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A duplicate bridge movement is a scheme used in a duplicate bridge session to arrange which competitors play which opponents when, and which boards they play. The arrangement has to satisfy various constraints which often conflict to some extent, requiring compromises. The resolution of these compromises is to a considerable extent a matter of taste, so players should be consulted as to their preferences if this is practicable.

Movements are categorized by the type of event —- Individual, Pairs, or Teams.

Contents

Requirements for MovementsEdit

There are three absolute requirements for a Bridge movement.

1. No entrant (individual, pair, or team, depending upon the type of the event) may play the same deal more than once.

2. The number of deals in each session must be appropriate to the level of competition and the circumstances.

3. The movement must provide enough stationary or nearly stationary positions to accommodate the needs of all players who have disabilities and/or mobility impairments.

With respect to the second point, an "open" (unrestricted) club or tournament session typically consists of around 26-28 boards (deals) in North America, but this may vary in other zones. However, a club may choose to play fewer deals in a session connected with a luncheon or party of some sort, and sessions on cruise ships also typically are shorter (about 18-20 deals). Sessions for less experienced players also typically consist of fewer deals, while sessions of some championship events may play more.

That said, there are several criteria that are desirable in Bridge movements.

  • It's generally desirable for each table to play a separate group of deals (boards) in each round, unless there are enough copies of the shared groups of boards for each table playing a group of boards to have its own copy. However, some movements frequently chosen for reasons of fairness do require two adjacent tables to play the same group of boards in each round.
  • In matchpoint scoring, all boards ideally should be played the same number of times so they all carry the same weight and influence in the scoring.
  • No two entrants should play against one another (at the same table) or, in an individual event, come together as partners in more than one round, except in the case of an individual movement in which players change direction from round to round wherein entrant must play against each of the other entrants in two rounds (ideally, one round as right hand opponent and one round as left hand opponent) to form a complete movement.
  • The number of boards per round must be reasonable. In standard matchpoint games, two boards per round is the practical minimum and four to six boards per round normally is the desirable maximum. In standard team games other than "board-a-match" competition where each round is a separate "head to head" match, six boards per match is the normal minimum and twenty-four is the normal maximum for open events. If there's an odd number of entrants, such that one entrant must sit out during each round due to lack of an opponent, it's desirable to minimize the number of boards per round to minimize the time that the affected entrants must wait for the start of the next round. When there's no sit-out, the decision to play more rounds of fewer boards or fewer rounds of more boards is solely a matter of preference.
  • It's desirable that all entrants play all of the deals that are in play.
  • The movement should be as fair as possible, as discussed below.
  • If there's a break for lunch or any other reason in the middle of a game, it's desirable to arrange the movement so play of all deals in play before the break comes to completion at the break and new deals go into play after the break.
  • Subject to the other constraints, the movement should be as simple as possible to minimize the possibility of errors such as players going to the wrong table, players sitting in the wrong direction at a table, or the players at a table playing the wrong group of boards. This applies to the movement of boards as well as to the movement of players.

The preferences of a particular club or tournament organizer may dictate other constraints. Here are some examples of organizers' preferences that might affect the choice of movement.

  • Some organizers may prefer to break a session into flights scored separately, with separate sections, for players of different ranking or experience levels, which may require different movements if they are of different size, while other organizers may prefer to have players of all rankings or abilities play together each other in the same section(s).
  • Some organizers may prefer to split larger events or flights into smaller sections that play fewer rounds with more boards per round, finding that the game progresses more quickly with fewer rotations, while other organizers may prefer to form larger sections that play more rounds with fewer boards per round, giving each entrant an opportunity to play against more entrants.
  • Some organizers may prefer to combine all entrants in one comparison field to produce a single winner while other organizers may prefer to have multiple comparison fields with separate winner for larger events.

In the absence of explicit requirements for a particular competition, these considerations are completely discretionary.

Fairness of Bridge MovementsEdit

There are several considerations in determining the fairness of a Bridge movement.

  • A complete movement, in which each entrant plays against each of the other entrants, is inherently the fairest choice. The worst scenario is a movement that is one round short of complete: one entrant does not play against a very strong competitor, thus gaining a significant advantage, while another entrant misses playing against a very weak competitor, thus coming into a significant disadvantage. When a movement is several rounds short of complete, averaging tends to take over -- each competitor misses both weaker and stronger opponents, diminishing the effect. It's possible to diminish this impact further by "seeding" that disperses entrants with higher and lower rankings or ability more or less homogeneously throughout the movement.
  • Within each scoring field, each competitor should have equal influence on the results of each of the other competitors, taking into account both direct opposition (at the same table) and indirect opposition (boards played in the same direction at different tables, thus generating direct comparisons).
  • When there is more than one scoring field in an event or a flight, all scoring fields should have entrants of comparable ability or ranking so that all competitors face opposition that's approximately the same strength. In individual and pair events, this extends to each direction of each section when each direction is a separate scoring field.
  • In matchpoint scoring, mathematical analysis[1] has determined that the relative positions in which two pairs play a deal exerts the weights in the following table to the play of that deal, based upon the impact of a hypothetical competitor getting either clear top or clear bottom scores on all deals compared to a hypothetical competitor getting average scores on all deals. A negative weight means that the entrants are effectively teammates on that board (that is, a particularly good result by either helps the other). If the movement is not complete, the directions of play ideally are arranged so each entrant has equal total weight, based on summing the weight for the individual boards, on each of the other entrants' results.
Relative Playing Position on Deal Weight of Result in Matchpoint Scoring
Opponent at Same Table +1 Scoring Unit x Number of Comparisons
Same Direction at Different Tables +1 Scoring Unit
Opposite Directions at Different Tables -1 Scoring Unit
  • Vulnerability also affects the fairness of a game scored either by Total Points or by International Matchpoints (IMP's) because a pair that's vulnerable receives more points (raw Bridge score) than a pair that's not vulnerable for making the same number of tricks in any game or slam contract while giving up more points for failing to make any contract. These higher scores for the same Bridge result also translate to more IMP's for the same Bridge result in IMP scoring. When scoring by either of these methods, all pairs should be vulnerable on an equal number of deals -- a condition most easily met by playing four boards per round since all regular groups of four boards (1-4, 5-8, etc.) have one board with each combination of vulnerability (none, North-South only, East-West only, and both), ensuring that each partnership is vulnerable on two deals and not vulnerable on the other two deals. Some movements that don't meet this criteria have very bad imbalances of vulnerability.[2] This issue does not apply in Matchpoint scoring because all boards award an equal number of matchpoints in each direction regardless of vulnerability.

When scoring multiple sessions as a single event, these criteria apply to the aggregate of all sessions of the event rather than on a session by session basis.

Pair movementsEdit

The two most prevalent types of pair movements in Bridge are Mitchell movements and Howell movements.[3] Normal Mitchell movements have separate scoring fields for the North-South pairs and the East-West pairs, so they can have separate winners in each direction or overall winners across both directions. All Howell movements and some variants of Mitchell movements have some pairs play in both directions, forcing all pairs to be combined into a single scoring field that produces a single winner.

There are also special movements for specific situations or specific numbers of tables that don't fit neatly into either category. One example is a hybrid movement in which the first several rounds operate as some form of a Mitchell movement and the last several rounds split the field into separate Howell movements for the pairs who were stationary and for the pairs who rotated.

Normal Mitchell MovementsEdit

The Standard Mitchell Movement, also known as Straight Mitchell Movement, has two separate groups of players. One group always sits North-South and remains at the same table through all rounds of play. The other group always sits East-West. At the end of each round, the pairs sitting East-West move up one table, with the pair at the last table going to the first table, and the boards (deals) move down one table, with boards from the first table going to the last table. Thus, the North-South pairs play consecutive groups of boards while the East-West players play alternate groups of boards as the movement progresses. Pairs usually are identified by the number of the table at which they start and their direction of play (for example, Pair 3 North-South or Pair 5 East-West). The North-South and East-West fields usually are scored and ranked separately, producing a winner in each direction, but combining both fields for ranking is an option (see below). The table below shows the East-West pair (EW) and the board group (BG) at each table in a Standard Mitchell Movement for five tables with five rounds of play.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 5 BG B EW 4 BG C EW 3 BG D EW 2 BG E
2 EW 2 BG B EW 1 BG C EW 5 BG D EW 4 BG E EW 3 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 5 BG A EW 4 BG B
4 EW 4 BG D EW 3 BG E EW 2 BG A EW 1 BG B EW 5 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D

The board groups are designated by letters in the preceding table because the specific boards in each group depends upon the number of deals in the game, as shown in the following table. A normal game for intermediate to advanced players would play 25 boards with this movement, while beginners typically would play fewer boards -- but the movement also can run with fewer boards if it's desirable to hold a shorter game for some other reason. Thirty boards typically would be used only in certain championship events.

Total Boards Played 10 15 20 25 30
Board Group A Boards 1-2 Boards 1-3 Boards 1-4 Boards 1-5 Boards 1-6
Board Group B Boards 3-4 Boards 4-6 Boards 5-8 Boards 6-10 Boards 7-12
Board Group C Boards 5-6 Boards 7-9 Boards 9-12 Boards 11-15 Boards 13-18
Board Group D Boards 7-8 Boards 10-12 Boards 13-16 Boards 16-20 Boards 19-24
Board Group E Boards 9-10 Boards 13-15 Boards 17-20 Boards 21-25 Boards 25-30

In a complete Mitchell movement, the number of rounds is equal to the number of tables and the number of board groups in play so each North-South pair plays against each East-West pair and all contestants play all of the deals in the session. It's possible to play an incomplete movement consisting of fewer rounds, but the variation known as a Web movement, described below, typically is a better option because it allows all pairs to play all of the deals (boards) in play during the session.

