User:Dhirendra Narayan
New concept of counting the points and bidding in the Game of Bridge
by Dhirendra Narayan,Bangalore ,India.
1.0 Introduction
In the game of Bridge, the bid of the partners plays a vital role in making the contract. Bids are made on the basis of the points in a hand as well as,the suit and distribution of the cards and hence counting of points in the hand is equally important.Sometimes it is seen that both the partners were having sufficient points for making the contract but they could not make the same, as distribution of cards in their hands were not good enough to make the contract.Many efforts have been made for evolving a method for bidding system in the game of Bridge but non of them is accurate.The effort for counting of points in a hand has also been made but that too is not projecting the real strength of the hand . In earlier counting system the points of honour cards,points of void card , shortage points,distribution points etc were counted but the counting was not properly done, due to which sometimes the bid could not be made properly and the contract could not be made.In many cases, the total points in the hands of both the partners and the number of tricks taken, does not match and can not be explained on the basis of earlier counting system. It was felt necessary to evolve a method for bidding,which should be accurate and simple.Here, an effort has been made to project the strength of the hands in a better way.The contract is made on the basis of the strength of the cards of the bidding partner and the dummy partner(supporting partner) and hence, it is necessary to know the strength of the cards of each other partener's hand.The strength of the cards is communicated in form of points and hence counting of points should be such that it projects the strength of the cards accurately.Seeing the importance of counting of points in a hand ,we will first discuss the method of counting of points in a hand. 2.0 Method of counting of points in a hand
2.1 Counting the points of honour cards
A variety of honour card valuation methods have been used during the past century.The most common and popular HCP valuation for the past half century has been the Work–Goren scale of 4-3-2–1.It is simple but some what inaccurate because A and K are under valued while Q and J are over valued.Work – Goren scale has been followed here . The values of A,K,Q,J has been taken care of latter.
Table I
Sl.No Cards in hand Points to be considered
1 Ace 4 2 King 3 3 Queen 2 4 Jack 1 5 10 0
The points of honour cards is said to be High Card Points (HCP)
2.2 Counting the points of short suit in a hand
A suit having 3 or less number of cards will be treated as short suit. Short suit sometimes helps in making the tricks and some times losing the tricks and hence counting the points of short suits is very essential.
2.2.1 Counting the points of void & singleton card suit
If in a hand void (no card in a suit) is available, 2 points is added in the total points of that hand provided the bid for trump is not for that particular void( no card of the suit) or the call is not No Trump.Earlier practice was to consider 3 points for void but here 2 points have been considered.
If in a hand singleton card (one card in a suit ) is available , 1 point is added in the total points of that hand provided the bid for trump is not for that particular singleton suit or the bid is not No Trump, but if that one card is King,Queen, Jack , no point is added for that King,Queen, Jack. If that one card is an Ace , the points for that Ace will be added in addition to 1 point for singleton card . Earlier practice was to consider 2 points for singleton card but here 1 point has been considered.
The above explanation is tabulated below :-
Table- II
Sl Cards in Points to Remarks No a hand to be added 1 void 2 Provided the bid for trump is not for that void or the bid is
not No Trump.
2 Singleton card 1 Provided the bid for trump is not for that singleton card suit
or the bid is not No Trump.Point of Ace only is added
and points of other honour cards not added.
3 Doubleton cards 0
2.2.2 Counting the points of doubleton card suit
Two cards in a suit normally reduces the strength of the hand because they do not take tricks as per their HCP, except AK, as well as they do not allow to ruff the opponent’s tricks. Earlier practice was to consider 1 point for doubleton card but here 0 point has been considered.If honour card is available in a two card suit , it also reduces the HCP of the hand indirectly except Ace, King combination.
