Bill:
Welcome aboard!
I am familiar with the pairing tables created by Johann Berger, a German chessmaster around 1900. By "seating" consecutive pairing numbers in every other chair within the ribbon, I was able to replicate his tables. This is an example of the setup and round to round rotation (ignore everything under the blue bar) and that page has a link to my table generator.
The Howell Movement in Duplicate Bridge you referred to seems to be an ordinary round robin except the cards have their own movement. Perhaps it is like chess RR except no person (pairs in bridge) can sit at the same table more than once? My own experience in bridge was over 25 years ago and never as a director.
This forum occasionally gets requests for three players in a game (e.g., cutthroat pool) or assigned partners (doubles tennis). I'll be interested to see your future posts here.
There are two types of pairs movements commonly used for duplicate bridge: the Howell movement and the Mitchell movement. The Mitchell is far and away the more common, since it is the movement usually played with 7 or more tables (14 or more pairs). The Mitchell movement has two "fields", one of which plays exclusively North-South and the other plays exclusively East-West. The North-South pairs remain at the same table for the entire session, while the East-West pairs move to the next higher table after each round -- if there is an even number of tables, then the East-West pairs have to skip a round at some point, to avoid playing the same hands (boards) twice. The boards always move to the next lower table after each round.
The Howell movement is more irregular. There is generally one stationary pair, and the other pairs (always an odd number of them) move in a cycle through various positions, both North-South and East-West, so that there is only one field consisting of all the pairs. However, there is the additional constraint that no pair can play the same boards more than once, which makes it effectively impossible to use a simple round-robin movement. (It's been a long time since I directed a bridge tournament, so I may have forgotten some details.) For example, it is
not possible to use the following schedule for 10 pairs:
| Round | Table 1 | Table 2 | Table 3 | Table 4 | Table 5 |
| 1 | 10-1 | 9-2 | 8-3 | 7-4 | 6-5 |
| 2 | 10-2 | 1-3 | 9-4 | 8-5 | 7-6 |
| 3 | 10-3 | 2-4 | 1-5 | 9-6 | 8-7 |
| 4 | 10-4 | 3-5 | 2-6 | 1-7 | 9-8 |
| 5 | 10-5 | 4-6 | 3-7 | 2-8 | 1-9 |
| 6 | 10-6 | 5-7 | 4-8 | 3-9 | 2-1 |
| 7 | 10-7 | 6-8 | 5-9 | 4-1 | 3-2 |
| 8 | 10-8 | 7-9 | 6-1 | 5-2 | 4-3 |
| 9 | 10-9 | 8-1 | 7-2 | 6-3 | 5-4 |
since it is not possible to arrange a simple board movement to handle it.
There's more than one way to skin a cat, though. The following layout, or something similar, might work:
| Round | Table 1 | Table 2 | Table 3 | Table 4 | Table 5 |
| 1 | 10-1 | 8-6 | 9-5 | 7-4 | 3-2 |
| 2 | 10-2 | 9-7 | 1-6 | 8-5 | 4-3 |
| 3 | 10-3 | 1-8 | 2-7 | 9-6 | 5-4 |
| 4 | 10-4 | 2-9 | 3-8 | 1-7 | 6-5 |
| 5 | 10-5 | 3-1 | 4-9 | 2-8 | 7-6 |
| 6 | 10-6 | 4-2 | 5-1 | 3-9 | 8-7 |
| 7 | 10-7 | 5-3 | 6-2 | 4-1 | 9-8 |
| 8 | 10-8 | 6-4 | 7-3 | 5-2 | 1-9 |
| 9 | 10-9 | 7-5 | 8-4 | 6-3 | 2-1 |
Even after the board movement issue is resolved, there is then an issue called "balance of comparisons". The issue is this: there are 9 sets of boards, played by each pair, 5 of them in the North-South direction and 5 in the East-West direction. The pairs who play a set of boards in the same direction are scored against each other, so you don't want two pairs to play in the same direction more than the average, since they are then weighted against each other too strongly, and likewise too weakly against some other pair(s). It gets messy very quickly -- suffice it to say that the normal cure for imbalanced comparisons is judicious arrow switches, i.e. on some round(s), the pairs who would normally play North-South plays East-West instead, and vice versa.
The bible of bridge movements is Alex Groner's
"Duplicate Bridge Direction", which is more practical than theoretical. It's worth looking at.
