Distribution of scores of 2 strong pairs in 7-table Mitchell
In the complete Mitchell movement we have 7 rounds, thus the top on a
board is 12 MP.
score card 1: pairs 1 and 2 are the strong pairs
Pair | Contract | Res. | Score | MP |
NS | EW | NS | EW |
1 | 3 NT | | +1 | +630 | | 11 |
2 | 3 NT | | +1 | +630 | | 11 |
3 | 3 NT | | C | +600 | | 4 |
4 | 3 NT | | C | +600 | | 4 |
5 | 3 NT | | C | +600 | | 4 |
6 | 3 NT | | C | +600 | | 4 |
7 | 3 NT | | C | +600 | | 4 |
8 | | - 1 - | | | -630 | 1 |
9 | | - 2 - | | | -630 | 1 |
10 | | - 3 - | | | -600 | 8 |
11 | | - 4 - | | | -600 | 8 |
12 | | - 5 - | | | -600 | 8 |
13 | | - 6 - | | | -600 | 8 |
14 | | - 7 - | | | -600 | 8 |
|
First let us look at the case where the 2 top pairs play in the same
subgroup, say NS. Then each score card contains 2 times 11 and 5 times 4
in the NS column, therefore 2 1's and 5 8's in the EW column. The
total score (for simplicity we assume 1 board per round) will be:
for the 2 strong pairs: 7 x 11 = 77
for the other NS pairs: 7 x 4 = 28
for all EW pairs: 2 x 1 + 5 x 8 = 42
In total 2 scores of 77,
5 scores of 28,
and 7 scores of 42.
score card 2: pairs 1 and 9 are the strong pairs
Pair | Contract | Res. | Score | MP |
NS | EW | NS | EW |
1 | 3 NT | | +1 | +600 | | 12 |
2 | 3 NT | | -1 | -100 | | 0 |
3 | 3 NT | | C | +600 | | 6 |
4 | 3 NT | | C | +600 | | 6 |
5 | 3 NT | | C | +600 | | 6 |
6 | 3 NT | | C | +600 | | 6 |
7 | 3 NT | | C | +600 | | 6 |
8 | | - 1 - | | | -630 | 0 |
9 | | - 2 - | | | +100 | 12 |
10 | | - 3 - | | | -600 | 6 |
11 | | - 4 - | | | -600 | 6 |
12 | | - 5 - | | | -600 | 6 |
13 | | - 6 - | | | -600 | 6 |
14 | | - 7 - | | | -600 | 6 |
|
score card 3: pairs 1 and 8 are the strong pairs
Pair | Contract | Res. | Score | MP |
NS | EW | NS | EW |
1 | 3 NT | | C | +600 | | 6 |
2 | 3 NT | | C | +600 | | 6 |
3 | 3 NT | | C | +600 | | 6 |
4 | 3 NT | | C | +600 | | 6 |
5 | 3 NT | | C | +600 | | 6 |
6 | 3 NT | | C | +600 | | 6 |
7 | 3 NT | | C | +600 | | 6 |
8 | | - 1 - | | | -600 | 6 |
9 | | - 2 - | | | -600 | 6 |
10 | | - 3 - | | | -600 | 6 |
11 | | - 4 - | | | -600 | 6 |
12 | | - 5 - | | | -600 | 6 |
13 | | - 6 - | | | -600 | 6 |
14 | | - 7 - | | | -600 | 6 |
|
Next consider the case where one top pair plays NS and the other EW.
Now most score cards will contain two 12's, 2 zeroes, and 10 6's. Except for
the one board where the 2 top pairs meet each other, this score card
has all 6's. The total scores in this case are:
for the 2 strong pairs: 6 x 12 + 6 = 78
for all other pairs: 6 x 6 + 0 = 36
In total 2 scores of 78,
and 12 scores of 36.
We can choose the pair numbers of the 2 strong pairs in 14 x 13 / 2 = 91
different ways. Of these 91 combinations there are 42 (i.e. 7 x 6) where
they play in the same direction and 49 (i.e. 7 x 7) where they play in
opposite directions.
All together we have the following distribution of possible scores
(In brackets the MP scores converted to percentages)
49 x 2 = 98 scores of 78 (= 92.86%)
42 x 2 = 84 scores of 77 (= 91.67%)
42 x 7 = 294 scores of 42 (= 50% )
42 x 5 = 210 scores of 28 (= 33.33%)
49 x 12 = 588 scores of 36 (= 42.86%)