Arrowswitching Howells

[shevek]

The old 3/4 Howell cards had heaps of arrowswitches. I've realised thanks to people like John Probst & Ross Moore that this was pointless. So what is a fair movement for 7T (9x3) ¾ Howell ?

 

Is it

1) 5 stationary NSs

2) 3 stat NSs & 2 stat EWs?

 

After you make the correct choice there, should you arrowswitch the last round?

 

Thx

[campboy]

The short answer is there isn't one. All movements will be significantly unbalanced, but some will be more unbalanced than others.

 

There is considerable freedom for choice even with the restrictions given in 1 and 2. There is also no consensus as to how to determine whether one movement is more balanced than another when it's close; I have a statistically plausible candidate function, but statistics isn't really my area of expertise. So if you post specific movements I'll tell you which one is better according to that.

 

I suspect the arrow switches on the cards have some merit -- possibly not enough to be worth the hassle. I doubt arrow switching the last round does anything useful.

[crazy4hoop]

This comes from ACBLscore: I entered 7 tables, 9 rounds, 3 boards per round, and this was the movement that popped up. Sorry I cannot be helpfu in offering an opinion but it looks like the ACBLscore program suggests 4 stationary NS pairs and 1 EW stationary pair, at least for round 1.

 

Tables: 7 6.5

 

Boards/Round: 3 3

 

Rounds: 9 9

 

Boards played: 27 24/27

 

Top on a board: 6 5

 

Average: 81 67- (Sit-out factor UP 1/8)

 

Check total: 1134 810

 

Movement: THREE-QUARTER HOWELL

 

 

INITIAL GAME SETUP

 

TABLE BOARDS N-S E-W (*=Stationary)

1 1- 3 14* 1

2 4- 6 6 7

3 7- 9 13* 4

4 10-12 2 12*

5 13-15 11* 8

6 16-18 3 5

7 19-21 10* 9

Bye-stand 22-27

 

BOARD MOVEMENT:

1<--2<--3<--4<--5<--6<--7<--BYE<--BYE<--

 

 

PAIR 1 PAIR 2 PAIR 3 PAIR 4

7 TABLES 7 TABLES 7 TABLES 7 TABLES

RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS

1 1E 14 1- 3 1 4N 12 10-12 1 6N 5 16-18 1 3E 13 7- 9

2 7N 10 22-24 2 1E 14 4- 6 2 4N 12 13-15 2 6N 6 19-21

3 5N 11 19-21 3 7E 10 25-27 3 1E 14 7- 9 3 4N 12 16-18

4 2E 9 13-15 4 5N 11 22-24 4 7N 10 1- 3 4 1E 14 10-12

5 2N 2 16-18 5 2E 1 16-18 5 5E 11 25-27 5 7E 10 4- 6

6 6E 8 4- 6 6 2N 3 19-21 6 2E 2 19-21 6 5E 11 1- 3

7 3N 13 25-27 7 6E 9 7- 9 7 2N 4 22-24 7 2E 3 22-24

8 6N 3 10-12 8 3N 13 1- 3 8 6E 1 10-12 8 2N 5 25-27

9 4N 12 7- 9 9 6N 4 13-15 9 3N 13 4- 6 9 6E 2 13-15

 

 

PAIR 5 PAIR 6 PAIR 7 PAIR 8

7 TABLES 7 TABLES 7 TABLES 7 TABLES

RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS

1 6E 3 16-18 1 2N 7 4- 6 1 2E 6 4- 6 1 5E 11 13-15

2 3E 13 10-12 2 6E 4 19-21 2 2N 8 7- 9 2 2E 7 7- 9

3 6N 7 22-24 3 3E 13 13-15 3 6E 5 22-24 3 2N 9 10-12

4 4E 12 19-21 4 6N 8 25-27 4 3E 13 16-18 4 6E 6 25-27

5 1E 14 13-15 5 4E 12 22-24 5 6N 9 1- 3 5 3N 13 19-21

6 7N 10 7- 9 6 1E 14 16-18 6 4E 12 25-27 6 6N 1 4- 6

7 5N 11 4- 6 7 7E 10 10-12 7 1E 14 19-21 7 4N 12 1- 3

8 2E 4 25-27 8 5N 11 7- 9 8 7N 10 13-15 8 1E 14 22-24

9 2N 6 1- 3 9 2E 5 1- 3 9 5E 11 10-12 9 7E 10 16-18

 

