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.

This article is principally directed at pairs tournaments, but many of the comments also apply to other types of tournament such as teams of four and individual tournaments. It is also mainly directed at tournaments with a relatively small number of players, as

• the organisers of larger tournaments are likely to have adequate experience of organisation, and
• for larger tournaments, some of the constraints listed below become less critical.

Requirements for movements

The requirements for the movement are as follows:

• The only really inflexible requirement is that no pair 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 at the same time. 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.

For relatively small tournaments (say up to 7 tables) the movement used is usually some variation of the Howell movement, the basis of which is that each pair plays against every other pair.

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.

Suggested 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 9 10 21 22
4	5	1 2 11 12 13
5	1	8 9 10 19 20
1	2	11 12 13 21 22
2	3	1 2 19 20

Table 3

NS	EW	Boards
5	2	14-18
1	3	16 17 18 23 24
2	4	3 4 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.

• 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: 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
• 27 boards: standard ¾ Howell movement, 9 rounds, 3 stationary pairs

6½ tables

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

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.

• 26 boards: standard 7 table Howell movement, 13 rounds, 2 boards per round

7 tables

• 21 boards: Mitchell movement, 3 boards per round
• 24 boards: 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.