*This page describes a movement I received from John Probst, and some improvements
of it. The result is a very nice movement for 7 or 8 pairs, playing 8 rounds.
*

The solution of John Probst was to apply the Worger principle to a standard Howell movement for 8 pairs and 7 rounds. This means that an extra set of boards is introduced at a few strategically chosen places in the movement, to substitute the original sets of the Howell movement. The boards thus released are played in an extra 8th round. This sounds complicated, but is really very simple as shown below:

VERSION 1 1 2 3 4 3- 6 A 7- 2 C 5- 4Compare this to the original Howell:H8- 1 E 4- 7 B 1- 3 D 6- 5 E 8- 2 F 5- 1 C 2- 4 E 7- 6H8- 3 G 6- 2 D 3- 5 F 1- 7 G 8- 4 A 7- 3 E 4- 6 G 2- 1 A 8- 5 B 1- 4 F 5- 7 A 3- 2H8- 6 C 2- 5 G 6- 1 B 4- 3 C 8- 7 D 2- 3 B 6- 7 F 4- 5 D 8- 1 H

1 2 3 4 3- 6 A 7- 2 C 5- 4 D 8- 1 E 4- 7 B 1- 3 D 6- 5 E 8- 2 F 5- 1 C 2- 4 E 7- 6 F 8- 3 G 6- 2 D 3- 5 F 1- 7 G 8- 4 A 7- 3 E 4- 6 G 2- 1 A 8- 5 B 1- 4 F 5- 7 A 3- 2 B 8- 6 C 2- 5 G 6- 1 B 4- 3 C 8- 7 DAs we see, the only difference is the extra 8th round, and, the occurence of board set H in rounds 1, 3 and 6, at table 3.

An elegant movement.

VERSION 2 1 2 3 4 3- 6 A 7- 2 C 5- 4 H 8- 1 E 4- 7 B 1- 3 D 6- 5 E 8- 2 F 5- 1 C 2- 4 E 7- 6 H 8- 3 G 6- 2 D 3- 5 F 1- 7 G 8- 4 A 7- 3 E 4- 6 G 2- 1 A 8- 5 B 1- 4 F 5- 7 A 3- 2 H 8- 6 C 2- 5 G 6- 1 B 4- 3 C 8- 7 D 3- 2 B 7- 6 F 5- 4 D 8- 1 HCompared to version 1 all that had to happen was to undo the arrow switches in the last round!

VERSION 3. 1 2 3 4 3- 6 A 2- 7 C 5- 4 H 8- 1 E 4- 7 B 3- 1 D 6- 5 E 8- 2 F 5- 1 C 4- 2 E 7- 6 H 8- 3 G 6- 2 D 5- 3 F 1- 7 G 8- 4 A 7- 3 E 6- 4 G 2- 1 A 8- 5 B 1- 4 F 7- 5 A 3- 2 H 8- 6 C 2- 5 G 1- 6 B 4- 3 C 8- 7 D 3- 2 B 7- 6 F 5- 4 D 8- 1 HMovement version 3 has again s.d.= 1.40, Qf=87.50.

We will show this version is the best. Tablecards for this movement are available.

For those who prefer the Universal Begin Position we also give a renumbered version:

VERSION 3b. 1 2 3 4 1- 2 A 3- 4 B 5- 6 C 7- 8 D 1- 5 E 8- 6 F 3- 2 G 4- 7 A 1- 3 H 7- 2 C 8- 5 A 6- 4 D 1- 8 B 4- 5 G 7- 3 E 2- 6 H 1- 7 F 6- 3 A 4- 8 H 5- 2 B 1- 4 C 2- 8 E 6- 7 B 3- 5 D 1- 6 G 5- 7 H 2- 4 F 8- 3 C 1- 2 D 3- 5 F 6- 4 E 7- 8 GThis is essentially the same movement as version 3.

See also a discussion in rec.games.bridge

We will now test them with the "two strong pairs" model. The following graphs show the distribution of the scores for all possible choices of the two strong pairs.

It is clear that the original version 2, is somewhat less fair to the average players then version 3, derived from the superperfect Howell. The scores with version 2 have a larger spread, and the extreme values are further away from the ideal value 38.1.

The difference in quality is larger in the Bussemaker model. With movement version 2 the following percentage probability table is obtained:

Pair 1 2 3 4 5 6 7 8 Pos 1 80 19 1 . 2 18 64 17 2 . 3 2 15 59 16 8 . 4 . 2 21 56 19 2 . 5 . 2 19 56 21 2 . 6 . 8 16 59 15 2 7 . 2 17 64 18 8 . 1 19 80 Qd 64.7We recall that in this model all pairs have different strengths and are ordered by their strength, pair 1 being the strongest pair. The table shows that within the framework of the model, pair 1 has an 80% probability of ending at the first place.

For movement version 3 the similar table looks as follows:

Pair 1 2 3 4 5 6 7 8 Pos 1 90 10 . 2 10 78 11 . . 3 . 11 69 13 7 . 4 1 19 62 18 1 5 1 18 62 19 1 6 . 7 13 69 11 . 7 . . 11 78 10 8 . 10 90 Qd 74.7A considerable improvement. The numbers on the diagonal are now a lot closer to the ideal value 100.

In movement version 2 we obtain Qf ranging from 51.82 to 73.08, depending on which of the pairs is absent. The best values are for leaving out pair 1, s.d. = 1.49, Qf = 73.08.

In movement version 3 the s.d. = 1.03, and Qf = 86.36 when one of the pairs is absent. This is independent of which pair is absent!

In other words movement version 2 has Qf1av=61.62 and Qf1max=73.08, while movement version 3 has Qf1av = Qf1max=86.36

It turns out that in this respect movement version 3 is really superior to version 2.

In conclusion we may say that version 3 (or the equivalent version 3b) is the winner, and is the best movement for 4 tables and 8 rounds.

Note. With a few extra arrow switches it is possible to further improve the 7-pair movement to s.d. = 0.70, Qf=95, but that implies separate movements for 7 and 8 pairs.