A Straight Mitchell Movement requires an odd number of tables so that the East-West pairs interleave with the boards that they have already played when they reach the midpoint of the movement. With an even number of tables, the East-West pairs would meet boards that they played in the first round at the midpoint of the complete movement so this situation requires a variation of the movement. The most common modifications are a Skip Mitchell if number of tables does not allow a complete movement or the Relay and Bye Stand Mitchell (also called a Relay and Share Mitchell in the United Kingdom) for a complete movement.

When there is an odd number of pairs, the most common practice is to add a phantom pair to complete the final table. Thus, a game with seventeen pairs uses a movement for nine tables with one position vacant. The phantom pair, which may be in either direction, follows the same progression as the missing actual pair. The pairs playing in the opposite direction "sit out" when scheduled to play the phantom pair, and do not play the respective deals (boards). However, the Rover Mitchell Movement and Two-Way Rover Mitchell Movement described below, in which the odd pair displaces a different pair each round with the displaced pair sitting out, also are options in this situation.

Skip Mitchell MovementEdit

The Skip Mitchell Movement is the simplest Mitchell movement for an even number of tables. When the East-West pairs come to the midpoint of the (complete) movement, and thus would encounter the deals (boards) that they played in the first round, they simply skip a table to play the boards that they crossed at the end of the first round. The boards that they play after the skip to interleave with the boards that they played before the skip with normal movement thereafter, as in a straight Mitchell. However, the skip limits the number of rounds to one less than the number of tables. Thus, a Skip Mitchell is normally preferred only when the number of tables makes a complete movement impracticable. The following table shows a Skip Mitchell movement for five rounds and six tables.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 6 BG B EW 5 BG C EW 3 BG D EW 2 BG E
2 EW 2 BG B EW 1 BG C EW 6 BG D EW 4 BG E EW 3 BG F
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 5 BG F EW 4 BG A
4 EW 4 BG D EW 3 BG E EW 2 BG F EW 6 BG A EW 5 BG B
5 EW 5 BG E EW 4 BG F EW 3 BG A EW 1 BG B EW 6 BG C
6 EW 6 BG F EW 5 BG A EW 4 BG B EW 2 BG C EW 1 BG D

It is very easy to accommodate players who arrive after a Standard Mitchell Movement or a Skip Mitchell Movement is set. The director need only place additional board groups on additional tables and add or remove the skip, depending upon whether the number of tables becomes even or odd.

American Whist League (AWL) MovementEdit

The American Whist League (AWL) Movement is a variation of the Standard Mitchell Movement in which the East-West pairs move down two tables rather than up one table. The following table shows the AWL Movement for five tables.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 3 BG B EW 5 BG C EW 2 BG D EW 4 BG E
2 EW 2 BG B EW 4 BG C EW 1 BG D EW 3 BG E EW 5 BG A
3 EW 3 BG C EW 5 BG D EW 2 BG E EW 4 BG A EW 1 BG B
4 EW 4 BG D EW 1 BG E EW 3 BG A EW 5 BG B EW 2 BG C
5 EW 5 BG E EW 2 BG A EW 4 BG B EW 1 BG C EW 3 BG D

Although it is a legal movement, the AWL movement is seldom used in standard Duplicate Bridge games because it offers no advantage whatsoever over a Standard Mitchell Movement. Rather, stripped of the first round, the AWL Movement finds its niche in "Board-a-Match" (BAM) team competition, as discussed below. Note that the numbers of the North-South pair (table) and the East-West pair playing each group of boards in Round 2 and Round 5 are reversed, and the same is true of the numbers of the North-South pair (table) and the East-West pair playing each group of boards in Round 3 and Round 4. In BAM competition, the North-South and East-West pair numbers are the two partnerships of the respective team.

Relay and Bye Stand Mitchell (or Share and Relay Mitchell)Edit

The Relay and Bye Stand Mitchell, also called a Share and Relay Mitchell in the United Kingdom, modifies the board sequencing of a standard Mitchell movement so that each East-West pair plays the even groups of boards on one side of the movement and odd board groups on the other side of the movement, permitting a complete movement with an even number of tables. To make this happen, two consecutive tables play the same group of boards in each round throughout the session while the opposite group of boards sits out of play on a table or stand between the tables directly opposite the tables that are playing the same deals -- and it is here that regional differences in terminology may be a source of confusion.

  • In the American Contract Bridge League (ACBL), the tables sharing boards are called a "relay" and the table or stand that holds the boards that are out of play is called a "bye stand."
  • But in the English Bridge Union (EBU), the tables sharing boards are called a "share" and the table or stand that holds the boards that are out of play is called a "relay."

The following table shows a Relay and Bye Stand Mitchell for eight tables with the relay between Table 2 and Table 3 and the bye stand between Table 6 and Table 7.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8
1 EW 1 BG A EW 8 BG B EW 7 BG C EW 6 BG D EW 5 BG E EW 4 BG F EW 3 BG G EW 2 BG H
2 EW 2 BG B EW 1 BG C EW 8 BG D EW 7 BG E EW 6 BG F EW 5 BG G EW 4 BG H EW 3 BG A
3 EW 3 BG B EW 2 BG C EW 1 BG D EW 8 BG E EW 7 BG F EW 6 BG G EW 5 BG H EW 4 BG A
4 EW 4 BG C EW 3 BG D EW 2 BG E EW 1 BG F EW 8 BG G EW 7 BG H EW 6 BG A EW 5 BG B
5 EW 5 BG D EW 4 BG E EW 3 BG F EW 2 BG G EW 1 BG H EW 8 BG A EW 7 BG B EW 6 BG C
6 EW 6 BG E EW 5 BG G EW 4 BG G EW 3 BG H EW 2 BG A EW 1 BG B EW 8 BG C EW 7 BG D
Bye Stand BG F BG G BG H BG A BG B BG C BG D BG E
7 EW 7 BG G EW 6 BG H EW 5 BG A EW 4 BG B EW 3 BG C EW 2 BG D EW 1 BG E EW 8 BG F
8 EW 8 BG H EW 7 BG A EW 6 BG B EW 5 BG C EW 4 BG D EW 3 BG E EW 2 BG F EW 1 BG G

Physical sharing of boards can slow down the progress of the game, especially when playing only two or three boards per round, and many players find the physical exchange of boards to be an inconvenience. With electronic scoring, it also increases the risk that players may forget to override the default board numbers supplied by the scoring system and thus enter results for the wrong boards. There are three solutions to this.

  • With an odd number of pairs, the director can position the phantom pair North-South at one of the tables that would share boards, creating a sit-out for East-West pairs at that table. The boards simply skip the phantom's table in the movement cycle.
  • In an event with two identical sections, the director can position the tables sharing boards at opposite points in the movement so that each section's share can use the boards on the other section's bye stand.
  • If a modern board duplicating machine is available, the director can duplicate an additional set of boards for one of the two tables that are playing the same deals. If there are two or more sections with an even number of tables, the director can position the tables sharing boards at a different location in each section so one extra set of boards can supply one of the tables playing the same boards in all of the affected sections.

Each of these options creates a more pleasant experience for the players while reducing the risk of scoring errors.

When using two sets of boards in the same, some directors prefer to have each set of boards played at about half of the tables that are not part of the share so that there are valid comparisons on any boards discovered to have been misdealt.

  • One option is to use one set of boards on one side of the movement, as demarked by the relay and bye stand (or share and relay). In the example movement above, Tables 1, 2, 7, and 8 would play one set of boards, with boards entering at Table 2 and exiting at Table 7, and Tables 3, 4, 5, and 6 would play the other, with boards entering at Table 7 and exiting at Table 3. The remaining boards of each set usually are placed on stands next to the respective table where they will enter. During the last round of the first half of the movement (Round 4 in the example), the director brings the boards that have exited on each side to the stand next to table where they will reenter later in the session.
  • Another option is to have one set of boards enter at the table with the lower number of the two tables that play the same deals in each round (or the table with the highest number if it plays the same deals as Table 1) and retire the other set of boards after play at the table with the higher number of the two tables that play the same deals in each round (or Table 1 if it plays the same deals as the table with the highest number). In the above example, one set of boards would enter at Table 2 and the other set of boards would be retired after Table 3 plays them.

The first of these options is generally preferable when both board sets are available at the start of the session, as it provides an equal number of plays of each version of every misdealt board. However, the latter option allows the director to complete duplication of the second set of boards after play has started.

Crisscross Mitchell Movement (or Double Weave Mitchell Movement)Edit

The Crisscross Mitchell Movement alters the movement of players and boards in a Standard Mitchell Movement to permit a complete movement without a relay and bye stand (or share and relay) if the number of tables is a multiple of four (4). This movement is used most commonly with eight or twelve tables, but it also can be used with four or sixteen tables.

  • The even-numbered East-West pairs and the odd-numbered East-West pairs move in contrary directions, so that pairs moving up trade places ("crisscross") with pairs at the next higher table moving down at the end of each round.
  • The boards move in the opposite direction from the East-West pairs leaving each table, thus also crisscrossing with the next higher or lower table, except at the midpoint of the movement when the boards go to the opposite table in the movement (also a crisscross) and reverse direction.

Thus, the odd East-West pairs play the odd board groups in the first half of the movement and the even board groups in the second half of the movement and the even East-West pairs play the even board groups do the reverse.