Table- III
Placed below is the points to be counted in a two card suit if not bid for trump :-
Sl. Cards in Points to Remarks No in a hand be added 1 AK 1 If in a hand, two card suit is available, the same will be available
in one of the form indicated in the left side of this column. The
point indicated against each form is counted in addition to the
point of honour cards, if available in the suit. In case two cards
suit is bid for trump ,no subtraction of point for the suit is
done, however point of AK if available is added.X is except A,K,Q,J
2 AQ ( - ) 1 3 AJ ( - ) 1 4 AX 0 5 KQ ( - ) 1 6 KJ ( - ) 1 7 KX 0 8 QJ ( - ) 1 9 QX ( - ) 1 10 JX ( - ) 1 11 XX 0
2.2.3 Counting the points of a three card suit
A suit having three cards helps in making the hand strong, if honour cards are placed properly. below is the points to be counted in a three card suit :-
Table- I V
Sl Cards in Points to Remarks No a hand to be added 1 AKQ 2 If in a hand, three card suit is available, the same will
be available in one of the form indicated in the left side
of this column. The point indicated against each form is
counted in addition to the point of honour cards, if
available in the suit. In case three card suit is bid for
trump ,no subtraction of point for the suit is done, however
addition of points if any is done.X is except A,K,Q,J
2 AKJ 1 3 AKX 1 4 AQJ 1 5 AQX 1 6 kQJ 1 7 KQX 1 8 AJX 0 9 AXX 0 10 KJX 0 11 KXX 0 12 QJX 0 13 QXX 0 14 JXX ( - )2 15 XXX ( - )2
2.3 Method of counting the points of trump cards
Sometimes, it is seen that, even if, more than desired points were available, but the contract could not be made due to shortage of the strength and the number of trump cards and hence proper weightage must be given to the trump cards.
2.3.1 counting the points of trump cards in the hand of the partner who bids the trump first.
Placed below is the method for counting the points of trump cards in the hands of the partner who bids the trump first.
TABLE - V
Sl Number of Trump cards Number of cards Points to be Remarks No with the partner who out of A,K,Q,J added /subtracted
bids the trump first
1 4 Trump cards 1 or no Substract 8 points Points for the combination
of AKQJ if any, indicated in
Table III Table IV & Table VI
is also added in addition to
the points indicated in the left
column
2 4 Trump cards 2 Substract 4 points 3 4 Trump cards 3 Substract 2 points 5 5 Trump cards Add zero points 6 6 Trump cards Add 2 point 7 7 Trump cards Add 4 points 8 8Trump cards Add 6 points
Note :-In case 5 or more trumps are available in the hand A K Q J is not seen as in case of 4
numbers of trump cards
TABLE – VI
Sl No Combination of cards Points to be added 1 AKQJ 2 2 AKQX 2 3 AKJX 2 4 KQJX 2 5 AQJX 2 6 AKXX 1 7 AQXX 1 8 AJXX 0 9 KQXX 1 10 KJXX 0 11 AXXX 0 12 KXXX 0 13 QJXX 0 14 QXXX 0 15 JXXX (-)2 16 XXXX (-)2 Note :- Two points is subtracted for the Suit having three or more number of cards not having single card out of A K Q J.
2.3.2 counting the points of trump cards in the hand of the partner who supports the trump.
Placed below is the method for counting the points of trump cards, in the hand of the partner who supports the trump :-
Table – VII
Sl Number of Trump cards Points to be Remarks No in the hand of the added/subtracted
partner who supports the trump
1 0 Trump card Subtract 6 points Points for the combination of AKQJ if any,
indicated in Table III Table IV & Table
VI is also added in addition to the
points indicated in the left column
2 1 Trump card Subtract 4 points 3 2 Trump cards Subtract 2 points 4 3 Trump cards Add zero point 5 4 Trump cards Add 2 points 6 5 Trump cards Add 4 points 7 6 Trump cards Add 6 points 8 7 Trump cards Add 8 points
2.4 Method of counting the points of a long suit in a hand
The suit of cards not bid as a trump , also plays an important role in making a contract. Similarly in No Trump bid, suit of cards again plays an important role in making a contract and hence proper weightage must be given to such suits.No extra point is added for the length of the suit . The points for the combination indicated in table III IV&VI, if available in the suit, is counted. The above explanations can be summerised as follows :-
For counting total points of a hand,the points for the following suits and trumps must be counted :- 1. HCP 2. Points for Void cards, if any. 3. Singleton cards, if any. 4. Points for the suit indicated in Table III, IV & VI,if any. 5. Points for trump cards.
