BIDDING SYSTEM OBJECTIVES
Of course, the main objective in a competitive bridge hand is to get the best score possible – bridge is a duplicate card game, and all partnership will have the same cards in N-S and E-W. So, we need to understand how the scoring table works. First all you must look for the board you are going to play to know if it is Vulnerable (Vul) and not Vulnerable (nVul) because there are different scoring tables for each one, and this makes significant difference in the bidding decision - depending on Vulnerability.

The points scored by each trick isn’t not counted for the first 6 tricks and subsequent tricks have the following values: 20 for minor contract; 30 for major contract; and for NT contract the 7^th trick has value of 40 and the additional have value of 30 points.

During the auction the final contract could be in:
- part-score (contract that scores less than 100 points) it is a contract in: 1♣ 1♦ 1♥ 1♠ 1NT 2♣ 2♦ 2♥ 2♠ 2NT 3♣ 3♦ 3♥ 3♠ 4♣ 4♦, then exist a bonus of 50 points in addition to tricks points if the contract is made – overtricks are additional tricks made but not include to score the necessary 100+ points to receive the game bonus;

- game (need scores 100 points 40+2x30 or 4x30 or 5x20): and if the contract is made in 3NT 4♥ 4♠ 4NT 5♣ 5♦ 5♥ 5♠ exist a substituted bonus of 300 points nVul or 500 points Vul in addition to tricks points;

- small slam (12 tricks) have additional bonus of 500 points nVul and 750 points Vul in addition to tricks points and game bonus;

- grand slam (13 tricks) have additional bonus of 1000 points nVul and 1500 points Vul in addition to tricks points and game bonus.

contract in major after six tricks: each trick additional equal 30 points
contract in minor after six tricks: each trick additional equal 20 points
contract in NT after six tricks: the first trick equal 40 points and subsequent 30 points
Example1: 3NT Vul made plus one = 40 + (3x30) + 500 = 630 points
Example2: 2♥ made 2 = (2x30) + 50 = 110 points
Example3: 4♠ nVul made 6 = (30x6) + 300 = 480 points
Example4: 5♣ nVul made 5 = (20x5) + 300 = 400 points
Example5: 6NT Vul made 6 = 40 + (5x30) + 500 + 750 = 1440 points
Example6: 7♦ nVul made 7 = (20x7) + 300 + 1000 = 1440 points

Link for ACBL scoring table here

Another important point to decide what is better to do is understand the bridge modality we are playing. There are 3 different main bridge modalities:

1- Tournament that uses Match Point (MP) scoring where each board played computes a score for each partnership and these scores at the final are added in terms of relative percentage. Suppose a board where NS had the following results: 480 450 420 200 170 140. Now the top relative will score 5 (100%) and the worst result will score zero (0%).

Thus, we have the top relative score 5 to the partnership that scores 480 points; 4 to the partnership that scores 450 points; 3 to the partnership that scores 420 points; 2 for the partnership that scores 200 points; 1 for the partnership that scores 170 points and zero to the partnership that scores only 140 points. To convert points in % we divided the partnership score by the top relative score possible or 5/5 = 1 => 100%; 4/5= 0,8 => 80%; 3/5= 0.6 => 60%; 2/5= 0,4 => 40%; 1/5= 0,2 => 20% and 0/5= 0 => 0%. 

Of course, the tournament will have two winning partnerships, one in NS and another in EW and the EW score, in terms of percentage, is the complement to 100%. This means, for each hand played, if NS has 40% in a specific hand, then EW will have 60% in this specific hand.
When there are some hands with same score like: 450, 420, 420, 420, 140, -50 then NS with 450 will receive maximum or 5 that is 100%; NS with -50 (or 50 to EW) worst score will receive 0%; the NS scores 420-420-420 will receive same score (4+3+2)/3= 3 so each one will have 3/5 = 0,6 => 60% and 110 will receive 1/5 = 0,2 => 20%.