The following table shows a Crisscross Mitchell Movement for eight tables.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8
1 EW 1 BG A EW 8 BG B EW 3 BG G EW 6 BG D EW 5 BG H EW 4 BG C EW 7 BG F EW 2 BG E
2 EW 2 BG B EW 3 BG A EW 8 BG D EW 5 BG G EW 6 BG C EW 7 BG H EW 4 BG E EW 1 BG F
3 EW 3 BG C EW 2 BG D EW 5 BG A EW 8 BG F EW 7 BG B EW 6 BG E EW 1 BG H EW 4 BG G
4 EW 4 BG D EW 5 BG C EW 2 BG F EW 7 BG A EW 8 BG E EW 1 BG B EW 6 BG G EW 3 BG H
5 EW 5 BG E EW 4 BG F EW 7 BG C EW 2 BG H EW 1 BG D EW 8 BG G EW 3 BG B EW 6 BG A
6 EW 6 BG F EW 7 BG E EW 4 BG H EW 1 BG C EW 2 BG G EW 3 BG D EW 8 BG A EW 5 BG B
7 EW 7 BG G EW 6 BG H EW 1 BG E EW 4 BG B EW 3 BG F EW 2 BG A EW 5 BG D EW 8 BG C
8 EW 8 BG H EW 1 BG G EW 6 BG B EW 3 BG E EW 4 BG A EW 5 BG F EW 2 BG C EW 7 BG D

One noteworthy feature of the Crisscross Mitchell Movement is that it has the same set-up as a Straight Mitchell Movement with one additional table. Thus, the director can add a table to accommodate players who arrive after the movement has been set or, conversely, can retreat to this movement after setting a Straight Mitchell Movement for one additional table if players who are running late fail to show or if a pair scheduled to have the first sit-out decides to withdraw.

Two Stanza Mitchell MovementEdit

A Two Stanza Mitchell Movement is a movement configured for a break, which could be for lunch, for a presentation of some award or recognition, for election of club officers or transaction of club business requiring discussion and vote of the membership, or for some other purpose, at the midpoint of the session. In this situation, it's best to have all entrants play approximately the first half of the deals before the break, constituting the first stanza, and the remaining deals after the break, constituting the second stanza, so that any discussion of deals that may occur during the break won't affect the play of any deals in the remaining rounds. The following table shows a Two Stanza Mitchell Movement for six tables with a break after the third round. The players and boards move in the normal manner for a Mitchell movement, except that all boards played in the first stanza go out of play and new boards come into play at the break.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6
1 EW 1 BG A EW 6 BG B EW 5 BG C EW 4 BG D EW 3 BG E EW 2 BG F
2 EW 2 BG B EW 1 BG C EW 6 BG A EW 5 BG E EW 4 BG F EW 3 BG D
3 EW 3 BG C EW 2 BG A EW 1 BG B EW 6 BG F EW 5 BG D EW 4 BG E
4 EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D EW 6 BG E EW 5 BG F
5 EW 5 BG B EW 4 BG C EW 3 BG A EW 2 BG E EW 1 BG F EW 6 BG D
6 EW 6 BG C EW 5 BG A EW 4 BG B EW 3 BG F EW 2 BG D EW 3 BG E

The pattern of movement shown in this example will work for any even number of tables that is not a multiple of four, provided that the number of rounds is equal to the number of tables. Another option, for any even number of tables, is to use the American Whist League (AWL) movement, described above, within each stanza with East-West pairs moving just one table, either up or down, at the break. Alternatively, there are specific movement patterns for eight tables and twelve tables.

>> With eight tables, all East-West pairs move up two tables after each round except at the midpoint, when they move up just one table. Thus, the odd-numbered East-West pairs visit the odd-numbered tables in the first stanza and the even-numbered tables in the second stanza while the even-numbered East-West pairs do the reverse.

>> With twelve tables, all East-West pairs move normally (that is, up one table after each round) except after Round 3 and Round 9, when they move up four (4) tables. Thus, the East-West pairs skip three tables after Round 3, but return to play at those tables in the last three rounds.

It's also possible to use the Double Web Movement, described below, to accommodate any number of tables. If the number of rounds is a multiple of four, this typically requires that the break be either one round before or one round after the exact midpoint of the movement (that is, after either Round 3 or Round 5 if the movement is eight rounds or after either Round 5 or Round 7 if the movement is twelve rounds).

It's also possible to configure movements with more than two stanzas to accommodate more than one break during a session, if circumstances suggest this.

Scissors Mitchell MovementEdit

The Scissors Mitchell Movement is an interesting creature. The movement begins like a Standard Mitchell Movement, but it has two scissors rounds where each board group is split in half. In the first scissors round, which must be in the first half of the movement, each table plays one half of the boards in the board group that it receives, then passes those boards to the next lower table, which also plays them, while retaining but not playing the other half of the boards in the board group that it received initially. At the end of the first scissors round, the boards played twice get passed again and join the boards not played in the previous round at that table to form a new board group. The new board group remains intact until the second scissors round, which is half of the total number of rounds after the first. In the second scissors round, the boards played twice in the first scissors round are set aside and the boards not played in the second scissors round are played twice in the same manner. After the second scissors round, the boards played twice are passed again to reconstitute the original board group. The following table shows a Scissors Mitchell Movement of six tables playing six full rounds, with the halves of the initial board groups designated numerically (that is, the initial board group A consists of halves A1 and A2).

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6
1 EW 1 BG A1,A2 EW 6 BG B1,C1 EW 5 BG D1,B2 EW 4 BG E1,C2 EW 3 BG D2,E2 EW 2 BG F1,F2
2 EW 2 BG B1,B2 EW 1 BG C1,D1 EW 6 BG E1,C2 EW 5 BG F1,D2 EW 4 BG E2,F2 EW 3 BG A1,A2
3 EW 3 BG C1,C2 EW 2 BG D1,E1 EW 1 BG F1,D2 EW 6 BG A1,E2 EW 5 BG F2,A2 EW 4 BG B1,B2
4 EW 4 BG D1,D2 EW 3 BG E1,F1 EW 2 BG A1,E2 EW 1 BG B1,F2 EW 6 BG A2,B2 EW 5 BG C1,C2
5 EW 5 BG E1,E2 EW 4 BG F1,A1 EW 3 BG B1,F2 EW 2 BG C1,A2 EW 1 BG B2,C2 EW 6 BG D1,D2
6 EW 6 BG F1,F2 EW 5 BG A1,B1 EW 4 BG C1,A2 EW 3 BG D1,B2 EW 2 BG C2,D2 EW 1 BG E1,E2

Most Bridge scoring programs expect board groups to be invariant throughout the entire movement, so it may take a bit of creativity to get a program to score this type of movement. The external movement M0612 supplied with the ACBLscore® program distributed by the American Contract Bridge League, for example, implements a Scissors Mitchell Movement for six tables as twelve (half) rounds with both pairs remaining at each table for two consecutive (half) rounds and half of each initial board group assigned to each (half) round so that the halves of each initial board group can move separately.

Rover Mitchell Movement (or Bump Mitchell Movement)Edit

A Rover Mitchell Movement, also called a Bump Mitchell Movement, is a modification of a Mitchell movement to accommodate an odd number of pairs without a phantom. This movement is most commonly employed to accommodate a pair who arrives after a movement is set, since it does not require addition of another table, or in situations in which there is not space for another table. In its standard form, the roving pair displaces only North-South or East-West pairs and scores in the respective field. The roving pair usually sits out in the first round, and other pairs sit out in subsequent rounds when the roving pair displaces them. The following table illustrates an East-West Rover Mitchell Movement for five tables playing five rounds; the roving pair is East-West Pair 6. Note that East-West Pair 5 is not "bumped" and thus plays all of the boards in the session.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 5 BG B EW 4 BG C EW 6 BG D EW 2 BG E
2 EW 2 BG B EW 6 BG C EW 5 BG D EW 4 BG E EW 3 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 5 BG A EW 6 BG B
4 EW 4 BG D EW 3 BG E EW 6 BG A EW 1 BG B EW 5 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
(Sit-Out) EW 6 EW 1 EW 2 EW 3 EW 4

The generation of a Rover Mitchell Movement involves some fairly complex number theory. If the number of full tables is a prime number greater than four, the roving pair can start anywhere and move either up or down two tables in each round, thus displacing and encountering a different East-West pair, a different North-South pair, and a different group of boards in each round. However, the generation of Rover Mitchell Movement is considerably more difficult if the number of tables is not prime because the roving pair typically must move in an irregular manner to avoid both the deals and the pairs that it has encountered or displaced in the preceding rounds.

If another pair arrives after a Rover Mitchell Movement has been set, it's possible to add a "party table" to the Rover Mitchell Movement. The pair that arrives late becomes a stationary pair at the party table, playing the boards that the roving pair otherwise would not play against the roving pair in the first round and the boards that the roving pair is playing against the pair displaced by the roving pair in each subsequent round. The following table shows the Rover Mitchell Movement above with the addition of a party table (in this example, Table 6, with the added pair becoming North-South Pair 6). It's best to duplicate a separate set of boards for the "party table" because the "party table" plays the same deals as each of the other tables in one round, creating an awkward situation with actual sharing of boards.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 5 BG B EW 4 BG C EW 6 BG D EW 2 BG E
2 EW 2 BG B EW 6 BG C EW 5 BG D EW 4 BG E EW 3 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 5 BG A EW 6 BG B
4 EW 4 BG D EW 3 BG E EW 6 BG A EW 1 BG B EW 5 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
6 EW 6 BG E EW 1 BG C EW 2 BG A EW 3 BG D EW 4 BG B
Web MovementEdit

The Web Movement is a variation of the standard Mitchell movement in which there are more tables than rounds, but all pairs play all of the boards (deals) that are in play. There is one mathematical constraint – a Web movement with an odd number of tables must have an odd number of rounds. A Web movement with an even number of rounds requires that East-West pairs skip a table at the midpoint of the movement, so East–West pairs would skip a table after the sixth round in a twelve-round Web movement.

