partscore

Duplicate bridge

Duplicate bridge is the most widely used variation of contract bridge in club and tournament settings. It is called duplicate because the same bridge hand (i.e. arrangement of cards) is duplicated at other tables, in order to allow a fair comparison of playing skill and reduce "luck of the cards". In this way, every hand, whether good or bad, is played in competition with others playing the identical cards, and the element of skill is heightened whilst that of chance is reduced. Duplicate bridge stands in contrast to rubber bridge where each hand is freshly dealt and scores depend as much on the cards as on the players.

Bridge boards, simple four-way card holders, are used to enable each player's hand to be passed intact to the next table that must play the deal, and final scores are calculated by comparing each pair's result with others who played the same hand. Bidding boxes are often used to facilitate the mechanics of bidding, prevent inadvertent passing of information, and minimize the noise level.

In duplicate bridge, a player normally plays with the same partner throughout an event. The two are known as a "pair". There are two exceptions: on team events with five or six members swapping partners for portions of the event, and in individual tournaments, in which players change partners for each round.

Game types

Pairs game

In a pairs game, each deal is played a number of times, after which all the scores are compared. Every score is written on the traveling sheet, which is contained within and travels with the board, containing at least the numbers of North-South and East-West pairs and the scores. The more common form of overall scoring is matchpoint scoring, with IMP scoring second. Every pair plays against many opponents, depending on the size of the field. Tournaments with up to about a dozen tables are usually played either as a Mitchell movement (each North/South pair plays against all or most East/West pairs) or a Howell movement (each pair plays against all or most other pairs and switches between North/South and East/West as required). A Howell movement is typically used if there are less than about 7 tables. With larger fields the tournament can be split into separate sections (every section being a "sub-field", but the results being reckoned across the entire field), each section normally played as Mitchell.

The tournament consists of rounds, which present a number of boards, usually two to five, to be played against the same opponents. After a round, some or all of the players reseat themselves according to a prescribed movement, so that each pair opposes a different pair in each round; the boards are also moved. The movement must be set up so that every pair does not play more than one round against same opponents, and, of course, does not play the same board not more than once. The tournament director will select the movement in order to allow the given number of players to play the desired number of boards each, without repetition. A session typically consists of between 24 and 28 boards in total, but this can vary. If there are an odd number of pairs, one pair will have to sit out in each round. Most games are single-session, but tournament events can consist of two, four or more sessions.

Table movements

The Mitchell movement is the most common. The North-South pairs remain stationary. After each round, the East-West pairs move to the next higher table and the boards move to the next lower table. If the number of tables is odd, every E-W pair will play different boards against every N-S pair after the full circle. In case of an even number of tables, the East-West pairs are told to skip a table after about half the rounds so that they do not encounter boards that they have already played; alternatively ("Relay-bystand Mitchell"), a "bystand" (playerless table) is introduced, while the two tables farthest from the bystand share the boards from each round (the "relay"). Usually, the bystand is placed at the half of the field, and the relay between the first and the last table. The "perfect" Mitchell is seven, nine, or thirteen tables, with four, three, or two boards per round respectively: all players play all boards, and all pairs of each direction play against all pairs of the other direction. A variation of the Mitchell movement employs "arrow-switching". This means that for approximately one-eighth of the boards played, the N-S pairs play the E-W cards and vice versa. This variation is used when it is desired to have one winner rather than two winners (see below).

The Howell movement is sometimes used instead, usually when there are a relatively small number of tables. The actual movement is more complicated and varies according to the total number of pairs. All boards and most pairs move after every round according to guide cards placed on the tables, or carried by the players (usually one pair, or sometimes more, remain stationary). The Howell is sometimes considered a fairer test than the Mitchell, because each pair faces all or nearly all of the other pairs, not just the pairs sitting in the opposite direction. However the fairness of a movement depends not only on who one plays against but also to a considerable extent on one's indirect opponents, ie those who play the same cards as you do. The Howell also tends to be more error-prone than the Mitchell due to its greater complexity.

Less common is the Chalfant movement. In this movement, the boards remain stationary while the players move according to guide cards. This requires significantly more physical tables, because several tables are not in play on any given round. (Like the Howell movement, this movement is typically used when there is a relatively small number of players, typically no more than 12 pairs. Also like the Howell movement, this movement produces a single winner and pairs face all or almost all of the other pairs in play.) This movement has the advantage that pairs are often moving to a table that was not in use on a previous round, so a slow pair does not delay as many other pairs as in a Howell. Also, for several sizes, this movement is technically superior in that more pairs face all other pairs than in the corresponding Howell movement. This movement has the disadvantage of requiring a larger number of physical tables, and thus more space. It also requires the players to carry guide cards with them and consult them, while the guide cards usually remain on the tables for Howell movements.