3.0 New concept of Bidding for the contract
From the above methods, total points (High Card Points + Other points) in a hand is counted and then bidding for a contract is started.
3.1 Opening Bid :- Among the partners who is having 13 points or more starts bidding. As
narrated earlier the strength of the cards, which is projected by the points in a hand,is
the key factor in making the contract and hence in the first round of bidding, the points
in hands are exposed.
TABLE - IX
The bidding is done as under:-
Sl Total points in the hand Bidding to be done No 1 Less than 13 points Pass 2 Between 13 to 17 points 1 Club or one step above the opponent’s bid 3 Between 18 to 22 points 1 Diamond or two steps above the opponent’s bid 4 Between 23 to 27 points 1 Heart or three steps above the opponent’s bid 5 28 points and above 1 Spade or four steps above the opponent’s bid
3.2 Bid by supporting partner :-
The bidding by supporting partner is done as under:-
TABLE – X
Sl Total points in the hand Bidding to be done No 1 Less than 6 points One step higher than the bid of the Declarer or one step higher
to the bid of the defender.
2 Between 6 to 9 points Two steps higher than the bid of the Declarer or two steps
higher to the bid of the defender.
3 Between 10 to 13 points Three steps higher than the bid of the Declarer or three steps
higher to the bid of the defender.
4 Between 14 to 17 points Four steps higher than the bid of the Declarer or four steps
higher to the bid of the defender.
5 18 and above points Five steps higher than the bid of the Declarer or five steps
higher to the bid of the defender.
After first round of bidding,both partners would know the total points possesed by both of them and accordingly they will decide how many tricks can be made.After first round of bidding both the partners will decide the trump .During decision of trump the total points are revised and a final decision is taken ,as to how many tricks can be made with the revised points. Placed below is probable points required for number of tricks:-
TABLE – XI
Sl Total points Probable Number Probable number No with both of tricks could of tricks could
the partners be made in bid of trump be made in bid of No Trump
1 14 points and above 7 6 2 17 points and above 8 7 3 20 points and above 9 8 4 23 points and above 10 9 5 27 points and above 11 10 6 32 points and above 12 12 7 35 points and above 13 13
For making 12 tricks, at least 3 nos of Aces, 3 nos of kings should be available in both the partner’s hand. Similarly for making 13 tricks 4 nos of Aces, at least 3 nos of Kings and desired points should be available in both the partner’s hand.In case of No Trump bid, suitable checks in all the suits is necessary, otherwise number of tricks made would not match the points indicated in Table XI. It may be seen from the above that for taking 12 or more tricks, it is necessary to know the number of Aces, Kings available with both the partners.For knowing the same the Declarer or the Dummy partner, after finalising the trump,bids 4 clubs.Bidding of 4 clubs means ,the partner wants to know the number of Aces in the hands of the other partner .
The other partner will bid as below:-
TABLE – XII
Bid of 4 clubs for knowing the number of Aces and reply there of :-
Sl.No No of Aces available Bid to be made 1 No Ace 4 Diamonds 2 1 Ace 4 Hearts 3 2 Aces 4 Spades 4 3 Aces 4 No Trumps
If due to some reason 4 clubs is not possible to bid for knowing the number of Aces the bidding can be started with 4 No Trump.
Similarly for knowing the number of Kings , one of the partner will bid 5 clubs and the other partner will bid as below:-
TABLE – XIII
Sl.No No of Kings available Bid to be made 1 No King 5 Diamonds 2 1 King 5 Hearts 3 2 Kings 5 Spades 4 3 Kings 5 No Trumps
Similarly for knowing the number of Queens , one of the partner will bid 6 clubs and the other partner will bid as below:-
TABLE –IVX
Sl.No No of Queens available Bid to be made Remarks 1 No Queen 6 Diamonds The number of Queens can be asked only if, the
trump to be called is No Trump
2 1 Queen 6 Hearts 3 2 Queens 6 Spades 4 3 Queens 6 No Trumps
After knowing the strength of the cards of both the partners, a contract tricks and trump is bid. If the bidding has been done properly , the probablity of making the contract becomes very high.