The actual web in a web movement always consists of an even number of tables not exceeding twice the number of rounds, split into two subsections of equal size. The first subsection plays the groups of boards in normal (ascending) order while the second subsection plays the groups of board in reverse (descending) order, sequenced so the boards move normally within each subsection, with additional groups of boards on a bye stand next to the highest table of each subsection. The East-West pairs move normally (up one table each round except in the case of a skip) within or through the web. The Web Movement in which six tables play five rounds, shown in the following table, illustrates how this works.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 6 BG B EW 5 BG C EW 4 BG D EW 3 BG E
2 EW 2 BG B EW 1 BG C EW 6 BG D EW 5 BG E EW 4 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 6 BG A EW 5 BG B
Bye Stand BG D, BG E BG E, BG A BG A, BG B BG B, BG C BG C, BG D
4 EW 4 BG B EW 3 BG A EW 2 BG E EW 1 BG D EW 6 BG C
5 EW 5 BG A EW 4 BG E EW 3 BG D EW 2 BG C EW 1 BG B
6 EW 6 BG E EW 5 BG D EW 4 BG C EW 3 BG B EW 2 BG A
Bye Stand BG D, BG C BG C, BG B BG B, BG A BG A, BG E BG E, BG D

One can prepend any number of additional subsections in which the number of tables is equal to the number of rounds onto any web, but each additional subsection requires an additional copy of the boards for the movement to run smoothly. Since the number of tables in the actual web must be even, this capability is what allows use of a Web Movement to play an odd number of rounds when the number of tables is odd. The following table shows the Web movement for eleven tables playing five rounds, obtained by prepending one subsection of five tables to the web in the preceding example (now at tables 6-11). The groups of boards move normally between the prepended subsection(s) and the lower half of the web, with boards from Table 1 going to the bye stand at the highest table in the lower subsection of the actual web (Table 8 in this example).

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 11 BG B EW 10 BG C EW 9 BG D EW 8 BG E
2 EW 2 BG B EW 1 BG C EW 11 BG D EW 10 BG E EW 9 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 11 BG A EW 10 BG B
4 EW 4 BG D EW 3 BG E EW 2 BG A EW 1 BG B EW 11 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
6 EW 6 BG A EW 5 BG B EW 4 BG C EW 3 BG D EW 2 BG E
7 EW 7 BG B EW 6 BG C EW 5 BG D EW 4 BG E EW 3 BG A
8 EW 8 BG C EW 7 BG D EW 6 BG E EW 5 BG A EW 4 BG B
Bye Stand BG D, BG E BG E, BG A BG A, BG B BG B, BG C BG C, BG D
9 EW 9 BG B EW 8 BG A EW 7 BG E EW 6 BG D EW 5 BG C
10 EW 10 BG A EW 9 BG E EW 8 BG D EW 7 BG C EW 6 BG B
11 EW 11 BG E EW 10 BG D EW 9 BG C EW 8 BG B EW 7 BG A
Bye Stand BG D, BG C BG C, BG B BG B, BG A BG A, BG E BG E, BG D

In the special case in which prepended subsections reduce the actual web to just two tables as in the following example of a web of seven tables playing five rounds, it's possible to use just one set of the boards for both sides of the web. In this situation, the two tables in the web play the same group of boards only in the middle round if the number of rounds is odd, as illustrated by the following table showing a web of ten tables playing five rounds (with asterisks indicating the shared group of boards in the middle round). The simplest board movement is that boards played at the highest table go to a bye stand at the next lower table and boards played at Table 1 going to the bye stand next to the highest table, as this movement remains constant throughout.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 12 BG B EW 11 BG C EW 10 BG D EW 9 BG E
2 EW 2 BG B EW 1 BG C EW 12 BG D EW 11 BG E EW 10 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 12 BG A EW 11 BG B
4 EW 4 BG D EW 3 BG E EW 2 BG A EW 1 BG B EW 12 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
6 EW 6 BG A EW 5 BG B EW 4 BG C EW 3 BG D EW 2 BG E
7 EW 7 BG B EW 6 BG C EW 5 BG D EW 4 BG E EW 3 BG A
8 EW 8 BG C EW 7 BG D EW 6 BG E EW 5 BG A EW 4 BG B
9 EW 9 BG D EW 8 BG E EW 7 BG A EW 6 BG B EW 5 BG C
10 EW 10 BG E EW 9 BG A EW 8 BG B EW 7 BG C EW 6 BG D
11 EW 11 BG A EW 10 BG B EW 9 BG C* EW 8 BG D EW 7 BG E
Bye Stand BG B, BG C BG C, BG E BG D, BG E BG E BG A, BG B
12 EW 12 BG E EW 11 BG D EW 10 BG C* EW 9 BG B EW 8 BG A
Bye Stand BG D BG A BG B, BG A BG A, BG C BG C, BG D

The number of tables in a web can be twice the number of rounds, but it's better to reduce the web to zero tables with two prepended subsections since this arrangement allows all boards to move in the normal manner of a Standard Mitchell Movement. To illustrate this point, the following tables show a web for ten tables playing five rounds (top) and the non-web alternative (bottom). The only difference is the boards in play the last plays the board groups in their natural order rather than in reverse order.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 10 BG B EW 9 BG C EW 8 BG D EW 7 BG E
2 EW 2 BG B EW 1 BG C EW 10 BG D EW 9 BG E EW 8 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 10 BG A EW 9 BG B
4 EW 4 BG D EW 3 BG E EW 2 BG A EW 1 BG B EW 10 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
6 EW 6 BG D EW 5 BG C EW 4 BG B EW 3 BG A EW 2 BG E
7 EW 7 BG C EW 6 BG B EW 5 BG A EW 4 BG E EW 3 BG D
8 EW 8 BG B EW 7 BG A EW 6 BG E EW 5 BG D EW 4 BG C
9 EW 9 BG A EW 8 BG E EW 7 BG D EW 6 BG C EW 5 BG B
10 EW 10 BG E EW 9 BG D EW 8 BG C EW 7 BG B EW 6 BG A
Table Round 1 Round 2 Round 3 Round 4 Round 5
1 EW 1 BG A EW 10 BG B EW 9 BG C EW 8 BG D EW 7 BG E
2 EW 2 BG B EW 1 BG C EW 10 BG D EW 9 BG E EW 8 BG A
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 10 BG A EW 9 BG B
4 EW 4 BG D EW 3 BG E EW 2 BG A EW 1 BG B EW 10 BG C
5 EW 5 BG E EW 4 BG A EW 3 BG B EW 2 BG C EW 1 BG D
6 EW 6 BG A EW 5 BG B EW 4 BG C EW 3 BG D EW 2 BG E
7 EW 7 BG B EW 6 BG C EW 5 BG D EW 4 BG E EW 3 BG A
8 EW 8 BG C EW 7 BG D EW 6 BG E EW 5 BG A EW 4 BG B
9 EW 9 BG D EW 8 BG E EW 7 BG A EW 6 BG B EW 5 BG C
10 EW 10 BG E EW 9 BG A EW 8 BG B EW 7 BG C EW 6 BG D
Double Web MovementsEdit

Web movements are normally used in larger games in which a complete Mitchell movement is impracticable. However, they are also useful in situations in which it is desirable to have a break (for lunch, for presentation of awards or transaction of club business, or for any other reason) in the middle of a session. The use of a movement consisting of two stanzas, each of which is itself a Web Movement, ensures that any discussion of deals that might occur during the break won't compromise the play of those deals after the break. The following table shows a movement for eight tables in which the first five rounds are the first Web Movement and the last three rounds are the second Web Movement. This movement will run very smoothly with two copies of the boards in Board Groups A-E and three copies of the boards in Board Groups F-H, with Table 7 and Table 8 sharing one copy of Board Group G in Round 7.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8
1 EW 1 BG A EW 8 BG B EW 7 BG C EW 6 BG D EW 5 BG E EW 4 BG F EW 3 BG G EW 2 BG H
2 EW 2 BG B EW 1 BG C EW 8 BG D EW 7 BG E EW 6 BG A EW 5 BG G EW 4 BG H EW 3 BG F
3 EW 3 BG C EW 2 BG D EW 1 BG E EW 8 BG A EW 7 BG B EW 6 BG H EW 5 BG F EW 4 BG G
4 EW 4 BG D EW E BG E EW 2 BG A EW 1 BG B EW 8 BG C EW 7 BG F EW 6 BG G EW 5 BG H
Bye Stand BG E BG A BG B BG C BG D
5 EW 5 BG C EW 4 BG B EW 3 BG A EW 2 BG E EW 1 BG D EW 8 BG G EW 7 BG H EW 6 BG F
6 EW 6 BG B EW 5 BG A EW 4 BG E EW 3 BG D EW 2 BG C EW 1 BG H EW 8 BG F EW 7 BG G
7 EW 7 BG A EW 6 BG E EW 5 BG D EW 4 BG C EW 3 BG B EW 2 BG F EW 1 BG G* EW 8 BG H
8 EW 8 BG E EW 7 BG D EW 6 BG C EW 5 BG B EW 4 BG A EW 3 BG H EW 2 BG G* EW 1 BG F
Bye Stand BG D BG C BG B BG A BG E BG G BG F, BG H BG G
  • - Table 7 and Table 8 share boards in this round unless a fourth copy of Board Group G is available.
Bowman MovementEdit

The Bowman Movement is the specific case of the Web Movement (see above) that consists of a web of two tables with one add-on block. The next to last table plays the same group of boards as Table #1 in each round, and the last table plays the board groups in reverse order beginning with the last board group. It's theoretically possible to run this movement with only one set of boards as described in the linked article, but players will not like it -- especially if there's no sit-out, as the last table shares boards with a different table in each round, with a three-way share between Table 1 and the last two tables in the middle round if the number of rounds is odd. It's considerably less intolerable if with a phantom pair seated North-South at the last table, leaving the between Table 1 and the next to last table as the only active share. Still, it is better to use two copies of the boards -- essentially, one copy for the last two tables and the other for the rest of the room, so the last two tables share a group of boards only in the middle round if the number of rounds is odd.

"One Winner" Mitchell MovementsEdit

In its most basic form, "One Winner" Mitchell Movement operates in the same manner as a Standard Mitchell Movement but combines all pairs into one field for ranking of results. The pairs seated North-South retain the numbers of their tables, but drop the designation of direction. The pairs seated East-West add the number of tables to their respective starting table to determine their pair numbers. All of the variants of the Mitchell Movement described above can convert to a corresponding "one winner" variant in this manner. Thus, way of example, one can have a "One Winner" Relay and Bye Stand Mitchell Movement or a "One Winner" Web Movement.

