Duplicate bridge movements

A duplicate bridge movement is a scheme used in a duplicate bridge tournament to arrange which competitors play which opponents when, and which boards they play. The arrangement has to satisfy a number of constraints which often conflict to some extent, and compromises may be required. The resolution of these compromises is to a considerable extent a matter of taste, and if possible the players should be consulted as to their preferences.

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

Requirements for movements

The requirements for the movement are as follows:

• The only really inflexible requirement is that no individual/pair/team plays the same boards more than once.
• The tournament should not be either too long or too short. A typical club session consists of around 24 boards, but a tournament for less experienced players may aim for rather fewer than this.
• No board should be required to be played at more than one table in the same round. Sometimes this rule is broken: the boards can be passed from one table to another during the course of a round.
• The movement should be as fair (or "balanced") as possible: in principle, this means that each pair should have an approximately equal opportunity to oppose each other pair, taking into account both "direct opponents" (who face one another at the same table) and "indirect opponents" (who play the same hands as each other at different times).
• For preference, the number of boards in each round should be as large as possible, since this reduces the number of rounds and saves some time.
• Subject to the other constraints, the movement should be as simple as possible, in order to minimise the possibility of errors occurring.
• In some countries it is usual for the boards to progress regularly, or as close as possible to regularly, from one table to the next lower numbered table. In other countries the boards are simply collected from a central table and this constraint does not apply.

It is important that once the movement is selected, it should be completed: uncompleted movements are likely to be unbalanced. Thus a movement should be selected which has a high probability of being completed.

Two-winner and one-winner movements

In two-winner movements, the NS pairs play the EW pairs, but never other NS pairs. There are thus two "fields" competing separately. If the average standard of the NS and EW pairs is different, this can give an unfair result.

In one-winner movements at certain points NS pairs play as EW and EW pairs play as NS, e.g. through an arrow switch (reversing the polarity of tables during some rounds). This creates a one-winner movement.

The number of rounds which are arrow switched affects the fairness of the result. Normally between one-eighth and one-quarter of the rounds are arrow switched. The English Bridge Union (EBU) recommends one eighth. So in a 7 or 8 round movement, you would arrow switch the last round.

Pair Movements

There are two basic types of pair movements - Mitchell and Howell. Mitchell movements can be two-winner or one-winner. Howell and variants of Mitchell are one-winner.

Mitchell Movements

In a standard Mitchell movement (also known as "straight Mitchell"), there are two separate groups of players - one group always sits North-South, and the other always sits East-West. North-South players remain at the same table throughout all rounds of play. After each round, boards move to the next lower numbered table (from table 1, boards go to the highest numbered table), and East-West pairs move to the next higher number table (at the highest numbered table, pairs move to table 1). Pairs are typically identified by the direction they are sitting, coupled with the table number they start at.

This arrangement can be followed without modification when there is an odd number of tables, with no additional pairs left over (no half-tables). Modifications to the straight Mitchell movement must be made whenever there is an even number of tables, or a half-table.

A straight Mitchell movement requires that the number of rounds played R is equal to or less than the number of tables T. Hence, if there are 8 tables and time to play 24 boards, a maximum of 8 rounds can be played and there will be 3 boards per round.

If it is desired to play one or two rounds more than the number of tables, a Hesitation Mitchell or Double Hesitation Mitchell movement may be used if feasible. Alternatively, a Howell type movement may be adopted.

Even number of tables

In a straight Mitchell with an even number of tables, after half of the rounds have been completed the East-West pairs will arrive at a table with boards that they have already played. To avoid this problem, there are two basic options -- "Skip Mitchell" and "Bye-Stand Mitchell" (the latter is called a "Share and Relay Mitchell" in the UK).

Skip Mitchell

In a Skip Mitchell, after the number of rounds played equals the number of tables divided by 2, in moving for the next round the East-West pairs must "skip" a table. The director must take care to announce the special movement when that round arrives, and North-South pairs should confirm that their new-arriving opponents did skip a table. This choice is far simpler for the director to manage and is simpler to adjust if a late pair must be accommodated, but has the slight drawback that each East-West pair misses the chance to play one set of boards. The Skip Mitchell requires that the number of tables is at least one greater than the number of rounds played, e.g. with 10 tables up to 9 rounds can be played, but with 8 tables the maximum is 7, otherwise EW pairs would encounter NS pairs more than once.

