Counting
(Page of 2)

In a recent Just Declare collegiate tournament on BBO a slam came down to a Q guess. Play went as followed (is this how you would've played it?):

Robot
Robot
QJ1063
AJ107
76
J6
Robot
You
AK984
K52
2
AK103
W
N
E
S

P
P
P
1
P
2
P
3
P
4N
P
5
P
6
P
P
P
D
8
6 South
NS: 0 EW: 0
A
6
5
2
0
0
1
3
7
K
4
3
1
1
A
7
10
2
3
2
1
K
9
3
5
3
3
1
K
7
6
2
3
4
1
A
8
J
5
3
5
1
3
Q
Q
4
1
6
1
6
3
9
8
3
7
1
10
4
7
4
3
8
1
9

Perhaps I should play one more spade before making you guess but I think there is enough information to guess it at this point in the hand.

The opponents collectively hold Q986 and QJT9. So far W has shown up with A83 Q987 and E with 52 K52 542. Additionally we can probably place Q with W since E played the K at trick 2. It seems we need to guess which opponent is still holding on to Qxx so let's first consider what the hand looks like if W has Qxx remaining then what it looks like if E has Qxx remaining.

If W has 3 hearts to the Q remaining that would give him 7 Qxxx AQ83 Q987 and E 52 xx KJT954 542. This hand seems improbable since E would very likely have bid 2 at his first bid.

If E has 3 hearts to the Q remaining then the hands would be W has 7 xx AQxxxx Q987 and E has 52 Qxxx Kxxx 542. This hand again seems improbable from the bidding since W would've opened 2.

So it seems like diamonds must be 5-5 and that the Q is dropping. Note that the robots will be less fearful than humans of pitching like this because they assume that you will always guess where the Q is (they base their plays on double dummy analysis).

Here was the full hand.

Robot
7
Q84
AQ983
Q987
Robot
QJ1063
AJ107
76
J6
Robot
52
963
KJ1054
542
You
AK984
K52
2
AK103
W
N
E
S

P
P
P
1
P
2
P
3
P
4N
P
5
P
6
P
P
P
D
8
6 South
NS: 0 EW: 0
A
6
5
2
0
0
1
3
7
K
4
3
1
1
A
7
10
2
3
2
1
K
9
3
5
3
3
1
K
7
6
2
3
4
1
A
8
J
5
3
5
1
3
Q
Q
4
1
6
1
6
3
9
8
3
7
1
10
4
7
4
3
8
1
9