Scrambled Mitchell MovementEdit

The direct conversion of any Mitchell movement into a "One Winner" movement can create unfairness, especially if the pairs seated in one direction are considerably stronger than those seated in the other direction or if one direction has pairs with considerable disparity in strength and the other direction has pairs of nearly equal strength. The Scrambled Mitchell movement changes the direction of play at most or all of the tables, customarily achieved by rotating the orientation of the table by one seat position and thus dubbed an "arrow switch" so the stationary pairs do not physically change seats, to remove, or at least greatly diminish, this disparity. The pairs that start North-South remain at the same table for the entire session and the pairs who start East-West continue to move after each round, even when they play in the opposite direction.

The selection of rounds with arrow switches affects the fairness of the result. The objective is for competitors who play against each other to have the same weighting as those who do not. If r is the number of rounds and s is the number of rounds in which all tables arrow switch, the pairs who play as opponents in the rounds that are not arrow switched have a relative influence of (r-1) for the board group played head to head, -(r-1-2s) for board groups played in opposite direction at different tables, and 2s for rounds played in the same direction for a total influence of (4s), while pairs that start in the same direction have a relative influence of (r-2s) for boards played in the same direction and -2s for boards played in opposite directions, for a total influence of (r-4s) in the absence of arrow switches on the same boards. Equating 4s=r-4s to equalize the influence yields the optimal solution s=r/8. Thus, the English Bridge Union determined that arrow switches at all tables on approximately one eighth (1/8) of the rounds provides the best achievable balance and thus formally recommends this practice. This roughly translates into arrow switches at all tables of the last round when playing six to nine rounds and in the last two rounds when playing twelve or thirteen rounds. Of course, the balance is not perfect -- the entrants who have arrow switches on the same group of boards, including those who play against each other on the rounds in which the arrow switches occur, are outliers.

The principle of using arrow switches to diminish unfairness extends to all of the variants of "One Winner" Mitchell Movements described below.

Two-Way Rover Mitchell Movement (or Two-Way Bump Mitchell Movement)Edit

The Two-Way Rover Mitchell Movement, also called a Two-Way Bump Mitchell Movement, is conceptually the same as the Rover Mitchell Movement described above, but the roving pair plays in both directions, bumping the North-South pair for half of the boards and the East-West pair at the same table for the other half of the boards in each round with the first bump occurring in the second half of the first round, thus cutting the duration of the sit-out in half. These movements, which require "One Winner" scoring because the roving pair has comparisons in both directions, are most commonly used for games with either thirteen or fifteen pairs, the respective underlying movements being the "one winner" variants of a Relay and Bye Stand Mitchell Movement for six full tables and a Straight Mitchell Movement for seven full tables. In this movement, the pairs that start East-West add the number of full tables to the number of their starting tables to obtain their pair number, and the roving pair receives the highest pair number. The original versions of these movements did not use arrow switches, but a common variation incorporates arrow switches in the last round to obtain a fairer balance of comparisons. The following table shows a Two-Way Rover Mitchell Movement for 4 1/2 tables with the underlying movement being the Crisscross Mitchell Movement.

Table Round 1 Round 2 Round 3 Round 4
1 1v5 BG A1,A2 1v8 BG B1,B2 9v7 BG D1 1v8 BG C1,C2
1v9 BG D2
2 2v6 BG B1 2v7 BG A1,A2 2v8 BG C1,C2 2v5 BG D1,D2
9v6 BG B2
3 3v7 BG C1,C2 3v6 BG D1,D2 3v5 BG B1,B2 9v8 BG A1
3v9 BG A2
4 4v8 BG D1,D2 9v5 BG C1 4v6 BG A1,A2 4v7 BG B1,B2
4v9 BG C2
Sit-out 9/2 4/5 1/7 3/8

If a pair arrives after either of these movements is set, it's possible to add a "party table" in the same manner as with the normal Rover Mitchell Movement described above. The pair that remains at the "party table" receives the new highest pair number and the other pairs retain the numbers already assigned. Note that each displaced pair should sit opposite its normal direction while playing at the "party table" to obtain a better balance of comparisons. Thus, both the pair that remains at the party table and the roving pair play half of boards of each round in each direction. The following table shows the addition of a "party table" to the above movement.

Table Round 1 Round 2 Round 3 Round 4
1 1v5 BG A1,A2 1v8 BG B1,B2 9v7 BG D1 1v8 BG C1,C2
1v9 BG D2
2 2v6 BG B1 2v7 BG A1,A2 2v8 BG C1,C2 2v5 BG D1,D2
9v6 BG B2
3 3v7 BG C1,C2 3v6 BG D1,D2 3v5 BG B1,B2 9v8 BG A1
3v9 BG A2
4 4v8 BG D1,D2 9v5 BG C1 4v6 BG A1,A2 4v7 BG B1,B2
4v9 BG C2
5 10v9 BG B1 10v4 BG C1 10v1BG D1 10v3 BG A1
9v2 BG B2 5v10 BG C2 7v10 BG D2 8v10 BG A2
Hesitation Mitchell MovementEdit

The basic Hesitation Mitchell movement allows play of one round more than the number of tables (eight rounds with seven tables, for example). The rotating pairs play in both directions at the hesitation table, which is usually the table with the highest number, before going on to the next table, and thus play the pairs before and after them in the rotation as well as the stationary pairs. The additional group of boards is on a bye stand directly opposite the hesitation table. The following table shows a Hesitation Mitchell Movement for five tables. The pair numbers show the North-South pair first and the East-West pair second, so "1v6" means Pair 1 plays North-South and Pair 6 plays East-West.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6
1 1v6 BG A 1v5 BG B 1v10 BG C 1v9 BG D 1v8 BG E 1v7 BG F
2 2v7 BG B 2v6 BG C 2v5 BG D 2v10 BG E 2v9 BG F 2v8 BG A
Bye Stand BG C BG D BG E BG F BG A BG B
3 3v8 BG D 3v7 BG E 3v6 BG F 3v5 BG A 3v10 BG B 3v9 BG C
4 4v9 BG E 4v8 BG F 4v7 BG A 4v6 BG B 4v9 BG C 4v10 BG D
5 5v10 BG F 10v9 BG A 9v8 BG B 8v7 BG C 7v6 BG D 6v5 BG E

A Double Hesitation Mitchell Movement has two points where moving pairs play North-South, though not normally at directly rotating tables. With an even number of tables, this allows two more rounds to be played than the number of tables. Thus, six tables can play eight rounds of three boards rather than six rounds of four boards. Two bye stand tables will also be needed. The position of the rotations and bye stand tables must be chosen precisely to prevent a conflict.

The Hesitation Mitchell Movement and Double Hesitation Mitchell Movement must be One Winner movements because the moving pairs play in both directions at one or two table. Some variations introduce arrow switches at the tables with stationary pairs to obtain better balance of comparisons.

Howell MovementsEdit

In a Howell Movement, most of the pairs rotate from table to table in a progression that causes each pair to play against most or all of the other pairs for one round and each pair to play all of the boards (deals) in play during the session. All moving pairs follow the same progression, so each pair goes to the position occupied by the pair with the next lower number in the preceding round with Pair #1 going to the place occupied by the pair with the number equal to the number of rounds. The pair with the highest number sits North-South, usually but not always at Table 1,[4] and does not move from that position. The moving pairs, with numbers corresponding to the respective round in which they play against the pair with the highest number, move from table to table in the same progression, sometimes sitting North-South and sometimes East-West. Thus, Pair 3 always goes to the position occupied by Pair 2 in the preceding round. If the number of rounds is less than the number of pairs by more than one, the additional pairs remain at one table for the entire session but play some rounds in each direction. The director may place a card at each table or issue a slip of paper called a guide card to each pair with the instructions for the movement.

The choice of a Howell movement does limit options to accommodate various situations.

  • The only practical way to accommodate an odd number of pairs in a Howell movement is with the addition of a phantom pair because the complexity of Howell movements make it impracticable to configure a Howell movement for a rover.
  • Except in the case of replacement of a phantom pair with a real pair, it's also impracticable to accommodate a pair that arrives after the movement is set. Each Howell movement is unique to the number of tables and the number of rounds, so one cannot simply add another table to a Howell movement.
  • Howell movements also have a limited number of stationary or quasi-stationary positions to accommodate players who have difficulty moving due to physical disabilities and other mobility impairments. The number of such positions in any Howell movement is the difference between the number of pairs and the number of rounds.
  • There's also no consistency to the location of quasi-stationary pairs among the various Howell movements, so addition or removal of a table to adjust for actual attendance may change the locations of quasi-stationary places, thus requiring relocation of players with disabilities or mobility impairments right at game time.

Howell movements for four or more tables typically sequence the tables in the reverse of the order in which they play each group of boards, with stands for the intervening boards where consecutive tables don't play consecutive board groups, so that boards move down in the same manner as in a Mitchell movement, with the caveat that a few Howell movements require the table with the highest number to share boards with Table 1.

Complete Howell MovementEdit

In a complete Howell movement, the number of rounds is one less than the number of pairs and the pair with the highest number is the only stationary pair. The following table shows a complete Howell movement for four tables, which consists of seven rounds. Note that pair numbers are indicated in the same manner as for "One Winner" variants of Mitchell movements.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7
1 8v1 BG A 8v2 BG B 8v3 BG C 8v4 BG D 8v5 BG E 8v6 BG F 8v7 BG G
(Bye Stand) BG B, C BG C, D BG D, E BG E, F BG F, G BG G, A BG A, B
2 6v3 BG D 7v4 BG E 1v5 BG F 2v6 BG G 3v7 BG A 4v1 BG B 5v2 BG D
(Bye Stand) BG E BG F BG G BG A BG B BG C BG D
3 7v2 BG F 1v3 BG G 2v4 BG A 3v5 BG B 4v6 BG C 5v7 BG D 6v1 BG E
4 4v5 BG G 5v6 BG A 6v7 BG B 7v1 BG C 1v2 BG D 2v3 BG E 3v4 BG F

A Complete Howell Movement normally is practicable only for smaller games with a few tables, as the number of rounds becomes prohibitive for normal games with eight or more tables, but it is sometimes used in tournament situations. The following table shows the practical maxima for boards per round and total boards played in a Complete Howell Movement for an open session. An event for less experienced players typically would play fewer boards per round.