2- Team events (match) uses scoring in International Match Points (IMP’s), that is a secondary table score (0–24) for the difference in points in each board – see table below:
  points   IMPs     points      IMPs      points      IMPs
..20-40     1       370-420        9     1500-1740   17
..50-80     2       430-490      10     1750-1990   18
..90-120   3       500-490      11     2000-2240   19
130-160   4       600-740      12     2250-2490   20
170-210   5       750-890      13     2500-2990   21
220-260   6       900-1090    14     3000-3490   22  
270-310   7     1100-1290    15     3500-3990   23
320-360   8     1300-1490    16     4000 or +     24

Playing IMPs if in “open-table” N-S bids 3♠ and make 3♠ + 1 overtrick this is 3x30 + 50 + 30 = 170 and if in “close-table” N-S bids 4♠ and make it the contract Vul then score 120 + 500 = 520. At the end this specific board the team that bid and make 4♠ gain a score difference of 620 – 170 = 450. Now looking at IMPs table, we see 450 (range 430 – 490) produces a score of 10 IMPs. So, in this board the team that bid and make 4♠ have a gain of 10 IMPs and after 20 boards the same process of IMPs score comparation occurs to determine what team have the victory.
Note: after 10 boards played in open-table these boards are changed by the boards played in the close-table. So, both teams played with same cards, because N-S in open-table is team-A and N-S is close-table is team B.   

3- Rubber Bridge is not duplicate cards. It is a social/home bridge with 4 or 5 players reversing partnership in the same table after 2 games made by same partnership. So, it is the best of three games and if your partnership win 2 games and opponent zero, then your partnership win a bonus of 700 point, but if the opponent partnership make a game and your partnership win 2 x 1, then the bonus is only 500.
Of course, Rubber Bridge it is also played in Bridge Clubs and normally by money, where each 100 points has a price fixed in dollars.
Rubber Bridge is not our focus here because our focus is the Bidding System and their conventions and Rubber Bridge usually use a simpler and more traditional bridge bidding system with poor conventions.

4- To read more about types of bridge go to here.

There are different approaches between MP and IMPs:

- Playing MP if you can make a part-score in 3♣ or 3♦ where you have a fit with partner to score 110 points but also may try 2NT to score 120 points with a little more risk many expert players will prefer the 2NT contract; or if you have a fit in a minor that will score 110 but also good 5-card major like AKJ9x where you can also score 110 points with some risk or even 140 points if cards divide normally then you may prefer the risk contract to try a better score.

- Playing IMPs, you should always prefer the part-score contract to play more safely. But if the decision is between to stop in a part-score of 3♥/3♠ or bid a game Vul in 4♥/4♠ where you estimate your chances in 50%, then probability shows that you should try the game because after many boards played you will have more profit due to the high bonus that you may gain versus the loss you may have if go down.

In fact, you will have an advantage of 2 IMPs per board if you declare a game Vul with chances to make around 50%. At the limit you will have advantage in declarer a game Vul if your chances are above 37,5% and a game nVul if your chances are above 45,5%.

The declaration of a small slam needs more than 50% of chances but the declaration of grand slam, due to large losses if down 1, you should try only with odds above 70% (Terence Reese opinion) or better only if you can count 13 tricks (Edward Kaplan opinion).

Of course, a good Bidding System provide conventions to search the hand and this allow you understand what are your chances. We explain here the Eddie Kantar (1932-2022) schema for search possibilities for bid slam (Aces and Key Cards).

Another interesting topic found in Culbertson’s Blue Book is the information that in average the 13 tricks played make 8 tricks using honors (A, K, Q …) and the others 5 tricks with length or ruffs. Thus, this means that a Bidding System must inform about honors (hcp), about long suits and about shortness in specific suits.

In fact, during the bidding we should have rules to inform our strength showing our weak range (12-15 hcp) or our strong range (16+ hcp). Thus, after we open in a 5-card major the rebid of this suit may be used to show weak range, not necessarily 6-card, but if we open in a minor suit that may have 3+ cards the rebid of this minor tends to show 6+ card, not only 5, because we are interested in explain our unbalanced hand (6322 or 6331). After partner opens in a major suit if we have 10+ hcp with good 4-card support and a singleton suit we jump to game at level 4 in this suit making an artificial bid that shows our shortness (singleton/void) with 4-card support (this is called splinter bid).

