Statistically unfair movements

Small club is growing and now regularly has more than 16 tables. Members are used to simple Mitchell movement and one section. The forthcoming AGM will discuss movement fairness and I need help in finding information describing how fair/unfair such a move is for various table numbers and boards played ie what is the statistical margin of error to the final results table.

Pointers to website giving such numbers would be greatly appreciated.


  • I'm not an expert on movements , so I'm afraid I'm not going to answer the substantive question, but I do rather wonder about how productive it will be to have a discussion of this sort at your AGM. In my experience when AGMs discuss matters of this sort (unless it is to have a brief discussion of a couple of well-researched options, before voting on which to adopt), the red herrings are very much in evidence, But perhaps your club is different - good luck, anyway.

  • You might want to look at and the link to "suggested movements".

    There are various ways of avoiding having 30+ boards in play with 15/16/17 tables. With 18+ tables you can play in two sections.

  • Great news about the expansion of your club. If your club has access to a dealing machine web mitchells are a good option. There is more about movements including web mitchells at

  • They may be used to one section but with ever increasing numbers two sections could be better.
    I don't know how easy it is to run Bridgemates with two sections. We do it with two separate computers.


  • Very easy with EBUScore. Can be totally different movements and number of tables if you wish. Currently up to 50 sections supported I think. So only need one server and computer.

  • If you can get duplimated boards then a Web Mitchell solves all problems. (You can of course duplicate hands at the table but a) people doing this the first time find it difficult b) the duplication has to be done on some boards during rounds 2 and 3 and c) playing an odd number (15/17/19) you have a problem on the 1st round when you have two boards for three tables.) The version I use (Gordon's I undersatnd) only has 1 table where the sharing/ extra set problem occurs. I use scorebridge and have no problems with 2 events on the same session.

  • I have a related question. Manning in his 1979 paper explores the idea of 'amount of competition' in movements. He concentrates mainly on the Mitchell and the arrow switched Mitchell. Does anyone know if there has been any later work including Howell v Mitchell for the same number of tables (e.g. 7, 8 tables with 24 boards). Intuitively, a Howell (or 3/4 Howell) should give more competition as each pair plays a higher proportion of opponents, but has that been quantified?

  • edited May 2018

    The EBU Manual of Duplicate Bridge Movements (2012) discusses 'balance' in different bridge movements. A two-winner Mitchell for an odd number of tables is balanced IFF the number of rounds is the same as the number of tables. As I am sure you know there are 4 categories

    Number of rounds they play against each other: amount of competition = matchpoints at stake
    Number of rounds they play the same direction: amount of competition = 2
    Number of rounds they play in opposite directions: amount of competition = -2
    Rounds where they do not play: i.e. boards that they don't compete on each other: amount of competition = 0

    For a 'balanced' movement every player should have the same numbers e.g. for a 4-table Howell, each player plays Once against each other, 3 times the same way and 3 times the opposite way (so everyone has a competition factor of the number of matchpoints with each other competing pair). However this is not usually the case - usually some players will play the same way as others more often than they play in opposite ways. So the level of competition will vary. e.g. if two pairs play the same direction 4 times and the opposite direction twice then the competition between them is (matchpoints + 8 - 4), whereas if the reverse is true then the amount of competition is (matchpoints +4 -8)

    To try and equalise the competition between every pair, we use arrow-switching. I do not understand the mathematics of arrow-switching (just the principle). In a serious competition arrow-switching can appear random but in normal club events arrow switching one or two rounds at the end is easy to do and improves the balance.

    Full Howells (everyone plays everyone) are obviously very rare.

    Obviously 'balance/ fairness' is not the same as 'competition'

    With regards to 'competition', you are right that, cateris paribus, the greater the percentage of opposing pairs you play the greater the competition, overall (because the number of times two pairs do not play each other is lower and thus the total number of rounds where they do play each other (where the competition is the total matchpoints rather than just 2) is greater). However that does not mean that the competition is absolutely fair (the aim of a movement is that the amount of competition between any two pairs does not vary)

    The Manual recommends that the number of rounds should be at least 80% of the number of tables - Obviously this is the case for Howells / 3/4 Howells for sensible table numbers: the EBU have compromised with the 70% rule which allows for a shorter session (17 tables 12 rounds, is a limit)

    So the short answer is: I do not know if ana lysis of the fairness of competition has been published (obviously it can be calculated by simply plugging in the numbers into the theory).

