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What do you make of the T?

Playing in sectional swiss there were a couple of boards where I had to take stock of the situation when LHO played a T. 

On the first very first board of the first round this is what you see. Plan your play on the lead of T.

West
North
A763
K72
KQ106
J8
East
South
J
QJ84
AJ74
A743
W
N
E
S
1
P
1
P
1
P
3NT
P
P
P
D
1
3NT South
NS: 0 EW: 0
10
1

Clearly you need 3 tricks to make the contract. What do you make of the T? There is only one line that will succeed if LHO has AT9x but it will fail anytime RHO has 9.  What is the percentage play? How do other considerations like a different lead at the other table affect your play?

In the penultimate round your decision point is much later in the play. Please click next to follow the play to the critical point.

West
North
A6
KJ63
J974
Q63
East
South
Q82
AQ984
AK2
84
W
N
E
S
1NT
X
2
P
2
P
4
P
P
P
D
1
4 South
NS: 0 EW: 0
A
3
7
4
0
0
1
K
6
2
8
0
0
2
10
Q
7
8
3
1
2
A
2
3
9
3
2
2
2
5
A
3
1
3
2
6
K
8
10
2
3
3
4
Q
10
J
1
4
3
6
7
Q
5
3
5
3
A
10
9

At the point when the 3rd was played LHO's distribution is counted exactly to 2326. So looks like the the percentage play is to play for Qx (including QT) with LHO which is 5 cases as opposed to Tx which is only 4 cases. In any case you can still decide to play for either after the cashing a high . Accordingly you cash A and see T from LHO. What do you make of the T? Let's assume LHO plays the 8 instead of the T. For the play to matter LHO has to have Q8 or T8. Does that mean it is now a straight tossup between dropping the Q and pinning the T? Or is it a restricted choice situation since LHO has to play 8 from Q8 but can play T or 8 from T8? Which brings us back to the play of the T. Could that be from T8 or any Tx?

 

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