All About Bridge Pair Movements (well, a lot anyway!)

Contents:

Two Winner Movement
..Mitchell Movement
....Skip Mitchell
....Share And Relay
..Blackpool
..Bowman

One Winner Movement
..Howell Movement
....Three Quarter Howell
..Hesitation Mitchell
..Arrow Switching
..Double Hesitation Mitchell
....Modified Double Hesitation Mitchell
..Triple Hesitation Mitchell
....Modified Triple Hesitation Mitchell
..Hesitation Bowman

Choosing a Movement
..24 Board Movements
..27 Board Movements

Movement

A "movement" in the game of duplicate bridge is a means of circulating the pairs and boards around the playing area such that, for every round, each pair meets a different opposing pair and meet to play a set of boards that neither pair has yet played. The requirement that the boards have not yet been played by either pair is, of course, paramount. Exceptionally, in some movements, a pair may encounter the same opposing pair a second time, though this is not ideal.

Two Winner Movement

In a two winner movement the North/South pairs only play with the North/South cards and are typically stationary. The East/West pairs only play the East/West cards and typically circulate around the room playing against different North/South pairs as they go. Thus the North/South pairs are playing against East/West pairs, but, in the course of the playing session play against all or most of these players, thus their true opponents are the other North/South pairs who are seeking to get a better result with the same cards. Similarly, the true opponents for the East/West pairs are the other East/West pairs. Thus there are two, separate competing fields and the results for each are not truly comparable.

Mitchell Movement

This is the simplest and most commonly employed movement. If there are an odd number of tables, by convention, after each round, the East/West pairs move to the next higher numbered table and the boards pass to the next lower numbered table (with table 1 passing their boards to the highest numbered table of course). For example, if there are 9 tables and the players are prepared to play 27 boards (9 sets of 3), in the course of the session, each East/West pair will visit every table and play all the boards. This is ideal assuming that you wanted to play as many as 27 boards in the first place. If you only wanted to play 24 boards then you can simply omit the last round (though this introduces a small amount of imbalance into the movement as each pair does not play every board or every pair).

If there are T tables, this movement plays for T rounds and requires T sets of boards.

If there is a half table, any pair may be omitted.

Skip Mitchell

If you have an even number of tables the simple Mitchell movement does not work as, half way through the playing session, the East/West pairs will encounter boards that they have already played. The simplest fix for this is for the East/West pairs to skip one table (move up two tables) at the midway point in the session.

If there are T tables, this movement plays for T-1 rounds and requires T sets of boards.

If there is a half table, any pair may be omitted.

Exceptionally, for an extra final round, the East/West pairs can move to the table where the one set boards is that they haven't yet played. This will be against a North/South pair that they have already enountered, so this additional round is not commonly employed (or certainly not by clubs that like to play 9 rounds of 3 boards - it may be of more use for those that typically wish to play 8 rounds of 3).

Share And Relay

(Known as Byestand in North America). This is another fix to the basic Mitchell movement for an even number of tables. This is normally set up such that table 1 and the last table share boards and a spare set of boards sits on a relay table at the opposite side of the room. For example, if there are 8 tables, tables 1 and 8 share boards (passing the boards to table 7 at the end of the round). The relay sits between table 4 and 5, table 5 passing their boards to the relay at the end of the round and table 4 receiving from the relay.

If there are T tables, this movement plays for T rounds and requires T sets of boards.

If there is a half table, any pair may be omitted in principle, but it is preferable to omit either the North/South pair at table 1 or the last table so that there is no need for sharing between tables.

This movement is generally preferable to the Skip Mitchell for clubs that wish to play 24 boards (and therefore normally an even number of rounds) provided that there are at least 3 boards per round (as sharing between tables when there are only 2 boards per round tends to produce significant delays), or that there is a half table (and thus sharing is not necessary).

