Characteristics and Criteria for Selection of Movements for Duplicate Pairs (All Formats)
These notes relate to all pairs competitions but are particularly relevant to single-session events.
A
Criteria for Selection
The types of movements (Howell, Mitchell etc,) are described later. In choosing a movements the main
considerations are Duration, Simplicity and Fairness but an overriding requirement is familiarity. Not
playing the optimum number of boards might lead to adverse comment, playing a badly balanced movement
is unlikely to be noticed but getting a movement wrong could be a disaster.
Nevertheless, some TDs continue with movements that they have inherited, assuming that they produce fair
results because they have always worked.
Duration
The competitors are mainly concerned about the number of boards played, particularly during a single
session. The length of such a session is usually restrained by the availability of the accommodation. In a
typical 3½ hours there is time to play 24 boards. This allows for a few minutes preparation followed by play
at the accepted rate of eight boards per hour and time to clear up at the end. Most competitors are keen to
play as many boards as possible in the available time and are prepared to accept moderate unfairness and a
complicated movement, provided it does not go wrong. Consequentially playing 24 boards is often both an
upper limit and a target for a normal single-session competition.
Simplicity
Organisation is easier if table cards are not needed. Detailed charts are provided on this site for all the
movements even the simplest. These show the position of pairs and boards for every round and most
importantly the position of relay tables and tables sharing boards..
Fairness
A Howell Movement for an even number of tables is perfectly balanced and gives competition that is as fair
as possible. The starting positions are unimportant. But there are few other movements that provide such
fair competition. A Howell for an odd number of tables has noticeable bias. A Mitchell without arrow
switching gives perfect competition but only if all rounds are played and only within the separate NS and EW
streams. Without arrow-switching there is no sensible way of combining the results to get one winner.
Switching the right number of boards can provide an acceptable single winner movement but there will
always be some bias that, hopefully, will not be obvious to even the discerning players.
In the weekly club meeting, achieving fairness in a single competition is not usually a matter of great
concern. Hopefully any bias will even out during the year. This could be facilitated by ensuring that the
players do not always sit in the same places but this is easier said than done. Drawing for starting positions is
normally unpopular and the regulars who arrive early and help set out the room expect to take their favourite
seats.
In contrast, in a County Championship there is only one opportunity to get a fair result. It might then be
preferable to play a shorter movement that is well-balanced rather then a normal full-length one that has
hidden bias.
B
The Variety of Movements
Howell Movements
Howell movements in which all the pairs face each other are suitable for a small number of tables. A
complete Howell movement for an even number of tables is perfectly balanced whereas one for an odd
number of tables is acceptable but does have some bias. In a six-table Howell, for example, eleven rounds
are played. Two pairs meets each other in direct confrontation for one round, hold the same cards while
meeting other opponents for five rounds and hold opposite cards for the remaining five rounds. When face to
face they are in direct contention for 10 match points (each board is played six times). If one pair gets a top
the other must necessarily get a bottom. But a good score by one also depresses the score for all the other
pairs who have or will hold the same cards and do not perform so well. They will each get two fewer match
points. At the same time the pairs holding the opposite hands are pleased to have their scores enhanced by 2
MPs. As each opponent holds the same card for five rounds and the opposite cards for five rounds the effect
balances out and the result of the direct confrontation is dominant. The contention between any two pairs can
be represented by
10 + (5 x 2) + (5 x -2) = 10 match points
In contrast, a five-table Howell movement played over nine rounds is good but not perfect. Each board is
played 5 times for a top of 8 MPs on each board. Two pairs again meet face to face for one round but now
hold the same cards for five rounds and the opposite cards for only three rounds (or vice versa depending
upon the starting position). The measure of competition then becomes
8 + (5 x 2) + (3 x -2) =12 match points
or
8+ (5 x -2) + (3 x 2) = 4 match points
The amount of competition between pairs depends upon their relative starting positions. Is this significant?
In a full movement of 9 x 3 =27 boards a score of 100% would be obtained with 27 x 10 = 270 MPs. A pair
fortunate enough to get an advantageous draw might hope to get 3 x (12 – 4) = 24 more MPs against the tyros
than they would against the masters. This difference of 24 / 270 = 8.8% could well affect the results but
fortunately any bias is unlikely to be noticed and certainly the bias is less than that of many alternative
movements.
