[BudH]

Thanks to some whining and some severe misconceptions by some members at my local club, I am not allowed to use any more arrow switched movements, defined as "all tables with stationary pairs have those pairs play the East-West cards all during the same round". Since we had a few games where the stationary pairs during the last (arrow switched) round did much better than their opponents, about 70% of stationary pairs and only 30% of the moving pairs received masterpoints, therefore it was deemed "unfair". That is not the reason for this post.

The reason is because I am making some changes to the arrow switched Hesitation and Double Hesitation Mitchell movements so the stationary pairs (probably all but one stationary pair) are playing the East-West cards more than 1 out of 9 rounds (likely 2 rounds) so it will look more like a Howell but retain some of the benefits of ease of movement by the moving pairs.

What criteria does one use to decide at the stationary pair tables how often the table guide card needs to be turned 1/4 turn? And which boards are involved in those rounds? Should it be most of them and no more than twice during the session should boards be played at an arrow switched table? Do I need to ensure those moving pairs don't show up at an arrow switched table for more than half their rounds?

In a 6-table Howell with 3 stationary pairs and Tables 2 and 3 arrow switching several times, I did not see any rhyme or reason on when those guide card turns happened. Is there any for proper "balance"? Is there any reference material I might look this up on?

I have a 7 Table 9x3 Double Hesitation Mitchell (pivot tables 2 and 7, Tables 1, 3, 4, 5, 6 have a stationary pair, pairs move 5EW>6EW>7EW>2NS>7NS>1EW>2EW>3EW>4EW) and an 8 Table 9x3 Hesitation Mitchell (7 stationary pairs at Tables 1-7, Table 8 pivot table, pairs move 5EW>6EW>7EW>8EW>8NS>1EW>2EW>3EW>4EW) which are my two prime candidates to change from a final round single round arrow switch at the stationary tables to having all but one stationary table arrow switch two to three rounds.

[steve2005]

Yes, for some people being a stationary pair is an advantage, less moving about. For some being a moving pair is better, for me and my wife we prefer moving so our muscles don't tie up. For some handicapped people a stationary pair is a requirement.
From a bridge standpoint there is no card advantage. Sure on any given night the cards can favour one side but next night it can be even or the other way. Your players are superstitious.

[mycroft]

There is an advantage - sometimes at least.

I realized one night at my 8 table game that, "don't care who grumbles, I *have to* arrow-switch" - when I realized that the second-strongest pair N-S was my (very good) 100-MP spare playing with the epitome of "people playing with the spare", and the second-weakest pair E-W was on par with me and my regular partner (comments on this point gleefully ignored).

Said spare-and-partner, with one round to go, had a 65% game, and were a board+ clear of the field. They ended up fourth.

It would not surprise me at all if Bud's N-S field was somewhat stronger than his E-W field (the "require stationaries" frequently map to "stronger", or at least "decades more experienced" players; and the "want stationaries" (aka "Lords of the Table") also skew toward the A field) and that when the weaker pairs' results (against the stronger pairs) suddenly had direct competition from the stronger pairs (playing against weaker defence), their scores went down.

If that is true, however, Bud, you're paddling against the tide. Because it doesn't matter what arrow-switch game you play, the "stationaries" are going to punch up to their place in the matchpoint results on average, just because the stationary field is stronger than the moving field. That's sort of how bridge works; the better players score better, in the long run. Try to convince some of the better "prefer to be N-S" pairs to sit east-west for a month or so, and see if the "stationary vs moving" ratios even out.

Either that, or go back to two-winner movements, and convince *exactly one* of the better "prefer to be N-S" pairs to sit east-west for a month or so. See if you get any comments about "that pair fishing the field to win more masterpoints"...

[blackshoe]

There is discussion of arrow switching in Hallen, et. al., Movements: A Fair Approach. The English disagree with the authors of this book on the subject of arrow switching. David Stevenson provides articles from several English authors, including mathematician and director John Manning, on his website.

[barmar]

We've been playing 6 and 7 table Howells much of the time lately. A recent player walks with a cane and struggles to get out of his chair, yet he never asks for a stationary table.

From what I remember, the pattern of arrow switches seems to be designed to maximize the different combinations of directions for the stationary pairs. So for 4 of them it's like this:

NNNNNNN
NNNNEEEE
NNEENNEE
NENENENE

[pran]

barmar, on 2017-April-29, 11:05, said:

We've been playing 6 and 7 table Howells much of the time lately. A recent player walks with a cane and struggles to get out of his chair, yet he never asks for a stationary table.

From what I remember, the pattern of arrow switches seems to be designed to maximize the different combinations of directions for the stationary pairs. So for 4 of them it's like this:

NNNNNNN
NNNNEEEE
NNEENNEE
NENENENE

Any two different pairs can for each board find themselves in three different situations:
1: They meet when playing that board
2: They are seated in the same direction when playing that board (i.e. they are competing on that board).
3: They are seated in opposite directions when playing that board (i.e. they are co-operating on that board).

A perfectly balanced schedule exists when for each and every pair in the event the counts of situations 2 and 3 are equal over the whole field.

This applies regardless of the movement schedules!

The stationary pair in a standard Howell will (obviously) always have perfect balance, but for the other pairs Perfect balance is only possible with certain numbers of tables. So the target when creating movements should be to obtain the best possible balance for every pair.

[Vampyr]

pran, on 2017-April-30, 00:17, said:

So the target when creating movements should be to obtain the best possible balance for every pair.

I do not think the OP was arguing against this; he is interested in how to achieve it.

[pran]

Vampyr, on 2017-May-01, 01:37, said:

I do not think the OP was arguing against this; he is interested in how to achieve it.

I believe the best answer is: Don't tamper with Mitchell.
The number of rounds can hardly be sufficient to obtain a good balance for every pair against every other pair.