Blackpool

(Sometimes called the Revenge movement). This movement is (primarily) yet another fix for the basic Mitchell movement for an even number of tables. It is similar to the Share and Relay in that there is a relay table half way round the room, but, instead of sharing at the other end, table 1 and the last table have their own set of boards (so there is no sharing) and there is another relay table between table 1 and the last table.

In the above form, if there are T tables, this movement plays for T rounds and requires T+2 sets of boards. It is a good choice if there are 12 full tables and 24 boards are to be played.

You can also play one or two extra rounds. For one extra round, both the boards and the East/West pairs move as per usual - thus the East/West pairs end up playing against the pair they played first (which is why it is known as the Revenge movement). For a second extra round, as with a Skip Mitchell, the East/West pairs move to the table where the set of boards is that they haven't yet played. The second extra round is not commonly used and many players dislike the revenge element of even one extra round and the imbalance that it creates (though some clubs reportedly like it - it is mainly a case of what the players are used to).

The above movement also works for an odd number of tables. In this case there is a double relay table between the first and last table and no relay table half way round the room. This also plays (normally) for T rounds and requires T+2 sets of boards. You can also play one revenge round. A second revenge round is theoretically possible, but one East/West pair will encounter the same North/South pair two extra times (a fix for this exists but two revenge rounds are not normally played anyway).

Bowman

Also known as an Appendix Mitchell or Ewing. If there are T tables, then you can think of it as a normal Mitchell (for an odd number of tables) or a Skip Mitchell (for an even number of tables) for T-2 tables which then has extra tables bolted on by means of board sharing. This movement plays for T-2 rounds and needs T-2 board sets.

Assuming an odd number of tables, the East/West pairs move up one table (including those at the last two 'bolted on' tables) in the normal manner for a Mitchell movement. The last but one table shares with table 1. If there is a half table, the missing pair is NS at the last table, making this one the sit out table. If there is no half table, the last table plays the boards in reverse numerical order, sharing with the table that happens to have that set at the time. Unfortunately this means that, for one round, the last table will want to share boards with table 1 that is already sharing with the penultimate table, making this not a very suitable movement for an odd number of full tables (but it does work nicely if there is a half table).

For an even number of tables, the movement works the same way except that, after half the boards have been played, there is a skip movement, just as with a Skip Mitchell. The good thing with an even number of tables, however, is that the last table will never need to share with table 1, so this movement is suitable for an even number of tables regardless of whether there is a half table or not.

One Winner Movement

In a one winner movement the pairs normally circulate in a more complex pattern compared to a two winner movement such that each pair plays some North/South hands and some East/West ones and, ideally, playing the same cards as a different selection of opposing pairs on each round. Thus the field is, in plain English, "mixed up" and a fair result can be computed for the whole field. There are different means by which this can be achieved.

Howell Movement

In a Howell movement, one pair sits stationary and all the other pairs move around the room. At the end of the session all pairs will have played all other pairs. Howell movements tend to be complex and require movement cards on each table telling the players where to move next and what boards they should be playing. Furthermore they can be tedious for the director to work out who should play who and where to put the relay tables. For this reason movement cards are usually prepared in advance (and also why I don't give general rules for how to set up a Howell movement as they generally have to be worked out on a case by case basis. Specific details will be given elsewhere).

If there are T tables, this movement plays for 2T-1 rounds and requires 2T-1 sets of boards.

Howell movements tend to work well for smallish numbers of tables (2 to 5, maybe 6, 7 at a stretch), but beyond that simpler movements are often preferred, if only because it reduces the amount of people milling around between rounds.

Howell movements are particularly preferable if there is a half table as these movements tend to have a relatively large number of rounds and therefore not too many boards per round. Thus the pair having to sit out for a round has not too long to wait before rejoining the game.