  • Thanks. Plugging in the numbers is what I was too lazy to do! No help for it. I must find out.
  • edited May 2018

    Ian McKinnon's free program Jeanie provides information on balance of movements.

  • Some useful comments -thanks.

    However, what I can't find is a clear analysis of WHY there is the 80%/70% rule. Members want to know just how unfair simple movements are if they break these rules eg what is the margin of error if 24 boards are played over 17 tables using a standard Mitchell movement. In simple terms, if pair A 'win' with 62.51% and pair B are second with 61.82%, did pair A win fair and square?

  • The 70% rule was originally going to be the 75% rule but was changed in response to feedback from clubs to allow them to play some existing, simple movements that would otherwise cause them problems with certain numbers. So it was a compromise and you won't get an objective answer to this question. However, I think everyone can see that it would be very undesirable to play 24 boards out of 48 in circulation (to take an extreme example, but one that has actually happened in the past) so that every pair is compared with another pair with whom they have no boards in common at all!

    However, this is not exactly the same question as that of balance: in a two-winner 8-table Share-and-Relay Mitchell you play 100% of the boards in circulation, as do you in a one-winner 8-table Skip Mitchell, but the first is much more balanced than the second.

  • well to take the case illustrated - there are 34 boards in play and each pair play 24 of them. The amount of overlap (pairs playing the same boards) varies considerably.

    The number of boards that NS1 play in common with other NS pairs varies from 11 to 7. with the result that the amount of competition varies substantially. If we assume 2 rounds arrowswitched

    NS1 and NS 2 (& NS 1 and NS 17)
    Play 11 boards the same: compete on 10 sets, co-operate on one set (set 12): CV = 9
    NS1 and NS 3 /16
    Play 10 boards the same: compete on 8 sets co-operate on two sets (11,12) : CV = 6
    NS1 and NS 4/15
    Play 9 boards the same: compete on 7 sets co-operate on two sets: CV = 5
    NS1 and NS 5/14
    Play 8 boards the same: compete on 6 sets co-operate on two sets: CV = 4
    NS 1 and NS6/13
    Play 7 boards the samer: compete on 5 sets co-operate on two sets CV = 3
    NS 1 and NS 7/12
    Play 7 boards the same: compete on 4, co-operate on 3! CV = 1
    NS 1 and NS 8/9/10/11
    Play 7 boards the same: compete on 3, co-operate on 4! CV = -1

    So the standard deviation in the competition of NS pairs ONLY is 3.18K - which is much higher than for a balanced movement.

    BUt, what is worse, is if you compare a NS pair with an EW pair and they don't play each other. (Which happens 5 times)

    In that case: They co-operate on 8/10 rounds and only compete on 2 or 4 rounds - giving a competition value of -8 or -4

    Adding in such a large -ve values greatly increases the standard deviation of the competition, making the movement less fair (as we would expect)

    The (tentative) conclusion I can draw (without doing a full analysis) is that in such a large movement it would be best to have a NS AND an EW winner. i.e. no arrowswitching at all.

  • I started to put numbers into various formulae but my brain hurt too much. Over 24 boards, a 1% change on one round equates to about .04% swing overall ie 2 pairs have identical results save for one board where each percent difference on that board is about .04% in the final result. I then looked at a couple of real results for two pairs with roughly similar overall results: in both cases one pair played boards that were essentially flat (c55% top) but another pair played boards with 80% tops: 1.8% change on overall score. One event yielded a possible 4% overall difference in scores on the hands played by only one pair (assuming both pairs got maximum percentages). Yes there are many factors involved, perfect movements are quite rare, and over time things may average out.....

    It looks like it comes down to how concerned people are about results being maybe 4% in error if only 70% of available boards are played......

    I take Weejonnie's point about arrow-switching.

  • Every time I look at movements, I come to the same conclusion - they are inherently unfair and imbalanced to greater to lesser extents. Competitiveness in movements are one thing, but how about playing against the one pair that bids a lay-down slam, you get 0% for that board. Every other pair that played the board in your direction now get 66% (or whatever) through no skill of their own.

    Or how about when someone makes a crazy false-sacrifice against you so you get 100%, every other pair in your direction gets 33% or whatever.