Searching for a fit (4-4 or 5-3 or 5-4) is a basic bidding objective. When a player find that his partner has 4-card in the same suit, he also has 4-card or find that partner has 5 cards in the same suit he also has 3 cards, then he should support partner suit to establish the agreement in that suit - maybe the future trump suit. In these cases, we say they found a fit 4-4 or 5-3 and the remainder 5 cards (residue) in that suit are statistically divided 3-2 or 2-3 in 67,8% between the opponent’s hands.

So, when we have a 4-4 fit and we play the top cards A K Q if the residues are divided 3-2 our remainder 2 cards may be used for ruff and then we make 5 tricks in this suit. If our fit is 5-3 and opponent’s cards in this suit are divided 3-2 in a similar way we can make a total of 5 tricks in this suit.

That is the reason why players during the bidding use rules, like syntax in language, to find a fit (at least of 8 cards) and explain the strength of their hand in high cards points (hcp) as information for partner be able to decide the final contract (pat-score game slam).

Exist a rule for a suit opening at level 1?
Not exactly, but normally a bidding system like 2/1 make use of the hcp to decide if stop in part-score or go to game or slam. If the opening hand has 13 hcp and Responder (partner of the Opener) also has 13 hcp, then partnership should play game contract that needs 25-26 hcp. But if opening is made with only 10 hcp, then Responder with 13 hcp has no way to know that and will bid a game contract with 10+13=23 hcp that statistically will not have success many times. So, using the Milton Work scale A=4 K=3 Q=2 J=1 an opening in first or second position must have a minimum hcp to allow partners to add hcp as a baseline to decide to play a game contract. But specifics system or partnerships can have its on rules, and, of course, any not usual convention need be alerted during the auction.

In fact, 70y ago an opening in suit at level 1 was 13-21 hcp or 3 “Quick Tricks”. Quick Tricks is the number of tricks that you expect to make in a suit on the first two rounds of that suit (AK=2 AQ=1½ A=1 KQ=1 Kx=½). In other words, the defensive tricks that an opening should have.

But nowadays an opening with 11-12 hcp with a good distribution like 5431 may be used to take initiative when it shows a good indication to partner lead in case opponent gain the contract.

The hand distribution is an important parameter to decide between to open or to pass. If you have a 4-card suit like ♦AKQ2 - ♦543, in case this suit has distribution 4333 (36%) you will make 4 tricks because after you play A K Q your last card, the “2”, will make a trick. But if your hand distribution is 3♠3♥4♦3♣ you have only one suit to promote the 4^th card. When your hand distribution is 4♠4♥3♦2♣ you now have two suits that might promote the 4^th card. When your hand distribution is 5♠3♥3♦2♣, and your 5-card suit is a fit 5♠-3♠ this suit may promote the 4^th and the 5^th card if Spades in opponent hands are 3-2 (5♠3♠3♠2♠).    

Therefore, if your hand distribution is 5422 or 5431 you have the chance to make the 4^th card in the 4-cards suit and the chance to make the 5^th and 4^th card in the 5-card suit. So, distributions may help you to decide optimistically for the opening with 10-11 hcp.

In the other hand, you should avoid opening hands with bad distribution like: ♠9xx ♥Axx ♦AKx ♣9xxx or ♠9xx ♥Qxx ♦AKQ ♣Jxxx despite you have 3 sure tricks. A good rule to follow is to consider a hand 4333 distribution with minus 1 point to decide to open.  

The initiative in the bidding is a parameter of success that justified a weak opening even in level one if it is also orienting partner for a good lead in case opponents win the auction.