Placed below are some typical hands to establish the above facts. Please note the symbols used:-
Table XIV
Sl.No Symbols Elaboration 1 A Ace 2 K King 3 Q Queen 4 J Jack 5 N North 6 S South 7 E East 8 W West 9 C Club/Clubs 10 D Diamond/ Diamonds 11 H Heart/Hearts 12 S Spade/Spads 13 NT No Trump 14 HCP High Cards Points 15 P Pass 16 T Table
Hand – 1 ♣ 10 4 2 ♦ J 2 ♥ J 10 7 5 2
♠ 6 4 2
N
♣ 6 3 ♣ A 9 8 7 ♦ Q 7 3 ♦ 9 6 5 4 W E ♥ K 4 3 ♥ 8 ♠ K J 9 8 3 ♠ A Q 7 5 S
♣ K Q J 5 ♦ A K 10 8 ♥ A Q 9 6 ♠ 10
Above is a card distribution for the game of bridge. North and South are partners. First of all the points in the hands of North and South is counted as below :- South HCP 19 Points Singleton Spade ,Table II – 2 1 AK 10 8 of Diamond , Table VI – 6 1 KQJ5 of club Table VI – 4 2 AQ96 of Hearts Table VI - 7 1 TOTAL 24 North HCP 2 J 2 of Diamond , Table III – 10 (-)1 For 10 4 2 of clubs , Table IV – 15 (-)2 For 6 4 2 of clubs , Table IV – 15 (-)2 TOTAL (-)3 points
( Points in negative is treated as Zero)
Now the bidding is started by South
South North 1 Heart , Showing 23 to 27 points 1 Spade , Showing less than 6 points ( T IX – 4) ( T X – 1) 1 NT Showing no suit 2 Hearts Showing suit in Hearts 4 Hearts Pass
Explanation of the above bidding :- Total points with South was 24 and so he bid 1Heart . In reply North was having(-)3 points,so he bid 1 Spade ( Less than 6 points , one step higher than the declarer). From the bidding South and North could know that they were having sufficient points to go ahead.Now South bid No Trump as he was not having 5 card suit. In reply North bid Hearts as trump.After revision of points by South , 2 points were added for 4 nos of Hearts (Table VII – 5) . His total points of the hand became 26 points which was enough for making 10 tricks and hence he bid 4 hearts ignoring the points of his partner. After completion of bid, the play started. East led by Ace of club and then by Ace of Spade . He then played 5 of spade which was ruffed by South by 6 of Heart. South then played Ace and 9 of Heart. West took 9 of Heart by king of Heart collecting total of 3 tricks. Rest of the tricks were of North and South.