Three Quarter Howell

Sometimes you have a modest number of tables, want to play a Howell movement, but the number of rounds will not be convenient for the number of boards you wish to play. For example a 4 table Howell plays for 7 rounds. This is OK if you wanted to play 27 boards, as you can have 7 rounds of 4 boards (for 28 in total) which is typically acceptable. However, if you wanted to play 24 you are faced with playing 28 (which probably won't be acceptable) or put out 3 board sets for 21 boards (which probably won't be acceptable either). One solution is to put out 4 board sets and only play 6 of the 7 possible rounds, which is reasonable. However, there are movements, similar to a full Howell, where there are 2 (or even 3) stationary pairs (instead of one) that play for one or two rounds less than a full Howell. These are generally called Three Quarter Howell movements (even though "three quarters" is not strictly accurate). These movements also require movement cards on each table.

If there are T tables and N stationary pairs, this movement plays for 2T-N rounds and requires 2T-N sets of boards.

Hesitation Mitchell

This is a means of squeezing an extra round out of a Mitchell movement which is sometimes convenient. If you want to play 24 boards and have 7 tables you are again faced with choosing between 21 or 28 boards or playing one round less than a normal Mitchell would ideally allow. This movement provides a potential solution. The North/South pair at the last table is used as an additional moving pair. So, for 7 tables, you have 6 stationary pairs and 8 moving ones. The circulation of the pairs and boards is normall for a Mitchell type movement, but the moving pairs, after they've played as East/West at the last table, instead of moving directly to table 1, play one round as North/South at the last table. The East/West pairs "hesitate" for one round (thus the reason why this movement is called a Hesitation Mitchell). The last table is sometimes called a pivot table.

To make this movement work you need to know where to put the relay table. For an odd number of tables, imagine you have one table less and put a relay table half way round. So, for 7 tables, this means a relay between table 3 and 4. Things are marginally more complex if there is an even number of tables. This time do not imagine there is one table less, and put the relay half way round (so for 8 tables, the relay goes between tables 4 and 5), but this time it is a double relay with 2 sets of boards on it and table 1 and the last table have to share.

If there are T tables, this movement plays for T+1 rounds and requires T+1 sets of boards. Thus, in our example at the beginning of this section, you can play 7 tables for 8 rounds of 3 giving 24 boards in total.

It is generally a good choice if there are an odd number of tables. It also works well for an even number of tables provided that there are at least 3 boards per round (as you don't really want sharing with only 2 boards per round due to the delays it creates), or if there is a half table (in this case, omit North/South from table 1 which again eliminates sharing).

Movement cards are usually unnecessary provided that there is a clear explanation at the beginning of the session of what the moving pairs need to do when they get to the last table.

There is, however, one last consideration when playing a Hesitation Mitchell, and that is "arrow switching" which really needs a section of its own:

Arrow Switching

We saw, when considering 2 winner movements, that the North/South pairs and the East/West pairs really made two separate competing fields which is fine if we want a two winner movement. With a movement like a Hesitation Mitchell, we have mixed the field up a little in that the East/West pairs play one round with the North/South cards - thus the North/South and East/West pairs are no longer separate and a Hesitation Mitchell is, therefore, inherently a one winner movement similar to a Howell. But unlike a Howell, the amount of mixing between North/South and East/West is very minimal, the mixing is not very thorough. Indeed, from the point of view of the stationary pairs, they are solely competing with each other, with one comparison only on each board between themselves and the East/West pair who temporarily takes the North/South cards. Thus a Hesitation Mitchell is not very suitable as a one winner movement without a further fix.

This fix typically takes the form of what is called an "arrow switch" whereby (again typically) one round (usually the last) is played such that the North/South pair takes the East/West cards and vice versa. When the board is scored, the "North/South" pair number written on the traveller is actually that of what would have been the East/West pair and vice versa and, if for example, the East/West moving pair (who are actually playinig the North/South cards) make 2 spades, then the score is +110 to North/South.

For a Hesitation Mitchell, the tables that are arrow switched is all of them except the pivot table. Two winner movements can be made into a one winner movement (as is sometimes necessary, for example if an overall winner of a cup is needed) by arrow switching all the tables. Howell movements typically do not require arrow switching as they are generally fairly balanced anyway.