So. the opening could be done more light (11-12 hcp) having good distribution (54xx or 64xx or 55xx) with two and half defense tricks like: ♠AQ109x ♥A109x ♦xxx ♣x or ♠AQ10x ♥A1098xx ♦x ♣xx or ♠AJ10xx ♥AJ109x ♦x ♣xx or yet in third position, as an indication for lead with something like: ♠x ♥xx ♦AK109x ♣K108xx with favorable vulnerability and a reasonable second bid available. But the partnership needs to know how to stop the bidding after a weak opening - to avoid overbids (when contract is too high to be made due to poor high cards).

There is an important convention called “Drury” used by a passed hand that allows a major opening major in third or fourth position with only 10-11 hcp because then a passed hand with 10-11 hcp might inform opener his strength with 3-card support bidding 2♣ or 4-card support bidding 2♦ giving reliable information to Opener bid sign-off with a rebid in his major suit. Thus, Responder must pass to avoid an overbid. Therefore, for major suits the problem in doing an opening very light is already solved and the bidding can be stopped at level 2 with 20-22 hcp together.

Of course, sometimes you can evaluate the strength of a hand counting its losers. Suppose you have a hand like: ♠10932 ♥AK ♦A ♣AKQJ10x where you have losers only in Spades. This hand has 9 tricks winers and if you are in third position a 3NT opening may have success unless opponents can make 5 tricks in Spades. But this opening is not recommended, if your partner has ♠Ax ♥Qxx ♦xxxx ♣98xx because you are missing a slam in Clubs with an opening in 3NT that may have another meaning depending on partnership agreement. A 3NT opening in 2/1 shows a solid minor suit 7/8 cards AKQxxxx(x) and no more A or K by convention.  

But in general, to evaluate the strength of a hand it is standard the use of high cards points (hcp) A=4 K=3 Q=2 J=1 published by Milton Work that is still our inaccurate guideline. For balanced hands the statistics shows:
- a game in 3NT 4♥ 4♠ needs 25-26 hcp;
- a game in 5♣ 5♦ needs 27-28 hcp;
- a small slam needs 32-33 hcp;
- a grand slam needs 37 hcp (or 13 tricks counted).

Thus, the Bidding System must have rules for in cooperative way both partners may show the range of their points to allow the choice between part-score / game / slam. Of course, to bid slam we need first assured that there are no missing 2 Aces or an Ace and King in same suit. If we bid a slam and opponents make initially 2 tricks before we can make our 12 tricks this is really a big blunder in our bidding procedure.

High Cards Points is a very easy way to evaluate hands, but it has inaccuracies. If we assume the value for K=3 then the more correct value for A is 4.25 and for Q<2 (almost 2). Furthermore, Milton Work points do not include a value for the 10 or a value when there are union of middle cards like J109x or QJ8 or KJ10, because their value for making tricks is very different from the value of Jxxx or Qxx or Kxx. So, each player should look carefully at his middle cards observing the consistency of the cards to make tricks and the hopeless losers. Of course, if A=4.25 then 4 Aces in the same hand means 17 hcp.

In the other hand, long suits with 7+ cards or 2 suits 5-5+ with good top honors should not be evaluated using hcp but for its losers and, evidently, we can’t compare suits like KJ543 x KJ1098 or KQ543 x KQ1098 or AQxxxx x AQ10987 only using hcp.

If your partner opens 1♠ and you have a special distributional hand like:
    ♠xx ♥KQ1098 ♦QJ10987 ♣-
you should ignore Milton Work points evaluation and despites you have only 8 hcp your response should be positive based in your hand distribution with only 4 losers, that means you should try a game independently how points your partnership have. Your question should be if you bid first 2♦ and after reverse in Hearts or if you bid first 2♥ (better) and after bidding Diamonds, because if hand fits you may also have slam. Of course, when hands do not fit, and a misfit is found, auction should be stopped as soon as possible.    

In modern evaluation for points counted for an opening hand we do not use any more points for doubleton or singleton or void. But we use +1 for each 5-card suit, +2 for each 6-card suit, +3 for a 7-card suit if the long suit has two top honors (AK / AQ / KQ). But when we find a fit 4-4 or 5-4 then we increase the value of our shorter side suit adding distributional points: singleton=3 void=5.