Comments about the above game
South was having 19 High Card Points and North was having 2.South was not having any good suit. In the above situation, it was very difficult to think of taking 10 tricks When South added his points for the strength of the cards as per Table VI, his points became 24 and when he further added 2 points for 4 numbers of trump , his total points in hand became 26.It may be seen from the hand of South , that he was having 19 points as HCP, which was not projecting the actual strength of the hand. The actual strength of the hand of South was of 26 points, instead of 19 points, as shown by HCP. When the points were exposed , North could know that South was having 23 to 27 points and hence North decided to support his partner,though he was having ( - ) 3 point.This is the advantage of the proposed system of counting of points and the concept of bidding narrated in previous pages. Hand - 2
♣ K Q 9 6 ♦ Q 5 4 2 ♥ Q 10 4 2 ♠ A
N ♣ A 8 2 ♣ Void ♦ A K J ♦ 9 8 W E ♥ 6 ♥ A 9 8 5 3 ♠ 10 9 6 5 4 3 ♠ K Q J 8 7 2
S
♣ J 10 7 5 4 3
♦ 10 7 6 3 ♥ K J 7 ♠ Void
West counted his points as below :- HCP 12 Singleton Heart, Table II – 2 1 AKJ of Diamond Table IV – 2 1 TOTAL 14
East counted his points as below :-
HCP 10
Void in club Table II – 1 2
KQJ8 of Spade Table VI – 4 2
6 nos of Spades( East ‘s intention was to project Spade 2
As trump) TOTAL 16
West North East South 1 C ( T IX -1) 1 NT 2 S ( T X - 4) P 2 NT P 3S P 4C P 4H P 5C P 5H P Small Slam in Spades P P P
Explanation of the above bidding :-
Total points with West was 14 and hence 1C was bid(13 to17 points).In reply East bid 2S,4 steps above 1 NT (bid by East) showing 14 to 17 points(Table X - 4). West was not having any strong suit,so 2 NT was bid.East was having strong suit in spade,so he bid 3 spades. On getting suitable trump, West revised his points and added 6 points for six number of Spades (To be finalised as trump, Table VII - 7).Now total points of West became 14 + 6 = 20 points. Adding 15 points ( Average of 13 to 17) of the declarer, the total points with both partners became 20 + 15 = 35 points ,which was suitable for Slam bid.For knowing the number of Aces, Kings, West bid 4 C&5C.After getting the reply from the partner ,West could Know that one Ace and 2 Kings were with the defenders. Seing the singleton card in Heart, 35 points in hands and 11 number of trumps ( West considered 5 number of Spades with East), he bid small slam in Spades.
After completion of the bid, the play was started. South led 3 of clubs which was taken by West with Ace of Club. S3 was played by West Which was taken by North by Ace of Spade.Afterwords all the tricks were taken by East – West making the contract.
Comments about the above game
It may be seen from above that East was having 10 points as HPC and West was having 12 points as HPC but the actual strength of the cards were not projected by HPC only. When the points were counted properly, the strength of hands could be known and total points of both hands became 36 points which was suitable for small slam and small slam was made. This is a good example of evaluating the strength of hands and taking advantage of making the contract at its optimum.
Hand - 3
♣ Q J 7 5 ♦ K 9 ♥ K J ♠ K 9 5 4 2
N ♣ 6 4 2 ♣ 9 8 3 ♦ Q ♦ A 7 2 W E ♥ 9 6 5 4 ♥ A Q 10 8 7 3 ♠ J 10 7 6 3 ♠ Q
S
♣ A K 10
D J 10 8 6 5 4 3 ♥ 2 ♠ A 8
North counted his points as below :-
HCP 13 KJ of hearts (-) 1
TOTAL 12
South counted his points as below :-
HCP 12 Singleton Heart 1 AK 10 of club 1
TOTAL 14
Now bidding started as follows :- West North East South P P ( 12 points T IX 1) P 1 C ( T IX 2) P 1 S(12 points T X 3) P 2 D P 3 D P 5 D P P P Explanation of the above bidding :-
Total points with South was 14 and hence 1C was bid (13 to17 points).In reply North bid 1S ,3 steps above showing 10 to 13 points(Table X – 3 ). South then bid his longest suit in Diamond ( 2 D) .On getting suitable trump, North revised his points and substracted 2 points for 2 number of Diamonds (To be finalised as trump, Table VII – 3).Now total points with North became 10,which is suitable for bidding further and hence he bid 3 D. On getting his partners support ,South also revised his points and added 4 points for 7 numbers of Diamonds to be made as trump. His points became 18.Expecting 10 points (As per the bid by North showing 10 to 13 points ) and 18 points in his hand , totalling 18 +10 = 28 points South bid 5 D ( Table XI -5 ). It may be seen from above that East and West took the tricks of H A and D A and rest of the tricks ( 11 Tricks ) were taken by South and North,making the contract.