The number of rounds to switch is, in general, one eighth (or as near as possible), not one quarter as some directors suppose. For more detail on arrow switching and related matters (for the technically minded) see: this page on the EBU site and this page on David Stevenson's site. So you don't really need to switch two rounds unless there at least 12 of them and, even for 12, there isn't much difference in the overall spread of competition between pairs for one or two rounds of arrow switching.

More exotic possibilities for arrow switching exist (such as switching one board only from each of the last three sets). However, while this is better, it relies on people remembering which board to switch and is rarely employed. Slightly less exotic strategies, such as switching one, two or three tables for several rounds are a little more easily managed, though, like Howell movement cards, these need to be worked out in advance and typically require computer analysis to work out what strategy is best (but this option is, at least rarely, employed for some specific movements).

Double Hesitation Mitchell

As the name suggests, this is similar to a normal Hesitation Mitchell, but there are two pivot tables instead of one. Thus, for T tables, this movement plays for T+2 rounds and requires T+2 sets of boards. The pivot tables are normally the last table, as in a normal Hesitation Mitchell and table 2. The order the moving pairs circulate is normally:

EW1->EW2...and so on...EW(last-1)->EW(last)->NS2->NS(last)->and back to EW1 again.

In other words, the circulation order is not too complex and you can just about get away without movement cards. For an even number of tables you need two relay tables, one just after the half way point (so, say, for a 6 table movement the relay is between table 4 and 5, not the half way point between 3 and 4). The other relay is between the table 1 and the last table. For an odd number of tables, there is no relay between the first and last table, but the other relay is double. Imagine that there is one more table and then the relay goes half way (so, for a 7 table Double Hesitation Mitchell, the relay goes between tables 4 and 5).

Arrow switching is required and the simple standard says that it takes place on all tables except the pivot tables.

Modified Double Hesitation Mitchell

This is exactly the same as the normal Double Hesitation Mitchell, except that table 2 is played, effectively, with a permanent arrow switch for the whole session. Thus the circulation order is:

EW1->NS2->EW3....EW(last-1)->EW(last)->EW2->NS(last)->and back to EW1 again.

This is marginally more complex to remember and it really is best now that at least the last table and table 2 have movement cards. The advantage is that the movement is slightly more balanced for some numbers of tables.

Triple Hesitation Mitchell

As the name suggests, this is similar to a normal Hesitation Mitchell, but there are three pivot tables instead of one. Thus, for T tables, this movement plays for T+3 rounds and requires T+3 sets of boards. These movements are not often played, but they can be useful for a club that wants to play 27 boards with 6 tables (9 rounds of 3) or 24 board clubs with 9 tables (12 rounds of 2). The circulation order and where to put the relays is slightly different depending on whether there are an even or odd number of tables. Lets take the even number of tables first. The pivot tables are normally the last 3 tables. Circulation order:

EW1->EW2...etc etc...EW(last-1)->NS(last-1)->NS(last)->NS(last-2)->EW(last)->and back to EW1 again.

The relay tables are:
1) A double relay table at (T/2)-1 and the table before it. (So between table 1 and 2 if there are 6 tables).
2) A single relay table between the last and last but one table.

For an odd number of tables, the pivot tables are the last table (T), T-2 and T-3 (i.e. all the last four tables except the penultimate one). Circulation order:

EW1->EW2...etc etc...EW(last-3)->NS(last-3)->EW(last-2)->EW(last-1)->NS(last)->NS(last-2)-> EW(last)->and back to EW1 again.

The relay tables are:
1) A double relay at (T-1)/2 and the table before it. (So between tables 3 and 4 if there are 9 tables).
2) A single relay two tables before that (so between 1 and 2 for nine tables. For 7 tables the relay will be between table 1 and the last table and, for 5 tables - well - the triple hesitation movement just doesn't work for 5 tables at all as far as I can work out).

