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Bridge scoring

Bridge scoring is keeping score in contract bridge. There are two main categories of scoring: duplicate and rubber scoring. While based upon the same basic elements of scoring, they differ in how the elements are applied to individual deals and in how these are then totaled. Chicago, being a variant of rubber bridge, uses an adaptation of rubber bridge scoring. Duplicate bridge has many variations for scoring, comparing and ranking the relative performance of partnerships and teams playing the same deals as their competitors.

Terminology

The following terms and concepts, defined in the glossary of contract bridge terms, are essential to understanding bridge scoring:

Scoring elements

Bridge scoring consists of nine elements. Not all elements are included in all game variants and the method of accumulation of the elements over several deals varies.

If the contract is made, the score for each such deal consists of:

1. Contract points, assigned to each odd trick bid and made
2. Overtrick points, assigned for each trick taken over the contracted number of odd tricks
3. A slam bonus for a small slam or grand slam contract bid and made
4. A bonus, colloquially known as 'for insult', is received at the end of any deal in which a doubled or redoubled contract is bid and made

If the contract is defeated, the defenders receive

5. Penalty points, assigned for every undertrick

In rubber bridge only,

6. A rubber bonus is received at the end of a completed rubber by the side that is first to win two games. A rubber bonus is also awarded for some game and part-game scores at the end of an unfinished rubber
7. An honor bonus is received by any player at the end of any deal in which he held particular honor cards.

In duplicate bridge only,

8. A partial-game bonus is received at the end of each deal for any partial game contract bid and made
9. A game bonus is received at the end of each deal for any game contract bid and made

Contract points

Contract points are awarded for each odd trick bid and made. Their values depend on the suit (or notrump)and whether the contract is doubled or redoubled; they are not affected by vulnerability. Tricks won beyond that necessary to fulfill the contract are referred to as overtricks and their scoring points are accounted for separately because their values are dependent upon declarer's vulnerability.

Denomination Contract Points Per Trick
Undoubled Doubled Redoubled
Notrump
- 1st trick
- Subsequent tricks

40
30

80
60

160
120
Major suits 30 60 120
Minor suits 20 40 80

Overtrick points

When declarer makes overtricks, their score value depends upon the contract denomination, declarer's vulnerability and whether or not the contract is undoubled, doubled or redoubled. In an undoubled contract each overtrick earns the same as in contract points (30 for notrump and major suit contracts, 20 for minor suit contracts); values increase significantly when the contract has been doubled or redoubled, especially when vulnerable.

Contract Overtrick Points Per Trick
Vulnerable Not Vulnerable
Undoubled in:
- Notrump
- Major suit
- Minor suit

30
30
20

30
30
20
Any doubled 200 100
Any redoubled 400 200

Slam bonus

Bonuses are awarded for all slam contracts bid and made:

Doubled or redoubled bonus

When a doubled or redoubled contract is made, a bonus is awarded to the declaring side. It is colloquially referred to as a bonus for "insult", meaning that the opponents have insulted the pair by suggesting that the declarer will not make the contract.

In scoring notation, a doubled contract is indicated by an 'X" after the contract (e.g. a contract of four hearts doubled is indicated by 4 X); a redoubled contract is indicated by "XX" (e.g. 4 XX).

Penalty points

When a contract is defeated, penalty points are awarded to the defending side. The value of the penalty depends on the number of undertricks, whether the declaring side is vulnerable or not vulnerable and whether the contract was undoubled, doubled or redoubled.

Number of
Undertricks
Points Per Undertrick
Vulnerable Not Vulnerable
Undoubled Doubled Redoubled Undoubled Doubled Redoubled
1st undertrick 100 200 400 50 100 200
2nd and 3rd, each 300 600 200 400
4th and each subsequent 300 600 300 600

Without a double or redouble, every undertrick has a fixed cost of 100 or 50 points. The scores for (re)doubled undertricks are such that after the first vulnerable undertrick, n vulnerable undertricks cost the same as n+1 undertricks when not vulnerable; for example, four undertricks when doubled and not vulnerable cost 800 points (100+200+200+300), the same as three undertricks when doubled and vulnerable (200+300+300).

Rubber bonus

In rubber bridge only, a bonus is awarded at the conclusion of the rubber as follows:

Honor bonus or honors

In rubber bridge only, a bonus is awarded for any one hand holding four or five of the honors, i.e. an ace, king, queen, jack or ten.

Honors may be declared and scored at any time after the auction but for strategic reasons it is best to do so at the conclusion of play so as not to give the opponents information about the lay of the cards. Honors may be held by any of the four players, including dummy.

