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