Bye-Stand Mitchell or Share and Relay Mitchell

In a Bye-Stand Mitchell, there are two modifications needed to the basic table setup. First, table 1 must be set up near the highest numbered table, because throughout the game, those two tables will share boards - after playing a board at one table it must be passed to the other to play. Second, a "bye stand" or "relay table" must be set up halfway between the first and last tables - for example, in an 8 table movement, the bye stand must be set up between tables 4 and 5. When moving boards after each round, boards at the table just above the bye stand go to the bye stand; the boards on the bye stand go to the table just below the bye stand. In the 8-table example, boards go from table 5 to the bye stand, and from the bye stand to table 4. This movement allows all pairs to play all boards, but the drawbacks are that the sharing of boards between two tables tends to slow down the movement, mistakes can be made with both the bye stand placement and the movement of boards to the bye stand, and late pairs are harder to accommodate.

Half Tables

Adjustments to the straight Mitchell for half tables depend on whether the number of full tables is odd or even.

Number of Full Tables is Even

In this case the adjustment is a "sit out". This involves setting up the movement as if there were an odd number of tables and then running a straight Mitchell. In an 8-1/2 table game, set up 9 tables with boards and assign North-South players to tables 1-8; East-West pairs are assigned to tables 1-9. The movement proceeds exactly as in a straight Mitchell, when East-West pairs arrive at table 9 they simply do not play that round.

Number of Full Tables is Odd

In this case the adjustment can be either

• a sit out combined with Skip Mitchell
• sit out combined with Bye Stand Mitchell
• "North-South Bump"

The sit out with Skip Mitchell has the disadvantage that one East-West pair will skip the sit out table. This is not a problem if the number of tables is greater than the number of rounds.

For a Bye Stand Mitchell, the East-West pair arriving at the highest numbered table (which normally shares boards with table 1) sits out. If desired and permitted, they may kibitz the deals at table 1 while they are sitting out. This is the best movement if the number of tables and rounds are equal, because it eliminates the share usually required.

For a North-South Bump, all but one pair are assigned to tables as in a straight Mitchell. The remaining pair is a "Rover", that moves according to a schedule that differs depending on the number of full tables. The Rover pair does not play the first round, at each subsequent round they move to a table according to their schedule and replace the North-South pair at that table for that round - the North-South pair at that table have been "bumped" and sit out that round. If desired and permitted, the bumped pair can kibitz the table they have been bumped from. Also, because the Rover pair does not play the first round, it can be a very good choice for handling a late-arriving pair.

Hesitation Movements

In a Hesitation Mitchell, the EW pair arriving at the highest numbered table rotate to sit NS at that table on the next round, and then move to Table 1. With an odd number of tables, this allows one more round to be played than the number of tables. For example, with 24 boards and 7 tables, 8 rounds can be played. A bye stand table will also be needed opposite the hesitation table; in this case between tables 3 and 4.

In a Double Hesitation Mitchell, there are two points where EW move to NS, 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. For example, with 24 boards and 6 tables, 8 rounds can be played. Two bye stand tables will also be needed. The position of the rotations and bye stand tables must be chosen precisely, otherwise a conflict will arise, so table cards are needed.

Howell Movements

In a Howell movement, pairs move according to a schedule that varies depending on the number of tables. Pairs are identified by a pair number that identifies the position they sit for the first round. Traditionally, the highest numbered pair sits North-South at table 1 and does not move from that position; the other pairs move from table to table, sometimes sitting North-South and sometimes East-West. In moving according to the schedule, each pair will arrive at table 1 and sit East-West in the round corresponding to their pair number. Directions are placed on each table telling each player what table and position they move to for the next round.

The Howell movement is better suited for smaller numbers of tables - as the number of tables grows, the number of rounds that must be played to have every pair play at every position becomes too large. For T tables, there will be (2T-1) rounds, e.g. 7 rounds for 4 tables, but 13 rounds for 7 tables. For larger games where a Howell-type movement is desired, "3/4 Howell" or "Part Howell" movements exist that provide balanced comparisons, accomplished in part by having in addition to the stationary pair at table one, pairs that remain at some higher numbered tables, but who may sit North-South in some rounds and East-West in others.

Suggested pair movements

Some suggestions for movements of from 3 up to 7 tables are as follows:

3 tables

• 20 boards: a standard Howell movement, 5 rounds, 4 boards per round
• 24 boards: a 5 round Howell movement as follows:

Table 1

NS	EW	Boards
6	1	1-5
6	2	6-10
6	3	11-15
6	4	16-20
6	5	21-24

Table 2

NS	EW	Boards
3	4	8-10, 21-22
4	5	1-2, 11-13
5	1	8-10, 19-20
1	2	11-13, 21-22
2	3	1-2, 19-20

Table 3

NS	EW	Boards
5	2	14-18
1	3	16-18, 23-24
2	4	3-5, 23-24
3	5	3-7
4	1	6-7 14-15

• 25 boards: a standard Howell movement, 5 rounds, 5 boards per round could be played, but this is not as balanced as the above 24 table movement.