Movement cards are required for the pivot tables and, ideally, for the penultimate table where there are an odd number of tables.

Arrow switching is required and the simple standard says that it takes place on all tables except the pivot tables.

Modified Triple Hesitation Mitchell

With some even numbers of tables, the Triple Hesitation Mitchell movement works out to be more balanced if the first pivot table is permanently arrow switched. The circulation order then becomes:

EW1->EW2...etc etc...EW(last-3)->NS(last-2)->EW(last-1)->NS(last-1)->NS(last)->EW(last-2)-> EW(last)->and back to EW1 again.

Hesitation Bowman

As the name suggests, this is a cross between a Bowman and Hesitation Mitchell movement. If there are T tables, it plays for T-1 rounds and needs T-1 board sets.

With an even number of tables, the East/West pairs move up one table and the boards move down as for a normal Mitchell movement. After getting to the last table, the moving pairs move to North/South at the last but one table before re-joining East/West at table 1. The last table shares boards with the last but two table on the first round, and plays the boards in reverse numerical order, but plays the highest numbered set last.

With an odd number of tables the movement works exactly the same way except that half way through there needs to be a skip movement.

In general with this and the normal Bowman movement, if there is no half table, it is best if the last table is centrally placed in the playing room to facilitate board sharing with different tables.

Choosing a Movement

In general there is no "right" choice for a movement. One of the biggest factors is what the players are used to and like. For example, some clubs are used to and like Howell movements, at others they tend to be disliked and, at some clubs they are disliked above a certain number of tables (often because the playing room is of restricted size and the extra pair movement tends to be somewhat stressful when there are a lot of tables). There can also be some more sensible choices and some less sensible ones based on other factors. For example, movements that require board sharing tend to go rather slowly if there are only 2 board rounds, but tend to be at least OK if the rounds consist of 3 or more boards (though, even then, movements that don't require sharing tend to have an edge). A relatively square playing room helps if you are playing a Bowman movement as the last table can usually be placed centrally, but a long thin playing room makes this movement inconvenient as somewhere during the session the last table will need to share with a table at the opposite end of the room.

The number of board sets that may be unplayed by all pairs is also a consideration. One set unplayed (as normally happens with a Skip Mitchell) or two sets unplayed (as happens with a Blackpool if the revenge rounds aren't played) tends to be acceptable, but 3 sets unplayed is generally considered less than ideal.

Probably the largest single factor, however, is deciding first how many boards you want to play. Clubs tend to fall into two camps, those that like to play 24 boards and those that like 27. 24 boards can be played as 12 rounds of 2 boards, 8 rounds of 3, 6 rounds of 4, 4 rounds of 6 or 3 rounds of 8. Exceptionally, 5 rounds of 5 (for 25 boards) is usually also acceptable.

A 27 board club normally wants to play 9 rounds of 3 (or 3 rounds of 9 in the case of very few tables). 13 rounds of 2 (for 26 boards) and 7 rounds of 4 or 4 rounds of 7 (for 28 boards) tend to be considered OK by such clubs.

For a one winner movement how balanced the movement is (how well competition is spread amongst the overall field) is also a factor.

Finally, sometimes you have to have a one winner movement (you need to determine who will win a cup or some other award), but, on typical club nights, two winner movements tend to be simpler and easier to manage so will usually be chosen unless there is a good one winner alternative.

24 Board Movements

The comments in the above section notwithstanding, here are some good choices for 24 (or possibly 25) boards:

* = requires arrow switching
# = is really a one winner movement, but seems preferable to the two winner alternative anyway.
Tables Two winners Rounds
(unplayed sets)		 One winner Rounds
(unplayed sets)		 Notes
2 Howell# 3 of 8(0) Howell 3 of 8(0)
3 Howell# 4 of 5+
1 of 4(0)		 Howell 4 of 5+
1 of 4(0)		 Really 10 rounds of 3, intermeshed to appear to be 5 rounds, with 6 boards removed
4 Share+Relay 4 of 6(0) 3/4 Howell 6 of 4(0) 3/4 Howell = Dbl Hes Mitchell for this number of tables
5 Mitchell 5 of 5(0) 3/4 Howell or
Hes Mitchell*		 8 of 3(0)
6 of 4(0)
6 Share+Relay 6 of 4(0) Share+Relay* or
Blackpool*		 6 of 4(0)
6 of 4(2)		 The Blackpool is well balanced, but leaves boards played only 4/5 times
7 Hes Mitchell*# 8 of 3(0) Hes Mitchell* 8 of 3(0)
8 Share+Relay 8 of 3(0) Share+Relay* 8 of 3(0)
9 Mitchell 8 of 3(1) Triple Hes Mitchell*
or Mitchell*		 12 of 2(0)
8 of 3(1) 		The Triple Hesitation Mitchell is significantly better balanced than playing a Mitchell one round short, but is also significantly more complex. Your choice :)
10 Bowman or
Skip Mitchell		 8 of 3(0)
8 of 3(2)		 Modified Dbl Hes Mitchell* 12 of 2(0)
11 Hes Mitchell*# 12 of 2(0) Hes Mitchell* 12 of 2(0)
12 Blackpool 12 of 2(2) Blackpool* 12 of 2(2)
13 Mitchell 12 of 2(1) Mitchell* 12 of 2(1)
14 Skip Mitchell 12 of 2(2) Skip Mitchell* 12 of 2(2)

27 Board Movements

These are some recommendations for 27 boards (or 26 or 28 if it seems better):

* = requires arrow switching
# = is really a one winner movement, but seems preferable to the two winner alternative anyway.
Tables Two winners Rounds
(unplayed sets)		 One winner Rounds
(unplayed sets)		 Notes
2 Howell# 3 of 9(0) Howell 3 of 9(0)
3 Howell# 4 of 5+
1 of 6(0)		 Howell 4 of 5+
1 of 6(0)		 Really 10 rounds of 3, intermeshed to appear to be 5 rounds, with 4 boards removed
4 Howell# 7 of 4(0) Howell 7 of 4(0)
5 Howell# 9 of 3(0) Howell 9 of 3(0)
6 Mod Triple Hes Mitchell#* 9 of 3(0) Mod Triple Hes Mitchell* 9 of 3(0)
7 Mitchell 7 of 4(0) Mitchell* 7 of 4(0)
8 Hes Mitchell#* 9 of 3(0) Hes Mitchell* 9 of 3(0)
9 Mitchell 9 of 3(0) Mitchell* 9 of 3(0)
10 Skip Mitchell 9 of 3(1) Mod Triple Hes Mitchell*
or Skip Mitchell*		 13 of 2(0)
9 of 3(1)		 The Triple Hesitation Mitchell is significantly better balanced than playing a Skip Mitchell, but is also significantly more complex. Your choice :)
11 Mitchell 9 of 3(2) Dbl Hes Mitchell* 13 of 2(0)
11.5 Blackpool or
Share+Relay		 13 of 2(1)
12 of 2(0)		 Hes Mitchell* 13 of 2(0) With 11.5 tables, the Hestitaion Mitchell is workable if NS1 is missing (no sharing). The one winner alternatives are: 1) 13 round Blackpool (some won't like the revenge round), 2) Share+Relay (but only 24 boards), 3) 12 round Blackpool (only 24 boards again) or 4) 9 rounds of a Skip Mitchell (but there will be 3 unplayed sets for everyone and 4 for the sit out pairs).
12 Blackpool 13 of 2(1) Blackpool* 13 of 2(1) With 12 full tables, you're really in a pickle for choosing a well balanced one winner movement for 26-28 boards. The 13 round Blackpool is intuitively unbalanced, but the maths says otherwise!
13 Mitchell 13 of 2(0) Mitchell* 13 of 2(0)
14 Skip Mitchell 13 of 2(1) Skip Mitchell* 13 of 2(1)