Three-Quarter Howell Movements
A complete Howell movement for n tables, where one pair is stationary and all pairs face each other, requires
(2n - 1) rounds. This number of rounds is inconveniently odd and does not fit easily into a desired 24-board
movement. There are “Three-Quarter Howell” movements with two or more stationary pairs where fewer
rounds are played These may not necessarily be significantly better balanced than a shortened Howell and
may require the sharing of boards.
.
Mitchell Movements
Contestants do not have to meet face to face for there to be perfect competition. A complete Mitchell
without arrow switching provides perfect competition but only within the two separate streams (the
stationary NS pairs and the moving EW pairs). A NS pair faces each EW pair in turn but is actually
competing against the other NS pairs who will be holding the same cards in other rounds. To the NS pairs,
the EW pairs are just a set of common obstacles to be negotiated. All NS pairs meet all EW pairs and all
play the same cards, albeit against different opponents.
Between pairs in different streams there is no net competition. In, for example, a straight 7 x 3 Mitchell
movement a NS pair does battle with one of the opposing EW pairs on three boards for the full 12 MPs each.
If the moving pair is good and does well, the stationary pair has the consolation (or hope) that the same pair
will perform as well against all the other NS pairs on the other 18 boards (worth an extra 2MPs per board).
The expectation for the competition against that pair is (3 x 12) + (18 x -2) = 0. When similarly three tops
are taken against the less gifted there is the matching fear that tops will be conceded to all the other NS pairs.
A complete un-switched Mitchell gives excellent competition to the two streams separately. But nothing can
be deduced about the relative abilities of the two streams. The average score for each stream is exactly 50%.
A very high score by a pair in one stream (accompanied by resultant low scores of other pairs) means only
that there is a greater spread of ability in that stream not that the performance of that stream is better than the
other.
Switched Mitchell Movements
Switching approximately 1/8th of the boards in a Mitchell movement can produce a reasonable single winner
movement. If 1/8th of the boards are switched, two NS pairs would play 1/4th of the boards in opposite
directions (because they switch different boards). The pairs are in direct competition for the ¾ of the boards
that they still play in the same direction but the effect is reduced to ½ by the ¼ of the boards where they are
in alliance. Similar reasoning produces the same amount of competition between pairs of the opposite
streams.
This is perhaps an over-simplification. Unfortunately switching exactly ¼ of the boards is never exactly
possible and switching has no effect upon the net competition between pairs that meet during a switched
round. But sufficiently good single-winner movements can be produced by switching about 1/8th of the
boards. Better balance might be obtained by switching single boards in different rounds but the benefits
seldom justify the extra trouble to the tournament director and the scorer.
In summary, switching can introduce competition between pairs in opposite streams at the expense of the
quality of competition in the two separate streams.
Hesitation Mitchell and Double Hesitation Mitchell Movements
The number of rounds in a full Mitchell Movement is the same as the number of tables. This can be
inconvenient. The number of rounds can be increased by one (or two) by getting both pairs at one (or two)
tables to move around the other tables making it easier to achieve a movement of 24 boards. Table cards at
the “pivot tables “alone are usually sufficient to guide the competitors.
C
The Nature of Competition and Assessing Fairness
At the end of a competition two rival pairs might study the travellers to see how well they did against each
other. They would look first at the boards where they met head to head recognising that they were competing
for the share of a maximum on each board. But, if enlightened they would also recognise that, even on
boards where they did not clash directly, they affected each other’s scores. When playing the same cards
against different opponents, the better performer depresses the score of the other by two MPs. But if they
hold opposite hands they are in alliance. They could congratulate each other with “didn’t we do well” or
more likely “If you hadn’t done so badly I would have been two MPs better off”.
They can get a measure of contention between them by accumulating in match points a “Top” for each board
where they meet head to head, adding 2MPs for each board where they hold the same cards against different
opponents and subtracting 2MPs for each board where they hold opposite hands. If the total is large then the
performance of one has a considerable affect upon the other. In a badly balanced movement it could even be
negative showing that the pairs are more in alliance than opposition. If you have such a negative score
relative to the champions you are lucky and gain from the imperfections in the movement.
Of course such an analysis is only valid if, when not facing each other directly, they both play boards from
the same set against opponents from the same set. It is as fallacious comparing the performance of pairs that
play the same cards but do not meet the same set of opponents as comparing the scores among the same set
of opponents that play different cards (such as a progressive Chicago with the hands redealt after each
round). We do not place much credence on the latter. For historical and charitable reasons some relish the
former when it is promoted as a simultaneous competition.