Game or part-game bonus

In duplicate bridge only, game and partial-game bonuses are awarded at the conclusion of each deal as follows:

Rubber bridge

For additional scoring information for the rubber bridge variant Chicago, see Chicago scoring
Rubber bridge score sheet

The score sheet

Rubber scoring is tallied on a score sheet divided into four parts where each partnership accumulates points either above the line or below the line.

The objective is to win by scoring the most total points in the rubber; the rubber is completed when one side has twice accumulated 100 or more contract points below the line.

Only contract points are recorded below the line; all other points are recorded above the line. Any of the four players may be the recorder, his side being represented in the "We" column and the opponents in the "They" column. In the ensuing examples, South is the recorder (the 'We' on the score sheet).

An example rubber

The following table summarizes the results of a rubber consisting of six deals.

Deal Declarer Contract Made Down Contract
Points
Overtrick
Points
Slam
Bonus
(Re)doubled
Bonus
Penalty
Points
Honor
Bonus
Deal
Total NS
Deal
Total EW
1 N 2NT 3 (1x40)+(1x30)=70 1x30=30 100
2 W 4 4 4x30=120 120
3 W 5 2 2x100=200 200
4 S 4 X 5 2x(4x30)=240 1x100=100 50 390
5 N 3 4 3x20=60 1x20=20 80
6 E 6 6 6x20=120 750 150 1020
Rubber Bonus  500
Total  770 1640

The following panels illustrate the progression of the scoring on the score sheet.

Deal 1 Deal 2 Deal 3 Deal 4 Deal 5 Deal 6 Rubber Bonus Total

Deal 1: South bids 2NT making 3. Only the contract points (70) are scored below the line; the overtrick points (30) are scored above the line.

Deal 2: West bids and makes 4. This scores 120 contract points below the line; since there are no overtricks, no points are scored above the line. The accumulation of 100 or more points below the line constitutes the end of the first game and is signified by the drawing of a horizontal line. Since no part-game or game bonus is awarded in rubber bridge, East-West do not receive an additional game bonus and North-South do not receive any part-game bonus. Furthermore, the part score of 70 by North-South is no longer available for accumulation towards a game by them; the 70 points are said to be "cut off" as signified by the drawing of the horizontal line. Having won a game, East-West are vulnerable for all subsequent deals of the rubber meaning that they are now eligible for a larger rubber bonus if they win a second game before their opponents win one and they are susceptible to increased penalties if they are defeated in a contract.

Deal 3: West bids 5 and goes down 2, vulnerable, undoubled. This scores 200 penalty points for North-South above the line.

Deal 4: South bids 4 doubled, not vulnerable and makes 5. North-South score 240 contract tricks below the line, 100 overtrick points above the line and 50 points for 'insult' above the line. Accumulating 100 or more points below the line constitutes the end of the second game, signified by the drawing of a horizontal line. Having won a game, North-South are now also vulnerable for all subsequent deals of the rubber.

Deal 5: North bids 3 and makes 4 scoring 60 contract points below the line and 20 overtrick points above the line.

Deal 6: East bids and makes 6 - a small slam holding all five top honors. This scores a game of 120 contract points and earns a slam bonus of 750 points above the line (East-West being vulnerable). 150 honor points are scored above the line for holding all five honors. Having again accumulated 100 or more points below the line, East-West win a second game; a horizontal line is drawn to end the rubber.

Rubber Bonus: At the conclusion of the rubber, a rubber bonus is awarded. In this case, East-West have won a slow rubber and receive a 500 point rubber bonus above the line.

Total: The scores for each side are totalled and East-West (the 'They' on the score sheet) win the rubber.

Duplicate bridge

Scoring in duplicate bridge is done in two stages:

  1. Each deal is scored as in rubber bridge but with some variations in methodology.
  2. The result of each deal by each partnership is compared to all other results for the same deal by all other partnerships.

Scoring deals

In duplicate scoring, the score for each deal is independent from all others and is a single number resulting from the addition of points awarded in accordance with either of two cases:

  1. when the contract is successful, the declaring side receives a positive score which is the sum of the following elements, if applicable: (i) contract points, (ii) overtrick points, (iii) a part-game or game bonus, (iv) a bonus for making any doubled or redoubled contract, i.e. for 'insult', and (v) a slam or grand slam bonus; the defending side receives a negative score of the same absolute value.
  2. when the contract is defeated, the defending side receives a positive score based upon the number of tricks defeated, declarer's vulnerability, and whether undoubled, doubled or redoubled; the declaring side receives a negative score of the same absolute value.

In duplicate bridge, the dealer and the status of vulnerability for each side is predetermined by the board, there being sixteen possible combinations, as illustrated in the following example.