Chapter – II
1. Low Point Bidding
1.1 Low point to one of the partner
Many times , it is seen that one partner is having sufficient points but the other partner is having low points .In this situation both the partners get limited scope of exposing the strength of their hands.Besides the opponant partners are also having point and they would also like to bid.When such situation arises , the partner,who is having sufficient points will count his points and expose the strength of his cards as per Table IX. The other partner,who is having low points would calculate the points of both hands and would see whether total points of both hands were sufficient for making at least 8 tricks or not.If the points are sufficient for taking 8 tricks , he will expose his points to his partner otherwise would pass. In the next round of bidding trump is to be decided and final bid is to be made.
Here is a hand which will make the bidding clear. Hand - 4
♣ A 7 5 ♦ A 9 ♥ A K 10 8 5
♠ Q 6 2
N ♣ K 10 8 4 ♣ J 6 ♦ Q J 8 2 ♦ K 7 3 W E ♥ Q J 6 2 ♥ 4 3 ♠ K ♠ J 10 9 8 4 3
S
♣ Q 9 3 2
♦ 10 6 5 4 ♥ 9 7 ♠ A 7 5
North counted his points as below :- HCP 17 AK10 of Hearts 1
TOTAL 18
South counted his point as below :- HCP 6 10 6 5 4 of Diamond (-)2
TOTAL 4
Now bidding has been done as follows :-
West North East South
P 1 D ( T IX – 3) P 1 H( T X – 1) P 2 H P P P
Explanation of bidding :-
North was having 18 points and hence he bid 1D as per table IX, showing the partner 18 to 22 points. In reply South bid 1 H showing the partner less than 6 points.North could know that total points with both partners may be around 18 + 5 =23, so he bid his trump Heart.South revised his points after bid of trump and found that he is having only 2 trumps and hence further 2 points were to be subtracted and practically only 2 points remained with him.South counted 18 + 2 = 20 points minimum available points with them,which was sufficient for making 8 tricks and hence he passed.
North – South made 3 tricks in Hearts, 2 tricks each in Spade and club, 1 trick in Diamond.
1.2 Low points to both partners
If in the first round of bidding both the partners passes,it means non of them is having 13 points. They may be having maximum 12 points each i.e 24 points.In second round of bidding if one of the partner is having 9 or more points and a good suit of trump , he will directly bid trump.Now the other partner will count the points in his hand considering the trump proposed by his partner and if points permit him to take tricks, he will bid for highest tricks or as per the requirement of the situation.If the trump proposed does not suit and total points of both hands, permits ,he may offer his trump to the partner. The partner then, will finalise,the trump. Hand - 5
♣ A K 10 9 ♦ 6 4 2 ♥ J 9 8 6 3 ♠ A
N ♣ 4 3 ♣ Q J 8 7 6 ♦ 10 7 ♦ K J 5 W E ♥ A Q 10 7 ♥ 5 4 ♠ K J 10 4 3 ♠ Q 9 7
S
♣ 5 2
♦ A Q 9 8 3 ♥ K 2 ♠ 8 6 5 2 West counted his points as below :- HCP 10 For AQ 10 7 of Hearts 1
TOTAL 11
East counted his points as below :- HCP 9
TOTAL 9
Now bidding started as follows :-
West North East South 1C P 1H P 2H P P 2 S P p P
North was having 13 points and hence 1 C bid was given . East was not having 13 points ,so he passed.South bid 1H showing 6 to 9 points. West passed as he was also not having 13 points.Then North bid his longest suit heart which did not suit to South and hence passed.West was having 11 points with a suit in Spade,so he bid 2S. East counted minimum 9 points with west and 9 points of his hand , totalling minimum 18 points.As per Table XI 2,17 points are required for making 8 tricks,.East could know that 8 tricks can safely be made and hence he passed.
North and South took 2 tricks in clubs 1 trick in Diamond and 1 trick in Spade . They could not take trick for H K as H4 was played by E which was taken by W with H Q and then H A was played West passed his hearts in East’s clubs. This way East and West took 9 tricks and made the contract with one over trick.
You may kindly post your valuable comments and suggestions to my mail ID dnarayan4448@gmail.com. Dhirendra narayan