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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
Denomination	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
Contract	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:

a small slam, or successful contract to win 12 of 13 tricks, earns a bonus of 500 points if not vulnerable and 750 points if vulnerable;
a grand slam, or successful contract to win all 13 tricks, earns a bonus of 1000 points if not vulnerable and 1500 points if vulnerable.

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.

50 points are awarded for a doubled contract made, and
100 points are awarded for a redoubled contract made.

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:

for a completed rubber, the side which wins the rubber, i.e. is first to win two games, receives a rubber bonus:
- if the opponents have won no games, i.e. they are not vulnerable, the rubber bonus is 700 points; colloquially known as a 'fast rubber'
- if the opponents have won one game, i.e. they are vulnerable, the rubber bonus is 500 points; colloquially known as a 'slow rubber'
for unfinished rubbers:
- if but one side has won a game, it scores 300 points, and
- if but one side has a part-score, it scores 100 points.

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.

100 points are awarded for any one hand holding any four of the five trump suit honors, and
150 points are awarded for any one hand holding all five trump suit honors, or all four aces in a notrump contract.

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:

any partial contract, i.e. one scoring less than 100 contract points, scores a bonus of 50 points, and
any game contract, i.e. one scoring 100 or more points, scores a game bonus of 300 if not vulnerable and 500 if vulnerable.

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:

Each deal is scored as in rubber bridge but with some variations in methodology.
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:

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.
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:

In team events, it is the score from the other table;
In pair events, it can be:
- The datum score, most often calculated as the average score on board, excluding a number of top and bottom results. Sometimes, the median score is used instead.
- In "cross-imps" or "Calcutta" scoring, every score on board is compared against every other score (sometimes excluding top and bottom results) and IMPs summed up (and possibly averaged, to reduce "inflation").
- Example of averaged cross-imp scoring: Assume that you are one of five pairs who play Board 2 as N/S (you are vulnerable). On this board you bid and make 4 Spades, scoring +620, while the other four N/S pairs score -100, -100, -300, and +650. To figure out your averaged cross-imp score, you would create a table like the Cross-IMP example table below: after writing in the scores of you and your opponents in the bolded areas, you would then fill in the Score Delta row by subtracting each of the opponent's scores from yours. Then, you would fill in the IMPS Gained row by converting each of the score deltas into IMPS via the standard IMP table (e.g. 720 equates to 12 IMPs, because it falls in the range of 600 to 740 in the IMP table). You then add up those numbers and get 37 IMPS. To turn the 37 IMPS into a averaged cross-IMP score, you simply divide that number by the number of competitors (37 IMPs divided by 4 competitors) to arrive at 9.25 as your averaged cross-IMP score.

Example of cross-IMP table
Our score on Board 2 is 620	Scores of the four other North/South pairs
Our score on Board 2 is 620	-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	IMPs	from	to	IMPs	from	to	IMPs
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):

The undertrick penalty when doubled, not vulnerable, used to be 100 for the first undertrick and 200 for each subsequent. This was changed because it was too easy to sacrifice against a grand slam. A vulnerable grand slam is worth 1500 (slam bonus) + 500 (game bonus) + 210 (major suit trick score) = 2210. Down 11, doubled not vulnerable, used to be 2100, a profitable sacrifice. Under the current scoring rules, down eight (-2000) would still show a profit, but down nine (-2300) would not.

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.

Also, the "insult bonus" for making a redoubled contract used to be only 50. This was changed to 100, so that playing 5 of a minor, redoubled, making an overtrick, is always worth more than an undoubled small slam.

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