Number of Tables Number of Rounds Boards per Round Total Boards
3 5 5 25
4 7 4 28
5 9 3 27
6 11 2 22
7 13 2 26
8 15 2 30

The fact that a Complete Howell Movement has only one stationary pair also limits its utility in games that must accommodate players with physical disabilities and impaired mobility.

In a Complete Howell Movement with n tables, each pair plays 2n-1 rounds -- one round against each of the other pairs and 2n-2 rounds at a different table from each of the other pairs. Ideally, each pair should play n-1 in the same direction and n-1 rounds in opposite directions at other tables with respect to each of the other pairs to achieve the proper balance of comparisons for a fair movement. There are Complete Howell Movements that achieve this for reasonable even numbers of tables, but not for reasonable odd numbers of tables. When the number of tables is odd, the Complete Howell Movements that come closest to meeting this goal have one pair with n-1 comparisons with each of the other pairs and 2n-1 pairs that have n-2 comparisons n-1 pairs, n comparisons with 1 pair, and n comparisons with the remaining n-1 pairs.[5] The consistency of this pattern is clearly suggestive of a fundamental mathematical limitation, but the present author has not yet found mathematical proof thereof. However, it this relationship strongly suggests that a pair that is an extreme outlier in terms of playing ability or ranking compared to the rest of the field -- either particularly strong or particularly weak -- should be seated in the position that has the perfectly balanced comparisons to avoid skewing the results of the rest of the field.

Complete Howell Movements for three tables, like the example shown in the following table, have major irregularities in the movement of the boards due to the limited degrees of freedom in configuring the movement. This limitation requires segmentation of the movement, with a highly irregular pattern of board movements in which all pairs play four of the five board groups in the first four rounds followed by a "free for all round" in which all three tables must share the same group of boards. The director normally will need to move the boards when running this movement, as few players understand the non-standard movements. The Extended Hesitation Mitchell Movement for three tables, described below, is usually a better choice for three tables, partly because the regular pattern of movements in the first four rounds allow it to run more smoothly and partly because it offers better accommodation for players with disabilities or impaired mobility.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 6v1 BG A 6v2 BG B 6v3 BG C 6v4 BG D 6v5 BG E
2 4v3 BG B 5v4 BG C 1v5 BG B 2v1 BG C 3v2 BG E
3 2v5 BG D 3v1 BG D 4v2 BG A 5v3 BG A 1v4 BG E
(Bye Stand) BG C BG A BG D BG B -
After Round Board Rotation
1 Triangle: Table 1 -> Bye Stand -> Table 2 -> Table 1; BG D Remains at Table 3
2 Swap: Table 1 <-> Table 2; Swap: Bye Stand <-> Table 3
3 Triangle: Table 1 -> Table 2 -> Bye Stand -> Table 1; BG A Remains at Table 3
4 All Boards Come Out of Play; Replaced by Board Group E at All Tables

The "free for all round" is so-called because it often results in a frenzy of players scrambling to get a board that they have not yet played when there's only one copy of the boards. This round runs far more smoothly with two copies of the affected group of boards (place about two thirds of the boards on each table with instructions to pass the first board or two, as required, to the next lower table after playing it) and most smoothly with three copies (so each table has its own). If there's only one copy of these boards, the director should manage the order of play at each table to ensure that each table completing a board moves on to the available board with the fewest completed plays. Otherwise, two tables inevitably end up needing the same board for their last play, forcing one table to wait while the other plays it.

In addition to the "free for all round" and the irregular board movements, the fact that each round consists of one fifth of the number of boards in play greatly amplifies the imbalance of comparisons that is common to all Complete Howell Movements with an odd number of tables. However, there is no ideal way out of this.

Partial Howell MovementEdit

A Partial Howell Movement, also sometimes called a "Three Quarter Howell Movement" even though the number of rounds is not exactly 3/4 of the number of rounds in a Complete Howell Movement, has fewer rounds and fewer board groups than a Complete Howell Movement for the same number of tables. The shortfall creates an equal number of number of quasi-stationary positions at "swivel tables" for the pairs with numbers greater than the number of rounds but less than the number of pairs. Each quasi-stationary pair remains at the same table throughout the session, but plays North-South in some rounds and East-West in other rounds -- most commonly achieved by rotating ("swiveling") the orientation of the table rather than by making the quasi-stationary players physically change seats. All stationary and quasi-stationary pairs play against each of the moving pairs, but the stationary and quasi-stationary pairs don't play against each other and the moving pairs don't play against an equal number of the other moving pairs. The following table shows the Partial Howell Movement for six tables playing eight rounds supplied by the ACBLscore® scoring program published by the American Contract Bridge League.. Pair 12 is truly stationary, playing North-South at Table 1 throughout. The quasi-stationary pairs are Pair 11 at Table 2, Pair 10 at Table 3, and Pair 9 at Table 4. In this particular movement, there are three sets of entrants who do not play against the other members of their own set -- the stationary and quasi-stationary pairs (Pair 9, Pair 10, Pair 11, and Pair 12), the odd moving pairs (Pair 1, Pair 3, Pair 5, and Pair 7), and the even moving pairs (Pair 2, Pair 4, Pair 6, and Pair 8).

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7 Round 8
1 12v1 BG A 12v2 BG B 12v3 BG C 12v4 BG G 12v5 BG E 12v6 BG F 12v7 BG G 12v8 BG H
2 11v8 BG B 11v1 BG C 11v2 BG D 11v3 BG E 4v11 BG F 5v11 BG G 6v11 BG H 7v11 BG A
3 10v6 BG C 10v7 BG D 8v10 BG E 1v10 BG F 2v10 BG G 3v10 BG H 10v4 BG A 10v5 BG B
4 5v9 BG D 6v9 BG E 9v7 BG F 9v8 BG G 1v9 BG H 2v9 BG A 9v3 BG B 9v4 BG C
5 7v4 BG E 8v5 BG F 1v6 BG G 2v7 BG H 3v8 BG A 4v1 BG B 5v2 BG C 6v3 BG D
6 3v2 BG F 4v3 BG G 5v4 BG H 6v5 BG A 7v6 BG B 8v7 BG C 1v8 BG D 2v1 BG E
(Bye Stand) BG G, H BG H, A BG A, B BG B, C BG C, D BG D, E BG E, F BG F, G

Most published Partial Howell Movements were developed well before the mathematical analysis described above determined the relative weight of entrants on each others' scores based upon playing position. Thus, the arrow switches at the tables with the quasi-stationary pairs were configured so the stationary and quasi-stationary pairs would have direct comparisons on about half of the boards, typically with little regard for the impact thereof on either comparisons between the moving pairs and the stationary and quasi-stationary pairs or comparisons among the moving pairs. The result is hideous imbalance in the fairness of the movement. The next table shows the frequencies of number of comparisons reported by the ACBLscore® scoring program for this movement and the subsequent table shows the pairs that represent the most extreme outliers as reported by the program, with asterisks (*) indicating pairs that do not play against each other at the same table. The pairings with asterisks in the first three rows and the pairings without asterisks in the last two rows are the most egregiously imbalanced in this movement.

Rounds Compared Frequency Rounds Compared Frequency
0 1 4 25
1 4 5 10
2 5 6 3
3 17 7 1
Rounds Compared Pairs
0 6&9
1 *1&7, 3&11, *4&6, *5&7
2 1&10, 1&11, 2&9, 2&10, 2&11
6 *1&5, 1&6, *10&11
7 4&9
Scissors Howell MovementEdit

The Scissors Howell Movement cuts each board group in half, with each half moving independently. This movement is most useful with three tables, where the boards can move in a manner that offsets the imbalance in comparisons for a Complete Howell Movement with an odd number of tables discussed above, amplified by the fact that each round plays 20% of the boards. The following table shows a Scissors Howell Movement for three tables in which the half board groups move in a complementary manner so that the imbalance of the upper half countering the imbalance of the lower half, creating a balanced movement.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 6v1 BG A1,A2 6v2 BG B1,B2 6v3 BG C1,C2 6v4 BG D1,D2 6v5 BG E1,E2
2 5v2 BG C2,D2 1v3 BG D2,E2 2v4 BG E2,A2 3v5 BG A2,B2 4v1 BG B2,C2
3 3v4 BG B1,E1 4v5 BG C1,A1 5v1 BG D1,B1 1v2 BG E1,C1 2v3 BG A1,D1

A normal scissors movement requires each complete board group to consist of an even number of boards so it can split exactly in half -- with the consequence that a scissors movement with five rounds would have to play either twenty (20) or thirty (30) boards. However, it's possible to play either 24 or 26 boards with the above movement by varying the size of the board subgroups as shown in the following table -- each table plays five boards in each of the first four rounds and four or six boards respectively in the last round.

Total Boards Played 20 24 26 30
Board Subgroup A1 1-2 1-2 1-3 1-3
Board Subgroup A2 3-4 3-5 4-5 4-6
Board Subgroup B1 5-6 6-8 6-7 7-9
Board Subgroup B2 7-8 9-10 8-10 10-12
Board Subgroup C1 9-10 11-13 11-12 13-15
Board Subgroup C2 11-12 14-15 13-15 16-18
Board Subgroup D1 13-14 16-17 16-18 19-21
Board Subgroup D2 15-16 18-20 19-20 22-24
Board Subgroup E1 17-18 21-22 21-23 25-27
Board Subgroup E2 19-20 23-24 24-16 28-30

It's theoretically possible to configure a Scissors Howell Movement for more than three tables, but there's no practical reason to do so. There are complete Howell movements for four tables and for six tables that are correctly balanced, and complete Howell movements for five tables consist of nine rounds, and thus would require play of either eighteen boards (generally too few for an open event) or thirty-six boards (too many for a normal session).