Board Dealer Vulnerability Declarer Contract Made Down Contract
Points
Overtrick
Points
Slam
Bonus
(Re)doubled
Bonus
Penalty
Points
Game
Points
Total
N-S
Total
E-W
1 N None E 1 3 30 2x30=60 50 -140 140
2 E N-S N 4 X 2 (1x200)+(1x300)=500 -500 500
3 S E-W N 2 4 2x20=40 2x20=40 50 130 -130
4 W Both W 1NT 3 40 2x30=60 50 -150 150
5 N N-S S 3NT 1 100 -100 100
6 E E-W S 3 4 3x30=90 30 50 170 -170
7 S Both W 3 3 3x20=60 50 -110 110
8 W None E 7 7 7x30=210 1000 300 -1510 1510
9 N E-W N 4 X 4 2x(4x30)=240 50 300 590 -590
10 E Both E 2NT 2 40+30=70 50 -120 120
11 S None N 6 6 6x20=120 500 300 920 -920
12 W N-S E 2 3 2x20=40 20 50 -110 110
13 N Both W 4 X X 4 2x2x(4x30)=480 100 500 -1080 1080
14 E None S 5 1 50 -50 50
15 S N-S E 4 5 4x30=120 30 300 -450 450
16 W E-W N 3NT 3 40+(2x30)=100 300 400 -400

Comparing deals

Matchpoint scoring

The most common form of pairs scoring is by matchpoints. On each board, a partnership scores two matchpoints for each other partnership that scored fewer points with the same cards, and one point for each other partnership that scored the same number of points. Thus, every board is weighted equally, with the best result earning 100 percent of the matchpoints available, and the worst earning no matchpoints; the opponents receive the complement score, e.g. an 80% score for a N-S pair implies a 20% score for their E-W opponents. Colloquially, a maximum matchpoints score on a board is known as a "top", and a zero score is a "bottom". The terms "high board" and "low board" are also used.

Note 1: using American Contract Bridge League (ACBL) methods, scoring is one point for each pair beaten, and one-half point for each pair tied.
Note 2: The rule of two matchpoints for each pair beaten is easy to apply in practice: if the board is played n times, the top result achieves 2*n-2 matchpoints, the next 2*n-4, down to zero. When there are several identical results, they receive the average. However, complications occur if not every board is played the same number of times, or when an "adjusted" (director-awarded) score occurs. These cases can result in non-integer matchpoint scores - see Neuberg formula.

These matchpoints are added across all the hands that a pair plays to determine the winner. Scores are usually given as percentages of a theoretical maximum: 100% would mean that the partnership achieved the best score on every single hand. In practice, a result of 60% or 65% is likely to win the tournament or come close. In a Mitchell movement (see above) the overall scores are usually compared separately for North-South pairs and for East-West pairs, so that there is one winner in each group (unless arrow-switching has been applied - see above).

Historical Note: At some time in the past, both North-South and East-West might be awarded the same matchpoint score. Using this arrangement, the lowest East-West Score would be the winner.

In Board-a-match team game, the matchpoints are calculated using a similar principle. Since there are only two teams involved, the only possible results are 2 (won), 1 (tied) and 0 (lost) points per board.

International Match Point scoring

In International Match Point (IMP) scoring, every individual score is subtracted from another score, and the difference is converted to IMPs, using the standard IMP table below. The purpose of the IMP table, which has sublinear dependency on differences, is to reduce results occurring from huge score differences ("swings").

The score that is being compared against can be obtained in the following ways:

Example of cross-IMP table
Our score on Board 2 is 620 Scores of the four other North/South pairs
-100 -100 -300 650
Score Deltas 720 720 920 -30
IMPS Gained 12 12 14 -1
IMP table
Point difference IMPs Point difference IMPs Point difference IMPs
from to from to from to
0 10 0 370 420 9 1750 1990 18
20 40 1 430 490 10 2000 2240 19
50 80 2 500 590 11 2250 2490 20
90 120 3 600 740 12 2500 2990 21
130 160 4 750 890 13 3000 3490 22
170 210 5 900 1090 14 3500 3990 23
220 260 6 1100 1290 15 4000 or more 24
270 310 7 1300 1490 16
320 360 8 1500 1740 17

Recent scoring changes

As of 1987, World Bridge Federation imposed the following scoring changes for duplicate bridge, and as of 1993 also for rubber bridge (however, since there are no official competitions, rubber bridge players accept them as they see fit):

Since a vulnerable small slam bid and made is worth between 1370 (6 of a minor) and 1440 (6 no trump), this change also means that for a non-vulnerable sacrifice, a result of down five (-1100) would show a profit, down six (-1400) might be a small loss or a small gain, and down seven (-1700) would be a loss. Under the old scoring rules, down seven (-1300) would have been a gain, down eight (-1500) would have been a loss.

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