    However, what I have also seen is that it makes very little difference which movement you choose over a reasonable timeframe. Any one-off night is naturally unpredictable as any crazy bid or play can work on its day.

    Even so, if you think about the top 5 pairs and bottom 5 pairs for any night there is (from my experience) and 90+% chance and 4 out of 5 will be at the top end and 4/5 will be at the bottom end.

    This is even more the case when looking at performances over a longer period of time, such as a year average, NGS etc.

    So, I think that those players that spend a lot of time considering the fairness (or otherwise) or various movements would better spend their time counting cards better, learning bidding systems more accurately or discussing possible bids with their partners.

    On a side note, does anyone actually think that winning with 62.5% in anyway means that they played better than second place with 62.4%?

    This to me is where the significance of the NGS really comes into play. I now care even less about winning or coming 3rd and I'm more interested in trying to keep my Ace Clubs ranking or maybe even pushing towards Ace Diamonds. This seems to be far more significant (if there is any significance to playing reasonably well at bridge) than coming top in a room of friends.

  • Overall I would agree: there is far too much variance and luck in the game for ability to be measured over 24, or indeed 240 hands. So I DO like the NGS: it is inherently stable.

    TBH I am not one who takes measures to improve their grade by avoiding random partnerships or whatever. To me it is the pleasure of playing.

    (Personally I think that teams is a better test of combined skill of the two pairs. Even in a short teams match the better team wins overwhelmingly often)

    (Example of variance: one player at our club scored 84%, 72% and 53% yesterday and today. Mind you it was in a novice, relatively social and competitive fields respectively :) )

  • I agree with Martin that the inherent unfairness of most movements makes a very small contribution to the results of most sessions. But it is still a good idea to choose a "good" movement over a "poor" one if one has the chance, which in practice is easier for some numbers of tables than for others.

  • Maybe the next time the EBU update their Manual of Duplicate Bridge movements (my version is 2012), they could include the SD of competitiveness in each one (for a specific number of tables) so Directors can make an informed decision. Alternatively they could just publish the values in a suitable location.

  • If you are planning to discuss this subject at your next AGM, you will probably have most of the members falling to sleep while two or three of you at most will be arguing technical detail. Choosing the best movements for your club is best done by you alone and maybe one or two others who may be sufficiently interested in the subject.

    You might like to take a look at - td guide - movements.pdf which lists the movements that we use for any given numbers of pairs at Sheffield BC. I last updated it nearly five years ago when we decided to not try to play 30 boards in a session but to keep as far as possible to 26 to 27 boards.

    My suggestion would be that you make up a list of the movements that you think would be best for your club sessions for any likely numbers of pairs (or tables) and simply recommend it to your AGM.

    You'll notice that for 15 to 18 tables, Sheffield uses an unusual set of movements that I have seen nowhere else (and I suspect that the originator was a member of the club who died many years ago) but which use a single set of duplimated boards for 9 rounds of three boards each with all players playing all 27 boards, simply by having many pairs of adjacent tables sharing sets of three boards.

    Although the EBU Movements Guide has been mentioned frequently in this thread, I would also suggest that you browse through your club's scoring program, whether EBUScore or Scorebridge as both these programs have many times more movements available than are mentioned in the EBU Movements Guide.

    As for movements being unbalanced or unfair, I wouldn't worry too much beyond keeping the number of boards in circulation down as far as possible to the number of boards to be played.

    Barrie Partridge - CTD for Bridge Club Live

  • Yes - I've read your article on Sheffield Bridge movements and we have a set of laminated movement cards stored in individual envelopes with a note of when they should be used. Our club plays 24 boards generally, rather than 27, For 13-18 tables you could probably use an appendixed Mitchell format based on an internal sequence of 9 rather than the 13 usually found. Easy enough to create if needed. If you want, I could create a specific movement in Scorebridge

    1 shares with 10, 2 with 11, 3 with 12 etc
    NS 1, EW 10 : NS 2, EW11 etc are stationary when sharing othewise : NS up 1, EW down 2, boards down 1. Probably arrowswitch the last round. You might note that when playing 18 tables the movment morphs into two straightforward mitchells.

    Until a few days ago I hadn't really considered 'fairness' in pair:pair competition, so the last few days have been very instructional.

    I now try and arrange matters so that my partner and I play the best players in the club on the arrowswitched rounds =)

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