Hybrid MovementsEdit

Whenever an event of two sessions draws only enough entrants to form one section, the normal practice is to play a Mitchell Movement in the first session, followed by separate Howell or equivalent movements for the entrants in the first session's North-South and East-West fields in the second session. Thus, an event with sixteen pairs would play a Relay and Bye Stand Mitchell Movement (eight rounds) in the first session followed by separate Complete Howell Movements (seven rounds) for each of the original fields in the second session, so that each pair would play against each of the other pairs only once. A Hybrid Movement takes the same approach to form two stanzas within a single session. A complete Hybrid Movement is functionally equivalent to a Complete Howell Movement, but it has several pairs that don't change tables after every round.

The following table shows a complete Hybrid Movement for four tables playing seven rounds. The first four rounds are a Scrambled Mitchell Movement in which each of the pairs that start East-West move to each of the four tables and play each of the pairs who start North-South. In the last three rounds, the pairs that started North-South play a Complete Howell Movement at Table 1 and Table 2 while the pairs that started East-West play another Complete Howell Movement at Table 3 and Table 4. The configuration of the arrow switches in the first four rounds and the positioning of pairs in the last three rounds conspire to create a perfectly balanced movement with each pair of entrants playing one group of boards against each other at the same table, three groups of boards in the same direction, and three groups of boards in opposite directions at different tables. This particular movement works best with two copies of the boards, as Table 1 and Table 2 play the same group of boards in each round and Table 3 and Table 4 play the same group of boards in each round, but it can run with just one set of boards (Table 1 shares one group of boards with Table 2 and Table 3 shares another group of boards with Table 4 in each round) if necessary.

Table Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7
1 1v5 BG A 1v6 BG B 1v7 BG C 1v8 BG D 1v4 BG E 1v3 BG F 1v2 BG G
2 2v6 BG A 2v5 BG B 8v2 BG C 7v2 BG D 3v2 BG E 2v4 BG F 4v3 BG G
3 3v7 BG B 8v3 BG A 6v3 BG D 3v5 BG C 5v7 BG F 5v6 BG G 5v8 BG E
4 4v8 BG B 7v4 BG A 4v5 BG D 4v6 BG C 6v8 BG F 8v7 BG G 7v6 BG E

Note that this Hybrid Movement provides much better accommodation for players with physical disabilities and mobility impairments than the equivalent Complete Howell Movement. Pair 1 is completely stationary, Pair 2 changes tables just once, Pair 4 changes tables twice, and both Pair 3 and Pair 5 change tables just three times, whereas all pairs except the stationary pair change tables at least five times in the equivalent Complete Howell Movement.

In the case of an odd number of tables, it's best for the first part of a Hybrid Movement to operate as a Scrambled Hesitation Mitchell Movement, as that reduces the number of stationary pairs to an even number permitting separate Howell movements for the stationary and rotating pairs. In the second part of the movement, the stationary pairs play a Complete Howell Movement while the moving pairs play a Partial Howell Movement in which they "miss" the pairs that they played at the hesitation table. With three tables, this movement becomes the Extended Hesitation Mitchell Movement described below.

Extended Hesitation Mitchell MovementEdit

In a game of just three tables, the Hesitation Mitchell Movement that would form the first part of a Hybrid Movement pits each pair against four of the other five pairs in the first four rounds. This reduces the second stage to one round in which each pair plays the fifth group of boards against the pair that it did not play in the first five rounds of the movement. The fifth round is really an extension of the Hesitation Mitchell Movement rather than parallel Howell movements that normally form the second part of a hybrid movement. The following table shows this Extended Hesitation Mitchell Movement.

Table Round 1 Round 2 Round 3 Round 4 Round 5
1 1v4 BG A 1v3 BG B 1v6 BG C 1v5 BG D 1v2 BG E
(Bye Stand) BG B BG C BG D BG A -
2 2v5 BG C 2v4 BG D 3v2 BG A 6v2 BG B 4v6 BG E
3 3v6 BG D 6v5 BG A 5v4 BG B 4v3 BG C 5v3 BG E

The Extended Hesitation Mitchell Movement is functionally equivalent to the Complete Howell Movement for three tables shown above, but it generally runs more smoothly because the rotating pairs and the boards move in a regular manner for the first four rounds. It has the additional advantage that Pair 1 is fully stationary, Pair 2 changes tables only once, and Pair 6 changes tables only twice -- generally acceptable accommodations for players who have some degree of mobility impairment. The imbalance of comparisons and the existence of a "free for all round" are the same as in any Complete Howell Movement for three tables, so there's no "down side" whatsoever to using this movement instead of the Complete Howell movement. The previous discussion pertaining to the "free for all round" in a Complete Howell Movement for three tables is also applicable here -- it is best to provide three copies of the boards in Board Group E for both movements so each table can have its own copy.

Choice of MovementsEdit

There are two or more possible movements to choose from for any combination of tables and session length. The choice depends on the preferences of the organizers.

  • Complete Howell Movements ensure that each entrant plays against all of the other entrants, but the number of rounds and boards varies and may not be convenient. All pairs, except one, move after every round, which slows down the move especially if one table is slow, and there is only one stationary table, which is problematic if some players have limited mobility. The move on each round is complex and table cards or guide cards are essential. Also, except for filling a phantom position, they offer no flexibility to add entrants who arrive after the movement is set.
  • Normal Mitchell Movements have a stationary pair at each table, and they are considerably simpler than Howell movements and thus easier to run so there's no need for special table mats or guide cards. It's also quite easy to add a table to most Mitchell movements if entrants arrive after the movement is set.
  • Hesitation Mitchell Movements and Partial Howell Movements are intermediate between the cases above. If the number of rounds is one more than the number of tables, the Hesitation Mitchell Movement is much simpler and thus much easier to run.

Complete Howell Movements are most convenient for small numbers of tables and Mitchell movements are best for large numbers of tables. In a typical club session of around 3 hours, a Howell can be used for seven or fewer tables and a Mitchell for four or more tables. Up to 11 tables, useful alternatives are given by Partial Howell Movements, Hesitation Mitchell Movements (odd numbers of tables), and Double Hesitation Mitchell Movements (even numbers of tables). However, the director needs to consider circumstances such as the need for stationary places to accommodate players with disabilities in making the final selection.

The present authors prefer the following movements, described above, for normal games of 2½ to 8 tables.

2½ or 3 TablesEdit
  • 20 Boards: Extended Hesitation Mitchell Movement (simplest), Complete Howell Movement, or Scissors Howell Movement (best balanced); all 5 rounds of 4 boards
  • 24 Boards or 26 Boards: Scissors Howell Movement with Modified Board Subgroups; 4 rounds of 5 boards + 1 round of 4 or 6 boards
  • 25 Boards: Extended Hesitation Mitchell Movement (simplest) or Complete Howell Movement; 5 rounds of 5 boards
3½ or 4 TablesEdit
  • 20 Boards: Crisscross Mitchell Movement, 4 rounds of 5 boards
  • 21 Boards: Hybrid Movement or Complete Howell Movement, 7 rounds of 3 boards
  • 24 Boards: Crisscross Mitchell Movement, 4 rounds of 6 boards
  • 28 Boards: Hybrid Movement of Complete Howell movement, 7 rounds of 4 boards

4½ TablesEdit

  • 18 Boards: Complete Howell Movement, 9 rounds of 2 boards
  • 24 Boards: Two-Way Rover Mitchell Movement, 4 rounds of 6 boards (3-board sit-out)
  • 27 Boards: Complete Howell Movement, 9 rounds of 3 boards

5 TablesEdit

  • 18 Boards: Complete Howell Movement, 9 rounds of 2 boards
  • 24 Boards: Hesitation Mitchell movement, 6 rounds of 4 boards
  • 25 Boards: Complete Mitchell Movement, 5 rounds of 5 boards
  • 27 Boards: Complete Howell Movement, 9 rounds of 3 boards

5½ or 6 TablesEdit

  • 22 Boards: Complete Howell Movement, 11 rounds of 2 boards
  • 24 Boards: Relay and Bye Stand Mitchell Movement, 6 rounds of 4 boards, or Double Hesitation Mitchell Movement, 8 rounds of 3 boards
  • 27 Boards: Partial Howell Movement, 9 rounds of 3 boards

6½ TablesEdit

  • 21 Boards: Complete Howell Movement, 7 rounds of 3 boards
  • 24 Boards: Two-way Rover Mitchell Movement, 6 Rounds of 4 Boards (2-board sit-out), or Hesitation Mitchell Movement, 8 rounds of 3 boards
  • 26 Boards: Complete Howell Movement, 13 rounds of 2 boards

7 TablesEdit

  • 21 Boards: Complete Mitchell Movement, 7 rounds of 3 boards
  • 24 Boards: Hesitation Mitchell movement, 8 rounds of 3 boards
  • 26 Boards: Complete Howell movement, 13 rounds of 2 boards
  • 28 Boards: Complete Mitchell movement, 7 rounds of 4 boards

7½ TablesEdit

  • 24 Boards: Relay and Bye Stand Mitchell Movement with Virtual Share, 8 rounds of 3 boards
  • 28 Boards: Two-Way Rover Mitchell Movement, 7 rounds of 4 boards (2-board sit-out)

8 TablesEdit

  • 24 Boards: Relay and Bye Stand Mitchell Movement or Double Web Movement, 8 rounds of 3 boards

Individual movementsEdit

There are two basic types of Individual movements—Shomate and Rainbow. Shomate movements are similar in concept to Howell movements for pairs—for smaller numbers of tables, a single individual is stationary and all other players move from place to place, sitting at different tables/positions each round. Rainbow movements are similar in concept to Mitchell movements. A key difference for Rainbow movements is that they require the number of tables to be a prime number, and there must be at least 5 tables. In a Rainbow movement, North players remain stationary throughout the game. All other players move after each round. Typically, boards move to the next lower table; South players move to the next higher table; East players move to the 2nd next higher tables (for example, moving from table 1 to table 3); and West players move to the 2nd lower table (for example, moving from table 3 to 1). It is common for the player moving two tables lower to carry boards to the next lower table on the way to their next seat. In a rainbow movement, if it is desired to increase the number of players a person has played with and against, this can be accomplished by having players at each table change positions at the same table within a round. For example, if the movement calls for two boards per round, after playing one board, the South and West players at each table could exchange seats for the 2nd board. If this is done, the players must remember to move back to their original position when moving at the end of the round. In a movement with 3 boards per round, East, South, and West can move clockwise after each board (skipping the North seat).