3½ or 4 tables

• 21 boards: standard Howell movement, 7 rounds, 3 boards per round
• 25 boards: as for 21 boards, but with 4 additional boards in play in rounds 1, 3, 4 and 5.
• 28 boards: standard Howell movement, 7 rounds, 4 boards per round

4½ tables

• 18 boards: standard 5 table Howell movement, 9 rounds, 2 boards per round
• 24 boards: 5 table Howell movement, 8 rounds, 3 boards per round, 2 stationary pairs one of which is the phantom pair.

Details of 4½ table movement

Starting positions: Table 1: 9v1; Table 2: 5v6; Table 3: 2v8; Table 4: 4v7.

Pair 3 sits out on first round. Pair 9 is stationary. Two relays between tables 3 and 4. Phantom table 5, plus one relay between tables 5 and 1.

• 27 boards: standard 5 table Howell movement, 9 rounds, 3 boards per round

5 tables

• 18 boards: standard 5 table Howell movement, 9 rounds, 2 boards per round
• 24 boards: 5 table Hesitation Mitchell movement, 6 rounds, 4 boards per round, rotation at table 5, relay table between tables 2 and 3
• 24 boards: Howell as for 27 boards but with one board not played in each of rounds 1, 5 and 9, selected so that each board is played at least 4 times
• 27 boards: standard 5 table Howell movement, 9 rounds, 3 boards per round

5½ or 6 tables

• 22 boards: standard 6 table Howell movement, 11 rounds, 2 boards per round
• 24 boards: Mitchell movement, 6 rounds, 4 boards per round
• 24 boards: Double Hesitation Mitchell movement, 8 rounds, 3 boards per round, 2 rotating tables, 2 relay tables
• 27 boards: standard ¾ Howell movement, 9 rounds, 3 boards per round, 3 stationary pairs

6½ tables

• 24 boards: 7 table ¾ Howell movement, 12 rounds, 2 boards per round, 2 stationary pairs, one of which is the phantom pair. Sitouts 2 boards.

Details of 6½ table movement

Starting positions: Table 1: 5v4; Table 2: 7v11; Table 3: 2v9; Table 4: sit-out table (with relay; pair 12 starts here);Table 5:3v6: Table 6: 13 (stationary) v 1; Table 7: 10 v 8

One relay between tables 6 and 7.

• 24 boards: Hesitation Mitchell movement, 8 rounds, 3 boards per round, rotation at table 7, relay table between tables 3 and 4, phantom pair at any table, sitouts 3 boards
• 26 boards: standard 7 table Howell movement, 13 rounds, 2 boards per round, sitouts 2 boards.

7 tables

• 21 boards: Mitchell movement, 3 boards per round
• 24 boards: Hesitation Mitchell movement, 8 rounds, 3 boards per round, rotation at table 7, relay table between tables 3 and 4
• 24 boards: Mitchell as for 28 boards but with one board omitted in each of the last 4 (or first 4) rounds, selected so that each board is played at least 6 times.
• 28 boards: Mitchell movement, 4 boards per round.

Web Movements

Web movements are a modern improvement over the standard Mitchell in some circumstances. The main advantage of Web movements is they can allow large single sections with a fixed number of boards. Each pair plays the same set of boards, which increases the overall fairness of the competition. Web movements can require additional sets of boards, which is facilitated by automatic dealing machines (now common in larger clubs).

Individual Movements

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; East players move to the next higher table; West players move to the 2nd next higher tables (for example, moving from table 1 to table 3); and South 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).

Team Movements

Teams movements are different from pairs movements as they have an extra requirement; not only do teams need to play all or most of the other teams and not play the same boards twice, each pair also has to play the same boards as their other pair against the same team, but in different rounds (this requirement can be avoided by using multiple copies of computer dealt boards).

The most common team movement, known as the American Whist League (AWL) movement, is again similar to the Mitchell movement, and requires an odd number of teams. Each team starts sitting together at its home table. For the first round, each team prepares the boards on its home table, and then its E-W pair moves down two tables and carries the boards with them, dropping them off at the first lower numbered table (for example, team 3's E-W pair would carry boards from table 3 to table 2, and then go sit at table 1). This movement of boards one lower, E-W two lower, continues every round; when the E-W pairs arrive back at their home tables the movement is complete.

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 competition

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.

• Double Hesitation Mitchell
• Hesitation Mitchell Movement at English Bridge Union