 

PAIR 9 PAIR 10 PAIR 11 PAIR 12

7 TABLES 7 TABLES 7 TABLES 7 TABLES

RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS RD SIT VS BOARDS

1 7E 10 19-21 1 7N 9 19-21 1 5N 8 13-15 1 4E 2 10-12

2 5E 11 16-18 2 7E 1 22-24 2 5N 9 16-18 2 4E 3 13-15

3 2E 8 10-12 3 7N 2 25-27 3 5E 1 19-21 3 4E 4 16-18

4 2N 1 13-15 4 7E 3 1- 3 4 5E 2 22-24 4 4N 5 19-21

5 6E 7 1- 3 5 7N 4 4- 6 5 5N 3 25-27 5 4N 6 22-24

6 3N 13 22-24 6 7E 5 7- 9 6 5N 4 1- 3 6 4N 7 25-27

7 6N 2 7- 9 7 7N 6 10-12 7 5E 5 4- 6 7 4E 8 1- 3

8 4N 12 4- 6 8 7E 7 13-15 8 5E 6 7- 9 8 4E 9 4- 6

9 1E 14 25-27 9 7N 8 16-18 9 5N 7 10-12 9 4E 1 7- 9

 

 

PAIR 13 PAIR 14

7 TABLES 7 TABLES

RD SIT VS BOARDS RD SIT VS BOARDS

1 3N 4 7- 9 1 1N 1 1- 3

2 3N 5 10-12 2 1N 2 4- 6

3 3N 6 13-15 3 1N 3 7- 9

4 3N 7 16-18 4 1N 4 10-12

5 3E 8 19-21 5 1N 5 13-15

6 3E 9 22-24 6 1N 6 16-18

7 3E 1 25-27 7 1N 7 19-21

8 3E 2 1- 3 8 1N 8 22-24

9 3E 3 4- 6 9 1N 9 25-27

 

I see the guide cards came out hard to read. I wish I knew how to make them look normal like they do when writing the post. Oh well.

[shevek]

This comes from ACBLscore: I entered 7 tables, 9 rounds, 3 boards per round, and this was the movement that popped up. Sorry I cannot be helpfu in offering an opinion but it looks like the ACBLscore program suggests 4 stationary NS pairs and 1 EW stationary pair, at least for round 1.

 

PAIR 13 PAIR 14

7 TABLES 7 TABLES

RD SIT VS BOARDS RD SIT VS BOARDS

1 3N 4 7- 9 1 1N 1 1- 3

2 3N 5 10-12 2 1N 2 4- 6

3 3N 6 13-15 3 1N 3 7- 9

4 3N 7 16-18 4 1N 4 10-12

5 3E 8 19-21 5 1N 5 13-15

6 3E 9 22-24 6 1N 6 16-18

7 3E 1 25-27 7 1N 7 19-21

8 3E 2 1- 3 8 1N 8 22-24

9 3E 3 4- 6 9 1N 9 25-27

 

I see the guide cards came out hard to read. I wish I knew how to make them look normal like they do when writing the post. Oh well.

 

This has switches for stationary pairs at various times. I believe this procedure has been discredited mathematically.

Also makes the guide card a bit messy. Need instructions like "Moving Pair to T1" rather then the usual "EW to 1 EW"

[campboy]

Ok. I get the following values (higher is more unbalanced).

 

For the movement exactly as described by crazy4hoop: 0.859

No arrowswitches, one EW (pair 12) four NS: 1.314

No arrowswitches, all stationary pairs NS: 0.730

No arrowswitches, two EW (pairs 12+13) three NS: 1.307

 

For comparison, a full Howell would get 0.0847, a switched Mitchell 0.0904 and an unswitched Mitchell 1.0.

 

So by my definition of "unbalanced", all stationary pairs NS is a clear winner. If you take *that* movement and arrowswitch the last round then you get a significant improvement: the figure drops to 0.605. Arrowswitching the last round only at tables with a stationary pair is slightly better: 0.599.

 

I doubt arrow switching the last round does anything useful.

I stand corrected :)