NO ARROW

SINGLE ARROW

1		NS	EW
NS	EW	MP	MP
1	11	12	0
2	13	5	7
3	15	5	7
4	17	5	7
5	12	5	7
6	14	5	7
7	16	5	7
2		NS	EW
NS	EW	MP	MP
1	17	12	0
2	12	5	7
3	14	5	7
4	16	5	7
5	11	5	7
6	13	5	7
7	15	5	7
3		NS	EW
NS	EW	MP	MP
1	16	12	0
2	11	5	7
3	13	5	7
4	15	5	7
5	17	5	7
6	12	5	7
7	14	5	7
4		NS	EW
NS	EW	MP	MP
1	15	12	0
2	17	5	7
3	12	5	7
4	14	5	7
5	16	5	7
6	11	5	7
7	13	5	7
5		NS	EW
NS	EW	MP	MP
1	14	12	0
2	16	5	7
3	11	5	7
4	13	5	7
5	15	5	7
6	17	5	7
7	12	5	7
6		NS	EW
NS	EW	MP	MP
1	13	12	0
2	15	5	7
3	17	5	7
4	12	5	7
5	14	5	7
6	16	5	7
7	11	5	7
7		NS	EW
NS	EW	MP	MP
1	12	12	0
2	14	5	7
3	16	5	7
4	11	5	7
5	13	5	7
6	15	5	7
7	17	5	7

1		NS	EW
NS	EW	MP	MP
1	11	12	0
13	2	5	7
3	15	5	7
4	17	5	7
5	12	5	7
6	14	5	7
7	16	5	7
2		NS	EW
NS	EW	MP	MP
1	17	12	0
2	12	5	7
14	3	5	7
4	16	5	7
5	11	5	7
6	13	5	7
7	15	5	7
3		NS	EW
NS	EW	MP	MP
1	16	12	0
2	11	5	7
3	13	5	7
15	4	5	7
5	17	5	7
6	12	5	7
7	14	5	7
4		NS	EW
NS	EW	MP	MP
1	15	12	0
2	17	5	7
3	12	5	7
4	14	5	7
16	5	5	7
6	11	5	7
7	13	5	7
5		NS	EW
NS	EW	MP	MP
1	14	12	0
2	16	5	7
3	11	5	7
4	13	5	7
5	15	5	7
17	6	5	7
7	12	5	7
6		NS	EW
NS	EW	MP	MP
1	13	12	0
2	15	5	7
3	17	5	7
4	12	5	7
5	14	5	7
6	16	5	7
11	7	5	7
7		NS	EW
NS	EW	MP	MP
12	1	0	12
2	14	7	5
3	16	7	5
4	11	7	5
5	13	7	5
6	15	7	5
7	17	7	5

Q: WHY ARROW SWITCH?

A: TO PRODUCE ONE WINNER (AS FAIRLY AS POSSIBLE)

Q: HOW ARE THINGS UNFAIR?

A: IMAGINE……

Seven table mitchell with one board at each table

Seven rounds. Seven results on each traveller.

14 pairs but pair 1 are bridge wizards. They get a clear TOP on every board.

All other pairs are competent but not wizards (NB EXACTLY competent they always TIE unless pair1 is involved).

The seven match is played no arrow switch and the travellers scored

The Men in Black come along and ZAP everyones short term memory

The seven match is played again with an arrow switch on the last round

Scoring to match point rules it is..

One mp for each score on your side equal to you

Two mps for each score on your side that you beat

TOP= 2(R-1) = 12

PAR= (R-1)=6

Side match points add to Rx(R-1)= 42 

NS+EW=TOP

With no arrow switch

See left column for  the expected scores

Pair 1 total is 12 12 12 12 12 12 12  = 84mps

Pairs 11-17 each total to 7 7 7 7 7 7 0 =42mps

Pairs 2-7 each total to 5 5 5 5 5 5 5  =35

If we rank all   totals to get a place then  pairs 2-7 suffer because they are on the same side as the wizards. They are damaged on all seven rounds. The EWs  are damaged once but are also compensated bythose 7s.

Q: WHAT CAN I DO

A: DO AN ARROW SWITCH

See right column

Pairs 11-17 not 12 now experience a side swap at some point on one traveller where they are exposed to the wizards - pair 1 so one of their 7s goes to 5

Pairs 2 to 7 also experience a side swap at some point on one traveller where they are released from the wizards so one of their 5s goes to 7

Pair 12 still gets a zero when swapping with pair 1 but pairs 11-17 not 12 get wiz’ed again and pairs 2 to 7 get released again, 5s and 7s swap.

Things have evened up if not slightly reversed.

Pairs 11-17 not12  each total 5 5 7 7 7 7 0 =38

Pairs 2 to 7  each total 7 7 5 5 5 5 5 = 39

Pair 12  escapes with  42 as before

Pair 1 get 84 as before.

So to make things fairer for those pairs on the same side as the wizards we do an arrow switch. If you are sneaky you want to select the table  that places you opposite the wizards on the arrow switch.

Apparently  to do more arrow swicthes  than 1 in 8 boards results in scores becoming unbalanced once again.

Q: WHAT IF THERE ARE A PAIR OF ZOMBIES

A: AS BEFORE

Pair 1 are now bridge Zombies they always get a bottom

Without arrow switch expected scores are

Pair 1 total is 0 0 0 0 0 0 0=0 mps

Pairs 11-17 each total to 12 5 5 5 5 5 5 =42mps

Pairs 2-7 each total to 7 7 7 7 7 7 7  =49mps

With arrow switch

Pair 1 total is 0 0 0 0 0 0 0=0 mps

Pairs 11-17 not 12 each total to 12 7 7 5 5 5 5 =46mps

Pairs 2-7 each total to 5 5 7 7 7 7 7  =45mps

Pair 12 total 42 mps as before

So to make things fairer for those pairs on the  side opposite to the zombies we do an arrow switch. If you are sneaky you want to select the table that avoids you opposite the zombies on the arrow switch: Preferentially head for a lower table.