Hand 1
Part 1
You pick up
9x
J86
Qxxx
AQxxx
You pass, Lefty (your lefthand opponent) passes, and your partner opens 1. Righty (the opponent on your right) passes, and you bid a "semiforcing" 1NT. Your partner passes, and it looks like you will finally get to play a hand.... but then Lefty then balances in with 2. You have no reason to compete, and apparently your partner does not either, so the final contract is 2.
You of course lead the 9, and dummy comes down with
82
Q4
9864
K8763
That's somewhat of a disappointment  you were hoping spades would be 33, or that you could overruff declarer. Fortunately, dummy can only overruff you once. Partner plays a small spade and declarer wins the K.
Actually, this is a somewhat surprising development  it appears that your declarer has both the K and A. Surprises are always a time to think about HCP. Your partner has only 3 HCP in spades, and none in clubs  that gives her a lot of points in the red suits.
Anyway, declarer leads the J. Winning this with the ace is a nobrainer  either declarer or your partner has a singleton club. But which is it? Your partner plays the 3.
I think the 3 is a pretty strong inference that partner has a singleton and declarer was leading the jack from J10 doubleton.
But wait one second. If partner has a singleton club, then what is partner's distribution? With 6331 partner almost certainly would have bid 2. If partner has 5431, then partner almost certainly would have bid her 4 card suit. She might hesitate to bid with xxxx of diamonds, but as noted, she has to have a lot of points in the red suits, so xxxx of diamonds is not likely.
It's your guess here  do you trust your partner's club or the bidding? The point is to think about the distribution and the points.
Of course, if partner is 5332, the doubleton is clubs. That gives declarer a 4531 distribution. It is possible that partner has AK of diamonds and you can cash 3 diamond tricks (though declarer could then use the club K for a spade pitch).
Seeing Things a Different Way
You pick up
QJ1074
K53
AKJ
103
Your partner passes, Righty (your righthand opponent) passes, and you open 1. Lefty (the opponent on your left) passes, and your partner bids 1NT. That's "semiforcing", which means you can pass it. Now looks like a good time to pass.
Lefty then balances in with 2, which everyone is content to pass.
Your partner leads the 9, and dummy comes down with
82
Q4
9864
K8763
Your partner cannot have 3 spades on this auction. The nine looks like a doubleton. That would give declarer 4 spades. Declarer wins the K and leads the J. Your partner wins the A. You follow with the 3. Your partner then leads a club, declarer winning win the king on the board and pitching a diamond.
You are going to be following suit for a while, so you don't need to stop and count right now. But you have gathered considerable information, and I like to put it together when I can. Declarer must have at least 5 hearts, at least 4 spades, and exactly one club. I rate declarer's most likely distribution as 4531, but the other reasonable possibilities are 5521 and 4621.
Declarer leads a spade to his ace, partner following suit. Declarer then leads a small spade. Your partner inserts the 6 of hearts, forcing declarer to win with the queen. Declarer ruffs a small club and leads another spade. This time your partner ruffs with the eight. And finally, partner leads a small diamond, suggesting a diamond honor.
Now you are in. Now you should piece together the hand. Declarer could have 6 hearts. That would mean he started with
AKxx
AJ10xxx
xx
J
Most players would find a 2 overcall with that hand. So, the most likely starting distribution for declarer is 4531.
The only missing high cards are the Q, A, and J. You don't really care about the diamond queen, but partner's lead suggests that he has it. If he does, he can't have the heart ace, that would give him 12 HCP. Some people would balance in with Jxxxx of hearts, but most would not, so declarer probably has the ace of hearts. You can't place the jack of hearts.
It is always nice to lead a suit that declarer is out of and partner is out of. Then, if declarer ruffs, partner might be able to overruff. If declarer ruffs high enough that your partner cannot ruff, that might set up a trump trick for the defense. Here you have the last spade.
However, before trying this play, it is usually important to eliminate the other losers from declarer's hand. Otherwise, declarer can just throw a loser on your lead. In this case, that will be successful. You don't have another spade to lead, and you won't stay on lead anyway  the dummy is ruffing spades, so your partner will have to ruff.
If declarer has 6 trumps, you need to lead a spade right away, there are no losers to eliminate. However, if declarer has 6 trumps, your partner doesn't have any and it is irrelevant what you lead. So give declarer 5 trumps, which seems very likely. That gives him one more diamond in his hand. Cash your king of diamonds and lead a spade. If your partner has the jack, that gives you two trump tricks no matter what declarer does. If you partner has the 10, declarer has to guess right to avoid losing two tricks.
On a Clear Day
Okay, scenario analysis. Dummy is down to

4
98
J8
and you have
Q
K53
A

Declarer probably is down to either

AJxx
x

or

A109x
x

You always have a diamond trick. If partner has the jack of hearts, you always get a heart trick. What if partner doesn't have the jack of hearts? No problem, you are not going to be finessed twice. The simplest play, if partner doesn't have the jack of hearts, is K and then lead either a spade or diamond for declarer to ruff. You can actually lead a trump, giving declarer a free finesse, because that is one finesse, not enough to capture your king.
Is there any way to get another trick? If you win your diamond and lead another diamond, declarer will have to ruff. Then, even if your partner has the jack of hearts, declarer will be looking at A109. Declarer will play the A, dropping your partner's jack, and you will get just your king.
Better is to lead a heart. If declarer has AJ10x, he can't go wrong. But if he has AJ9x or A109x, you have given declarer a losing option. He might play his ace, again hoping that either the remaining trump are 22 or that a singleton honor will drop. But he might also try a heart finesse. (However, he can count too. He knew you started with 5 spades and probably a 5332 distribution. So you have 3 hearts. Would you really lead a heart from KJx? Unlikely. So his only play is the ace. In actually play, declarer did play the ace.)
What if you lead a spade. If declarer ruffs, partner might be able to overruff. In fact, if partner has the src=h.gif>J, partner will definitely be able to overruff. If partner has the 10 or 9, declarer might misguess the heart situation.
But declarer is one of the best players at the club, and he will not ruff if you lead a spade. He will throw a diamond. Because there is still a trump on the board, your partner will have to ruff. You will get that trick, which you were counting on anyway, and your trump king.
Instead, you first cash your winning diamond, stripping the last loser from declarer's hand. Then you lead a spade. If your partner can overruff, you will have to trump whatever your partner leads, but you can beat the 4 on the board, so declarer will have to overruff, and you will make your king of trump, for down two.
Time to look at vulnerability: They are vulnerable. Down 1 gives you 7 out of 11 matchpoits; down 2 gives you 10.5 out of 11.