Using a spreadsheet and some diligence the contentions between a “base” pair and each of the other pairs can
be calculated and displayed using the above method. For a perfectly balanced movement the values would
all be constant whatever the “base” pair. The relative starting positions would then not matter. But,
unfortunately, there are very few such movements. Most have imperfections and it is a matter of careful
judgment whether these override the requirements of duration and simplicity.
A value, such as100 x Standard Deviation / Mean, could be calculated to show the spread of a set of values.
This might be a useful indicator but would not a substitute for sound bridge judgement.
D
Incomplete Movements
Incomplete movements are noticeably unfair and the smaller the movement the greater the unfairness.
Acceptable results in a Mitchell Movement, whether switched or not, are dependent upon every pair in one
stream facing every pair in the other. With a small number of tables the effect of missing one of the
opposing pairs is significant. In a seven table Mitchell movement, 14% of the MPs are scored in one round.
Meeting the champions in the last round and getting three bottoms could knock a 50% down to 43%, whilst
getting three tops could raise it to 57%. Not playing the last round could affect the final score by this 14%.
It is usually better to play only 21 boards of a complete (7 x 3) movement rather than only 6 rounds (24
boards) of a truncated (7 x 4) movement. The bias is particularly noticeable in a truncated Mitchell
Movement or a Mitchell with Skip as players can identify the opponents whom they will be missing.
E
Half Tables
With an odd number of pairs, some pairs are obliged to sit out for one round each. For a Howell movement,
it is usually convenient to omit the stationary pair. In a Relay and Share Mitchell dispensing with the NS pair
at one of the sharing tables makes sharing unnecessary. If there is sharing between Table 1 and a “pivot
table” in a Hesitation Mitchell then NS1 is omitted. An extra pair, arriving after the first round of a full table
movement has started, can be accommodated by designating the pair as a “Rover” replacing a different pair
in each round. This can be complicated, requires a detailed schedule of “sit outs” and can easily go wrong if
the Rover Pair are slow in finishing a round.
Whenever there is a half table, a movement with a larger number of rounds and a smaller number of boards
in each round is preferable More pairs then sit out for a shorter time each.
F
Movements for a Large Number of Tables
To achieve results that are fair to all competitors a movement has to be complete. For a Mitchell Movement
this means that there should be as many rounds as there are tables. In a 13 table movement each pair misses
one pair of the opposing stream and should the pair missed be good players a not insignificant advantage
could be gained. When two opposing pairs are missed (14 tables) then hopefully they will not both be good
pairs. Drawing lots for starting positions is perhaps the best that can be done. As the number of tables
becomes larger so the fairness of the movements becomes more and more suspect. But in practice there is no
appetite for turning away players so that a less than perfect result has to be accepted
There is a mistaken belief that the problem can be solved by playing the competition in two sections, playing
with duplicated boards and scoring the results across the whole field rather like a miniature simultaneous
pairs competition. This could make matters worse.
Dividing a 16 table field would result in two sections. The competition within each section would be
immensely improved. Not only would the pairs compete in three-board rounds but the scores on each board
would be more discriminating having been moderated by the play in the other section. But the competition
between sections would be none existent. Any comparison would be based upon the assumption that the
standards of players in the two sections (both level of ability and range of abilities) were comparable
G
How to Take Advantage
This section is not intended as a guide for cheats but rather as a warning to TDs about deficiencies of which
they should be aware. In an important competition it is best to assign places randomly whether it is crucial or
not. But in many clubs early arrivals select their favourite seats. This could become significant if the same
pattern of seating becomes established.
In a typical club, where an annual prize is associated with a series of competitions, it is less important that all
the individual competitions are themselves perfectly balanced providing that any distortion is not regularly
repeated. It would be perfectly acceptable to base an Annual Pairs Championship upon the results of a series
of un-switched Mitchell Movements but not if the same players regularly took the NS seats. In general,
unbalanced movements can be combined for an annual ladder if the starting positions are random or are not
by self selection.
.If a movement with a “revenge round” is expected (i.e. the starting opponents are met again later) then it is
of course only good manners to invite a novice pair to join your table. A travelling pair starting at the table
just above tough opponents might gain an advantage by only meeting them when the boards are switched or
even missing them completely if the movement is incomplete.
It is unlikely that players would deliberately pick such a table but they might subconsciously consider it a
lucky or a friendly table. Upon a similar matter, it is advised that in England it is not, of itself, improper to
adopt such tactics. If they are thought undesirable then the rules should be adjusted.
gde17.2.10