Movements for Team GamesEdit

The movement selected for a team game depends upon the type of competition and the number of entrants.

Standard Swiss Team CompetitionEdit

The movement for a standard Swiss Team competition depends upon the number of entrants. If the number of entrants is small enough, each entrant should play each of the other entrants -- called a "Round Robin" format. If the number of entrants is too large for a single Round Robin competition, the entrants may be divided into brackets based on ability or ranking and play the other entrants in their own bracket in a "Round Robin" format or the first match may be assigned randomly and subsequent matches assigned dynamically based upon the outcome of the previous matches across the entire field.

A event or bracket with an odd number of entrants requires that at least three of the entrants play interleaved matches in each pair of rounds. Each set of interleaved matches requires two rounds of play. Each team's North-South pair plays one side of one match while its East-West pair plays one side of another match in the first round of the interleaved matches. In the second round, each pair the other side of the match that the other pair played in the first round. The team then scores both matches.

The following table shows interleaved matches for three teams. The teams are designated by lower case letters in this table rather than numbers because their numbers don't necessarily match the numbers of the tables, but the movement the really consists of the second and third rounds a Standard Mitchell Movement for three tables. In competitions in which the players shuffle and deal the cards for each match, the cards are shuffled for the first round but not for the second round in this format.

Table First Round Second Round
1 xvz BG A xvy BG B
2 yvx BG B yvz BG C
3 zvy BG C zvx BG A

Round Robin MovementsEdit

In a Round Robin Movement, the number of matches is one fewer than the number of entrants so each team plays against each of the other teams. Realistically, a Round Robin movement is impracticable with more than six teams in an event of one session and with more than ten teams in an event of two sessions because the matches play too few deals.

Even Numbers of TeamsEdit

When a Round Robin event or bracket has an even number of teams, all of the teams can play each other in head to head matches. The following table shows the simplest arrangement of matches for four teams.

Round Match A Match B
1 1v2 3v4
2 1v3 2v4
3 1v4 2v3
Odd Numbers of TeamsEdit

An odd number of entrants must play each other in rings of interleaved matches or using the American Whist League Movement described in the section on Pair Movements (above) with the first round removed.

  • Three tables normally use the format for three interleaved matches shown above.
  • The format recommended by the American Contract Bridge League (ACBL)[6] for five teams consists of two rings of interleaved matches shown in the following table, as this allows the players to score the first two matches after the second round. The last two rounds can use the same deals as the first two rounds if the groups of boards move as shown in the table. The ACBL recommends shifting the home tables (North-South pairs) of four of the teams after the first ring of matches, as shown in the table, so that the North-South and East-West pairs of each team are not playing at adjacent tables.
Table Round 1 Round 2 Round 3 Round 4
1 1v4 BG A 1v3 BG C 1v5 BG D 1v2 BG E
2 2v5 BG B 2v4 BG D 4v3 BG B 4v5 BG C
3 3v1 BG C 3v5 BG E 2v1 BG E 2v3 BG A
4 4v2 BG D 4v1 BG A 5v4 BG C 5v1 BG D
5 1v3 BG E 5v2 BG B 3v2 BG A 3v4 BG B
  • A round robin for seven or nine teams could operate as three or four rings, respectively, of interleaved matches, but the more prevalent practice is for three teams to play interleaved matches and the remaining teams to play head to head matches in each pair of rounds. With nine teams, there's also the option to play four three-way interleaved matches as shown in the following table.
Header text Rounds 1&2 Rounds 3&4 Rounds 5&6 Rounds 7&8
First Ring Teams 1, 2, 3 Teams 1, 4, 7 Teams 1, 5, 9 Teams 1, 6, 8
Second Ring Teams 4, 5, 6 Teams 2, 5, 8 Teams 2, 6, 7 Teams 2, 4, 9
Third Ring Teams 7, 8, 9 Teams 3, 6, 9 Teams 3, 4, 8 Teams 3, 5, 7

The American Whist League (AWL) Movement, described above as a pair movement, also can be employed for a round robin of five, seven, or nine tables simply by removing its first round. Alternatively, the first round of this movement can be employed to duplicate boards since the boards at each table are precisely the boards that the respective team will not play in the competition.

Movements for Larger GamesEdit

When an event draws too many entrants for a Round Robin movement and it's not desirable to divide the field into brackets, the normal practice is to assign matches for subsequent rounds dynamically by the cumulative total of Victory Points awarded based upon the margin of victory or loss in the preceding rounds, subject to the constraint that no team can play against another team in more than one round. This causes teams stronger teams to come into competition with other stronger teams that are doing well in the fight for the top, weaker teams to come into competition with other weaker teams in the fight to the bottom, and average teams to gravitate toward the middle of the standing (because an average team that beats a weaker team by a significant margin then must play against a stronger team and vice versa). Most computer scoring programs now generate subsequent matches automatically, with algorithms that are sophisticated enough to ensure that undesirable assignments won't arise in the later rounds.

Knockout CompetitionEdit

In a knockout competition, the entrants are typically divided into brackets of nine to sixteen teams and assigned initial positions within each bracket by a random draw for starting positions on the bracket chart. Each round of matches may consist of either head to head or three-way matches, or some combination thereof, each of which is one round in duration (so each side of a three-way match plays half the number of deals of a head to head match in the same round). The winner of each head to head match continues into the next round while the loser is eliminated. In a three way match, two teams may continue with one team eliminated or vice versa. The brackets typically are configured to come down to four teams in the semifinal round of competition.

Standard knockout competitions usually consist of four rounds.

  • In a full knockout competition, each round is a separate session with each head to head match consisting of twenty-four deals, usually played over two days with two sessions on each day. The pairs eliminated in the third round tie for third and fourth places overall. The final round assigns first place overall to the winner and second place overall to the loser.
  • In a Compact Knockout competition, there are two rounds in each session with each head to head match consisting of twelve deals, usually played on the same day. The teams that lose in the first round play consolation matches in the second round, but cannot place overall. The teams that lose in the third round play head to head in the fourth round, with the winner placing third and the loser placing fourth overall.

Various championship events may consist of more sessions and more matches with a larger single field.

Board-a-Match (BAM) MovementsEdit

A Board-a-Match (BAM) event is a Swiss Team competition in which each board is deemed to be a separate match, with a winner and a loser. These events typically consist of each team playing a few boards against each of the other teams, using a movement similar to that for pair games but engineered so any two teams play the same boards in both directions. The most common team movement is the American Whist League (AWL) movement described above, with the first round removed (so a team's North-South pair does not play against its own East-West pair). However, the teams may shuffle and deal the boards that would be at their table in Round 1 of the AWL Movement, which are boards that they won't play, before moving for the first round of actual competition.

For an even number of tables, things become more difficult. A simple solution is to use an American Whist movement with an even number of rounds but with one or more teams not playing each other, which is not ideal. One or two of the moves between rounds will be different, to avoid board/team conflicts. There are alternative movements which are better balanced but more complex, see EBU Movements Manual.

Other forms of team competitionEdit

Because the AWL movement is a round-robin movement (each team plays a match against all other teams), when the number of teams is large the number of boards per match must be small. When this is not desirable, some other form of arranging competitors to play must be used. The most common are Knockouts and Swiss. In both of these, teams play head-to-head matches of a convenient number of boards in each round. In Knockouts, match winners advance to the next round; the losers are eliminated from the event. In Swiss, after each round, the tournament director examines the record of each team and assigns pairs of teams with similar records, but that have not played against each other, to oppose each other in the next round. In either form, if there is an odd number of teams, one or more round-robins involving 3 teams must be used. In knockouts, if a round robin is used, the number of boards in each match must be half the number used in the head-to-head matches (a "half-match"), to allow all competitors to finish a round in approximately the same amount of time. In Swiss, it is possible to use either the half-match technique (in which case the subsequent pairings need to give less weight to the half-match results), or, to have the teams involved play the full number of boards, in which case the results will not be known until the other competitors have completed two matches. This means that the number of rounds must be even. Also, because the teams involved will not have results to compare for future pairings for two rounds, in the later rounds it is desirable to avoid assigning the leading teams to the round robin.

External linksEdit

ReferencesEdit

  1. ^ "Balanced Movements in Bridge" published by the Brisbane Water Bridge Club
  2. ^ Tim Delaney, "How Fair Are Howell Movements?" on "bridgewinners.com" web site, 12 June 2013.
  3. ^ The ACBL Club Director's Handbook, American Contract Bridge League, Horn Lake, MS
  4. ^ Examination of Howell movements supplied by the ACBLscore® scoring program published by the American Contract Bridge League shows this to be the case. Both complete Howell movements for five tables playing nine rounds from this source put the stationary Pair #10 at Table 3, and thus are among the exceptions.
  5. ^ Analysis of Comparisons for Howell Movements in the ACBLscore® Bridge Scoring Program published by the American Contract Bridge League (ACBL).
  6. ^ Course Notes from the American Contract Bridge League's course for club directors.
  • EBU Movements Manual