So, in moderns bridge system splinter is a reliable information that partnership should prioritize to establishing game-forcing (GF) even with only 10 hcp since a fit exist. Splinter shows also support of 4+ cards in partner’s suit and give to partner the decision if hand fits or no fits – it is like ask to partner: - should we try slam or stop in game?

During the auction partnership change information using Bidding System rules about the strength of each hand to decide if they should stop in a part-score (1NT 2♣ 2♦ 2♥ 2♠ 2NT 3♣ 3♦ 3♥ 3♠ 4♣ 4♦) due to less than 25-26 hcp when both hands are balanced, or if they may try game or even slam considering the astonishing distributional hand showed by splinter (void or singleton) during the auction:
Opener: ♠- ♥AK10983 ♦AQ7 ♣8532  
Responder: ♠Q7652 ♥QJ432 ♦K109 ♣-
Opener Responder
  1♥        4♣ <= by convention 4♣  means shorter clubs suit (called splinter convention) with implicit support of 4♥+ cards and 10-14 hcp. Thus, in this example Opener may try a slam in 6♥ because his immediate losers are in Clubs – this means hand fits. In fact, if the bidding follows with 4♠ by Opener showing control in Spades suit (called cuebid) and Responder rebid their splinter showing now void in Clubs, Opener may cuebid in 5♦ that will be followed by a support cuebid in 6♦ allowing an invitation to grand slam.

However, although finding a fit (4-4 or 5-3) be an important task for a partnership the information about specific high cards like A K Q of trump and A K at side suits is very relevant for the decision in stop in part-score, bid game or try slam. In these notes of 2/1, we emphasize that Opener’s second bid and Responder’s second bid must give reliable information of the strength of their hands and put the information of the distribution in secondary plane. Like if the hand is 5332 or 6322. Our approach is to know if the hand has a range 12-15 hcp or 16-20 hcp for Opener and Responder. 

Considering that an opening in suit at level 1 normally has a range between 12-20 hcp, the main objective of the Opener is to inform his partner if his strength is minimum (12-15 hcp) or better (16+ hcp). So, the Bidding System must have rules for that.

In similar objective Responder can show his strength bidding depending on his range, per example:
0 – 5 hcp   <= pass
6 – 9 hcp   <= bidding other suit only at level 1
…………..   <= bidding 1NT
…………..   <= support partner major at level 2
10-11 hcp <= bidding other suit at level 1
…………..   <= bidding 2NT with a passed hand
…………..   <= support partner suit at level 3
12+ hcp    <= making a game forcing bid at level 2.
In general these rules are not standard - depending on conventions.

Opener in his second bid informs Responder of his limited strength, per example:
12-14 hcp <= bid 1NT
…………..   <= support Responder at level 2
18-19 hcp <= Opener second bid jump to 2NT
18-20 hcp <= Opener jump in other suit at level 3
16-17 hcp <= support Responder suit at level 3
18-19 hcp <= support Responder suit at level 4
All these considerations are rules of the Bidding System that we must study. So, add points (hcp) during the action it is a usual function of any player to evaluate if it is possible to have 25+ points together or with less than 25 points to abort game try. 

But the opponents (N-S x E-W) also interfere in auction making Overcall to compete and so to find also their fit to try a part-score or game in the opposite position. This is the beauty of competitive bidding when both partnerships want to obtain the best score for the present hand playing in their own fits. A good Bidding System should give tools or rules to make possible a safety level to compete for a good score. 

Suppose the following bidding with both sides nVul:
                 Joan (dummy)       Joan  Maria Paul John
                   ♠ A42                      1♦     2♣     2♥    pass
                   ♥ QJ8                      4♥     all pass 
                   ♦ AQJ3                    Contract: 4♥
                   ♣ 852                      Declarer: Paul
    John                      Maria        Lead from Jean: ♣7
♠ 109876       N       ♠ QJ5
♥ 765        O       E   ♥ 2
♦ 10876         S       ♦ 954
♣ 73                         ♣ AK1094
                Paul (Declarer)
                   ♠ K3
                   ♥ AK10943
                   ♦ K2
                   ♣ QJ6
Paul loses ♣AK and a ruff in Clubs and makes the contract, but if Maria don’t bid 2♣ (overcall) that makes an indication to the lead, then John may lead ♠10 and Declarer will make 6 tricks in Hearts + 4 in Diamonds + 2 in Spades. Thus, 12 tricks and 2 overtricks (additional tricks).