Whatever movement is used, if the number of pairs is odd, obviously one pair must sit idle during each round; that situation is referred to as a bye or sit out. In that undesirable case, the missing pair (sometimes called the phantom pair) is treated as if it exists, i.e. the movement is set up for (number of actual pairs + 1)/2 tables. The phantom pair may be North-South, East-West or an arbitrary pair number in a Howell movement. In a Mitchell movement, having an East-West phantom pair is advantageous in that there are non-phantom players at each table responsible for correct movement of the boards. During the movement, one pair in each round will sit out ("play" against the phantom pair). Since, as result, pairs will usually play unequal numbers of boards, their final results are normally scaled in the final calculation (known as factoring), or less commonly they might be awarded "bye points" for that round (normally, a result slightly above average).

Another arrangement for an odd number of pairs is called a bump movement, in which the number of tables is rounded down to (number of actual pairs - 1)/2. Normally, the extra pair sits out the first round and then, according to a schedule, substitutes for a different North-South pair for each subsequent round (the "bumped" pair having a sit out for that round). In particular, the bump is preferable to the sit out for 11½ tables: it allows every pair to play at least 24 boards while having only 33 boards in play.

Trials are usually reserved for high-level competitions (such as regional and national championships, invitation tournaments etc.). There, a fixed number of pairs (usually 16) play a full round-robin tournament (Swiss can be also used to shorten the tournament) with relatively long matches (8-32 boards) against each other, the entire tournament lasting for two to four days. One session consists of only one round, with boards circulating among the tables and pairs remaining seated. Results are calculated after each round using IMP or Calcutta scoring, converted to Victory points, and added up to the running score. The pair with highest VP score becomes the winner.

Team game

In a teams tournament, two pairs normally constitute a team. (Teams of five or six members are often permitted, but only four members play at any given time.) If there are just two teams, they compete using two tables and having one pair from each team seated at each table, in opposite directions. (For example, Team A may sit North-South at table 1 and East-West at table 2; then Team B would sit East-West at table 1 and North-South at table 2.) Similar arrangements apply if there are more than two teams in the competition. Depending on the number of teams competing and the structure of the tournament, a relatively larger number of boards may be played (usually six to eight for "Swiss teams", usually 12, 24, or more for knockout events). The boards are moved (usually by a caddy) so that they are all eventually played at both tables.

Suppose Team A plays Team B. The first time a hand is played, one partnership from Team A takes the North-South cards and one partnership from Team B takes the East-West cards; when the hand is played again, it is played by the other two partnerships, but this time with Team A holding the East-West cards and Team B holding the North-South cards. Of course the teams may not discuss the deals between the two plays. Normally, each of the two tables deals and plays half of the scheduled boards at the beginning of the match, and they're exchanged in the halftime. After each deal has been played twice, the scores per deal are compared, and a score is given depending on the net total score from the two times the deal was played. For example, if one pair scores +620 on a deal, and their teammates score -600, then the team's net score on that deal is +20.

Several forms of scoring are then used to calculate the winner of the match. IMP scoring is most frequently used in team games, with Board-a-match (resembling matchpoint scoring) second.

At IMP scoring, the net score is converted using the IMPs table that "compresses" big differences in score. If the match between the two teams is just part of a larger competition, then usually the total difference in IMPs in a single match is converted into so-called Victory points or VPs. The VPs awarded to each team in their matches are summed up to determine the overall team ranking.
At Board-a-match (BAM), each hand has equal weight; each hand is won, lost, or tied.

Those are the two commonly used methods; sometimes are also used:

Total point score uses no conversion whatsoever; total-point scoring was more popular in the past, and is applied mostly for events where only two teams play an extremely long match.
Patton scoring combines the methods of Board-a-match and Total point scoring.

Individual events

An individual event in duplicate bridge is one where each round a player is paired with a different partner. Scoring is usually using matchpoint pairs scoring, but IMP pairs scoring can be used. There are various methods for assigning partners. In some methods, a given set of players always sit North, another set sit South, another set sit East, and a final set always sit West. This can be used to ensure that each pair consists of a relatively experienced or skilled player, and a relatively inexperienced player.

Individual events are more complex to run, and require that the players get accustomed to new partners on a frequent basis. Also, the outcome depends more on luck than in other types of events, as a good player often cannot do much when paired with a bad player, especially if the deal is complex. For those reasons they are less popular and less common than pair or team events, but some players are very fond of them.

Scoring

Matchpoint scoring

The most common form of pairs game is the matchpoint pairs game. (See Bridge scoring for the scoring method of individual deals.) In the final calculation, each partnership scores two matchpoints for each other partnership that scored fewer points with the same cards, and one point for each partnership that scored the same number of points. Thus, every board is treated equally, with the best result earning 100 percent of matchpoints available for given board, and the worst with 0 percent matchpoints; the opponents receive the complement score, i.e. 80 percent result for N-S pair implies 20 percent for their E-W opponents. Colloquially, scoring the maximum number of matchpoints on a certain board is known as a "top board", and scoring zero matchpoints is a "bottom board". The terms "high board" and "low board" are also used.

Note 1: in the United States, scoring is one point for each pair beaten, and ½ point for each pair tied.

