or 5 key cards with the trump queen.

The 4NT bidder can usually (!) determine if responder has 0/3, 1/4, or 2/5 key car

Asking for the Trump Queen

The 5 or 5 replies don't indicate whether responder holds the queen of trumps. The 4NT bidder can bid the cheapest non-trump suit to ask this question. The responses to the queen-ask are:

Bidding the trump suit  

No trump queen


The trump queen without any side-suit kings

Bidding any non-trump suit  

The trump queen AND the king of that suit

"One of the beauties of using Roman Key Card Blackwood instead of regular Blackwood is that it allows the 4NT bidder to ask partner whether he holds the queen of the agreed suit, as well as for other goodies. (Ed. note: See 'Asking for the Trump Queen', above.) To do this economically the asker needs room. The optimal response to 4NT, therefore, is 5 (as opposed to 5 allowing a follow-up bid of 5 to become the queen-ask.

"Playing 1430 the 5 response shows one or four. It doesn't take a rocket scientist to work out that it shows '1'. Now if the asker wishes to ask for the queen, 5 is available. This lower step is especially important when hearts is the agreed suit. Now the queen-ask can be made beneath the five level of the agreed suit.

There are more conventions related to the Roman Key Card Blackwood system but they are out of the frame of this lesson. (see

Bridge for beginners

Remember, a balanced hand contains no void, no singleton, and at most one doubleton.

With a balanced hand of:-
12-14 points, open 1NT
20-22 points, open 2NT
15-19 points, open one of your longest suit, then rebid NT at the appropriate level

With an unbalanced hand, the most frequent opening is one of your longest suit.
If you open with 10 points you need a 6-card suit.
If you open with 11 points you need a 5-card suit
With more points, even very strong (18-19 points, say) open one of longest suit.

Special hands
23 + points, balanced, or to make a game force (shape important), bid 2C
With 8 playing tricks (your long suit being trumps), bid 2 of suit.
With less than 10 points and a 7-card suit, bid 3 of that suit - this is pre-emptive with the intention of silencing the opposition.
Guide For a game in NT you need a combined strength of 25-26 points.
For a game in a trump suit, about 24-26 points is usual, but shape is crucial.


Partner opens 1NT
With balanced hands, Pass or bid NT at the appropriate level:-
With 0-10 points - Pass
With 11-12 points - Bid 2NT (invitational)
With 13-15 points - Bid 3NT (game, sign-off)
With unbalanced hands, - more later!

Partner opens 1 of a suit
With 4-cards (or more) in partner’s trump suit, show support:
With 6- 8 points, raise to 2 of partner’s suit
With 9-12 points, raise to 3 of partner’s suit (limit bid)
With 13-15 points, raise to game (4 major, 5 minor)
(Later on, you will learn to use more advanced sequences, but initially, it reassures
partner that you have agreed to play in that trump suit.)
With a balanced hand, bid 1NT at the appropriate level:-­
With 6- 9 points hid 1NT (limit bid)
With 11-12 points bid 2NT (limit bid)
With 13-15 points bid 3NT (game)

If your hand is unbalanced, use the following responses:
1. You need 6 points to respond at the one level. (e.g. 1C-1D or 1H-1S or 1D-1S)
This shows at least a 4-card suit. Always show a 4-card major rather than NT.
2. You need 9 points to respond at the two level without jumping (e.g. 1S-2C or 1D-2C) The alternative is to bid 1NT so partner doesn’t over-value you.
3. You need 16 points to jump in a new suit e.g. 1C-2H or 1H-2S. It is forcing.

Some important points to bear in mind:
1. Bids may be:
Forcing - you must bid again to keep the bidding open
Invitational - partner would like you to bid again if you have anything worthwhile to communicate. Sign-Off - “This is all I have to say partner.” (See 2 below.)
2. Partner opens 1NT. You have poor point count and an unbalanced hand. Bid two of your longest suit to tell partner to pass and let you play in this ‘cheap’ contract. This is a weak take out.
3. Every opening bid of a suit guarantees a rebid (unlike NT). If partner responds in a different suit, it is forcing and opener must bid again .

Quantitative Bidding (Wikipedia)

In natural bidding systems most notrump (NT) bids are made with balanced hands and within a narrowly defined high card point (HCP) range. In these systems, such as Acol and Standard American, NT bids are limit bids and therefore are not forcing. Bearing in mind the need to bid only to the optimum contract and no higher, bids above game are made only in specific circumstances, one of which is to alert partner to the fact that a slam may be possible and inviting partner to take part in the decision making process.

Before looking at the detail, it is necessary to understand that bridge theory and practice suggest that the HCP method of hand evaluation, together with common sense concerning balance and cover in all suits, is the best for deciding the level of NT contracts, thus:

25+ HCP is sufficient for a game 3NT

33+ HCP should yield 12 tricks

37+ HCP will probably produce a grand slam

Assuming a weak NT bidding system, for example Acol, this is how quantitative bids work:

An opening bid of 1NT shows 12, 13 or 14 HCP.

If responder has 21 HCP, then a small slam looks certain (21 + 12 opener's minimum = 33) and should be bid.

If responder has 18 HCP or less, then even a small slam is not possible (18 + 14 opener's maximum = no more than 32)

If responder has 19 or 20 HCP, then a small slam is a possibility but more information is needed about opener's hand before it should be bid. This is where a quantitative bid should be made:

A bid of 4NT "invites" opener to bid 6NT with a maximum holding of 14 HCP (19 + 14 = 33 which is sufficient)

to pass with a minimum 12 HCP (20+ 12 = only 32)

with partnership agreement, to bid 5NT holding 13 HCP - asking partner to bid 6NT with 20 HCP and to pass holding 19 HCP.

An opening bid of 2NT shows 20, 21 or 22 HCP.

If responder has 13 HCP, then a small slam looks certain (13 + 20 opener's minimum = 33) and should be bid

If responder has 11 or 12 HCP, then a small slam is a possibility but more information is needed about opener's hand before it should be bid. This is where a quantitative bid should be made:

a bid of 4NT "invites" opener to bid 6NT with a maximum holding of 22 HCP (11 + 22 = 33 which is sufficient)

to pass with a minimum 12 HCP (12+ 20 = only 32)

with partnership agreement, to bid 5NT holding 21 HCP - asking partner to bid 6NT with 12 HCP and to pass holding 11 HCP.

When responder is even stronger and is considering whether a small or grand slam is better (and only these two options), then the initiating bid is 5NT (not 4NT)

Similar bids can be made using a strong no trump bidding system, for example Standard American, by adjusting the HCP count accordingly