Now let’s change the hand considering N-S Vul and E-W nVul but now West having 4 cards support and a singleton:
                   Joan           Joan  Maria Paul John       
                   ♠ A42          1♦      2♣      2♥    3♣
                   ♥ QJ8          4♥      5♣  double all pass 
                   ♦ AQJ3        Contract: 5♣ => 11 tricks
                   ♣ 85            Lead from Paul ♥A
   John                     Maria (Declarer)  
♠ 9876            N      ♠ KJ105
♥ 5              W    E   ♥ 762
♦ 10876          S      ♦ 9
♣ QJ73                    ♣ AK1094
                    Paul
                   ♠ Q3
                   ♥ AK10943 
                   ♦ K542
                   ♣ 62

 

Analysis: N-S makes 4♥ whose score Vul is 620 points and E-W in defense bids 5♣ that may be down doubled only 2 tricks whose score nVul is 300 or down 3 whose score is 500 also good advantage. Thus, the 5♣ bid was great defense made for E-W. This is bridge in competition where both partnerships compete for the best score in a board.

In fact, there are distributional hands that may fit in high positive combination that Aces might be ruffed, and the importance of long fit makes game or slam possible with few hcp in both hands:

 

If you have a hand distribution ♠7♥6♦0♣0 and your partner ♠6♥0♦4♣3 distribution. That means that your partnership has together 13 cards in a suit and sides suits may be ruffed. Thus, your partnership can make 13 tricks with only 10 hcp. Of course this is a dreamer hand with probability zero, but sometimes there are, per example, deals with eleven cards fit, that ruff a side suit from one side e ruff another side suit in the other side, like the follow hand.

                 North       South West North East       
                 ♠ A8742     1♣       X     1♠       X*
                 ♥ 8643       2♣       3♥    6♣      X**
                 ♦ -                all pass Contract: 6♣X
                 ♣ 8543                Lead by West K♥
   West                     East    *double shows 4♥ cards 
♠ QJ106        N      ♠ K95    **punitive double
♥ KQJ10   W      E  ♥ A976             
♦ AJ76           S      ♦ K10983      
♣ 7                         ♣ J
                 South
                 ♠ 2
                 ♥ 9
                 ♦ Q542
                 ♣ AKQ10876
Explanation: South opens 1♣, West double to show another opening hand. North bids 1♠ after West double to show by convention 5♠+ cards. Then East double promises 4♥+ cards. South rebids 2♣+ that shows 6/7♣ cards and denies by convention 3♠ cards support. West bidding in jump 3♥ shows invitation to game with 15-16 hcp and this allows North (with 4♥ cards) to see South with singleton ♥.
Thus, North considering his 4 cards support in Clubs and being void in Diamonds noticed that partnership has a game in Clubs or even a slam if South has singleton Spades. So, he jumps preemptively to 6♣ against a possible opponent 5♥ (in case one opponent has void in Clubs). In the other hand, East having one Ace and two Kings bids double not believing in a possible slam.

The card playing:
trick01: East leads K♥ and after see 4 cards ♥ in dummy and void in Diamonds makes the best defense playing trump in the second trick.
trick02: South makes A♣.
Considerations: South have 4 losers in Diamonds and now only 3 trumps in dummy, so South must establish a winner trick in Spades to discard his 4^th Diamond loser. Thus, Spades needs be 5431, that is a chance near 62%, so:
trick03: South plays A♠.

trick04: South plays low Spades and ruff.

trick05: South plays Diamond and ruff.

trick06: South plays Spades and ruff.