Note 2: The above rule of 2-versus-1 matchpoint is actually easy to apply in practical calculation. 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 when not every board is played equal number of times, or when an "adjusted" (director-awarded) score occurs. These cases can result in non-integer numbers of matchpoints – 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 percent would mean that the partnership achieved the best score on every single hand. In practice, the results in 60 to 65 percent range are likely to win the tournament. 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).

A Historical Note: At some time in the past there were games in which both North--South and East--West would be awarded the same matchpoint score. In such a game the low East--West Score would be the winner. Example: There is one North--South Pair with a score of +500 in a U.S. Twelve Top Game. Currently that North--South would score 12 matchpoints on that board and the East--West would score Zero.

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.

IMP scoring

In IMP (International Match Points) scoring, every individual score is subtracted from another score, and the difference is converted to IMPs, using 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").

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

Scoring and tactics

The type of scoring significantly affects a pair's (team's) tactics. For example, at matchpoints, making one more overtrick than everybody else on a board gives the same result (the top) as making a slam that nobody else bid, whereas at IMP scoring, the difference comes down to 1 IMP (30 points) in the first case, but 11 or 13 IMPs (500 or 750 points) in the second case. In general, matchpoint scoring requires a more "vivid" and risk-taking approach, while IMP scoring requires a more cautious approach (sometimes referred to as "cowardly" by those who dislike it). The main features of the tactics are:

Matchpoints

Overtricks are important
Safety play is often neglected in the hunt for overtricks
Thin games and slams are avoided
Sacrifices are more frequent; e.g. going down 500 points doubled is a good result if opponents can score 620 points for a game.
Doubles are more frequent, as they increase the score for the penalty. For example, "the magic 200" refers to the situation when a pair beats the vulnerable opponents one trick doubled — the obtained score of 200 will likely outscore all partial contracts played on other tables.
Playing in higher-scoring denominations (notrump or major suits) is important, as it may lead to an extra 10 or 20 points.

IMPs

Overtricks are not important, as it's not worth the risk of losing e.g. game bonus (300-500 points = 8-11 IMPs) for a potential 1-IMP gain for an overtrick
Safety play is very important, for the same reason
Thin games and slams are often bid. Bidding a game with 40 percent probability of success vulnerable and 45 percent nonvulnerable, or a small slam with 50 percent probability, is worth the risk, and anything over that increases the probability of a positive IMP score in the long run.
Sacrifices are less frequent, as they may be risky.
Doubles are less frequent, as they may be risky. Often, when an opponents' contract is doubled, it turns declarer's attention to the bad lie of cards, and may induce him to take a successful line of play that he wouldn't take otherwise.

Contrast with rubber bridge

Duplicate bridge, especially matchpoint games, differs significantly from rubber bridge: whereas the goal in rubber bridge is to win more points than the pair of people you are playing against, in duplicate bridge the goal is to do better than other pairs playing the exact same cards. Because of this, strategies are different. In rubber (as in IMP scoring), 30 points above the line for an overtrick is unimportant and hardly worth risking a set. In match-points duplicate, it is common for those 30 points to mean you get a top score instead of average – and may be worth risking going down. In rubber, an occasional 800-point penalty is disastrous, but on matchpoints it is no worse than any other bottom score. International match points is in the middle of these extremes. Huge penalties are worse than small penalties, but 30 point differences are only moderately important.

A more subtle difference is in the bidding of partscore hands. In duplicate bridge, once a pair recognizes that they are playing for part score (less than a game), their objective is to win the auction with the minimum bid. In rubber bridge, it may occasionally be desirable to bid above this minimum as points below the line may be needed to complete a game.

Duplicate bridge also has the advantage of compensating for a run of bad luck. A pair that has had poor hands all night may still have the highest score for the evening – as long as they play those cards better than the other pairs with the same poor cards (however in such cases the pair will probably have had less opportunity to exercise skill and their result will be more heavily dependent on the skill displayed by their opponents).

Bridge organizations

The worldwide governing body in bridge is World Bridge Federation, formed 1958 as the joint effort of American Contract Bridge League (ACBL) and European Bridge League (EBL), which are the largest zonal organizations, with around 160,000 and 400,000 registered members respectively as of 2006. There are eight zonal organizations:

Zone	Organization	Area	Member Countries	Total Membership
1	European Bridge League (EBL)	Europe	47	387,684
2	American Contract Bridge League (ACBL)	North America	4	158,429
3	Confederacion Sudamericana de Bridge (CSB)	South America	9	3,700
4	Bridge Federation of Asia & the Middle East (BFAME)	Asia	11	11,980
5	Central American & Caribbean Bridge Federation (CAC)	Central America	24	1,811
6	Pacific Asia Bridge Federation (PABF)	Pacific Asia (Far East)	13	30,098
7	South Pacific Bridge Federation (SPBF)	Australia and Oceania	4	49,095
8	African Bridge Federation (ABF)	Africa	17	6,308