Answers:
1.
Partner leads the
♠2. Dummy plays the
♠3. Your play?
Hint: Do you know the standard play in this situation?
Answer: When there are no high cards in the dummy to matter, you play third hand high, but the lowest of touching cards.
Play the queen. Partner won't necessarily know that you have the king, but you do deny the jack. If you play the king, you will deny the queen. Playing the ten can't help and could hurt if declarer has the jack. This is standard.
2.
Partner leads the
♠2. Dummy plays the
♠3. Your play?
Hint: If partner gets in, what do you want him to do? What's the best way to accomplish that?
Answer: The "normal" play would be the
♠Q. However, when partner gets in, you really want partner to lead a club. Fool partner into thinking that there is no future in spades; play the king and make partner think declarer has the
♠AQ. Partner, when in with a red card, will lead a club because a spade lead looks futile. You'll cash your two club tricks and your "impossible"
♠Q to set the contract one trick. The recommended play is the
♠K, a falsecard intended to fool partner into doing the right thing.
3.
You ask what 3NT shows and North says "undiscussed."
Partner leads the
♠10. Dummy plays the
♠Q. Your play?
Hint: Will partner know what to do if he gets the lead?
Answer: First, let's look at the suit in isolation to see what the normal play is.
First, you have the king, dummy played the queen, and partner led the ten. Where are the other cards that matter?
Who has the ace?
Partner can't have it because we don't underlead aces in suit contracts. Declarer has the
♠A.
Who has the jack?
Partner can't have it because we lead top of two touching honors and would lead the jack from
♠J 10. Declarer has the jack.
Who has the nine?
The unsupported
♠10 is too valuable of a card to waste (see example below.)
...........Q 5 2
10 8 7............K 6 4 3
...........A J 9
If partner leads the
♠10, it goes
♠Q from dummy and whether you play the
♠K or not, declarer gets three tricks (if you don't play it, declarer simply finesses against it.)
...........Q 5 2
10 9 7............K 6 4 3
...........A J 8
Here the
♠10 is backed up by the
♠9. Covering the queen with the king will create a trick for partner's
♠9.
Partner should have the
♠9 (or a doubleton) for the lead of the
♠10. So, the above situation shows you where all the cards from the ace down to the nine should be based on partner's lead. If partner has a doubleton, there's nothing you can do. However, if partner has the
♠9, covering the
♠Q with the
♠K holds declarer to two spade tricks, while playing low lets declarer finesse the
♠J later for three tricks. In a vacuum, you should cover the
♠Q with the
♠K.
However, this is not a vacuum. Declarer can take six diamond tricks and if declarer doesn't have a trump loser, will take all the tricks (6 diamonds, 5 hearts, 2 spades.) If declarer has two trump losers, you set 6H. The critical case is when declarer has one trump loser. Partner will win an early trump trick. At this point, declarer will have a second spade winner whether you played the
♠K or not, and declarer will have the rest of the tricks when he gets the lead back. You would really like partner to lead a club to your ace. How do you do that?
Go back to trick one. You know what declarer's problem is if he has one. You know that partner will be wondering what to lead when in with his trump trick. If you let dummy's
♠Q win, you give declarer three spade tricks instead of two, but that is irrelevant because declarer has tons of diamonds to discard spades on anyway. The upside of not covering the
♠Q is that partner will think there is no future in spades. The only possible trick (other than an unlikely diamond ruff) is in clubs, and partner will lead a club to your ace. If you cover the
♠Q with the
♠K, partner will win his trump trick and may hope for you to have the
♠J rather than the
♣A. That would lead to a very bad result.
So, while playing the king is best when the spade suit is taken in isolation, playing low at trick 1 is recommended for this hand.
OLD PROBLEM 3 (note: this problem doesn't work as ahydra pointed out)
3.
Partner leads the ♠10. Dummy plays the ♠Q. Your play?
Hint: Will partner know what to do if he gets the lead?
Answer: First, let's look at the suit in isolation to see what the normal play is.
First, you have the king, dummy played the queen, and partner led the ten. Where are the other cards that matter?
Who has the ace?
Partner can't have it because we don't underlead aces in suit contracts. Declarer has the ♠A.
Who has the jack?
Partner can't have it because we lead top of two touching honors and would lead the jack from ♠J 10. Declarer has the jack.
Who has the nine?
The unsupported ♠10 is too valuable of a card to waste (see example below.)
...........Q 5 2
10 8 7............K 6 4 3
...........A J 9
If partner leads the ♠10, it goes ♠Q from dummy and whether you play the ♠K or not, declarer gets three tricks (if you don't play it, declarer simply finesses against it.)
...........Q 5 2
10 9 7............K 6 4 3
...........A J 8
Here the ♠10 is backed up by the ♠9. Covering the queen with the king will create a trick for partner's ♠9.
Partner should have the ♠9 (or a doubleton) for the lead of the ♠10. So, the above situation shows you where all the cards from the ace down to the nine should be based on partner's lead. If partner has a doubleton, there's nothing you can do. However, if partner has the ♠9, covering the ♠Q with the ♠K holds declarer to two spade tricks, while playing low lets declarer finesse the ♠J later for three tricks. In a vacuum, you should cover the ♠Q with the ♠K.
However, this is not a vacuum. Declarer can take six diamond tricks and if declarer doesn't have a trump loser, will take all the tricks. If declarer has two trump losers, you set 6H. The critical case is when declarer has one trump loser. Partner will win an early trump trick. At this point, declarer will have a second spade winner whether you played the ♠K or not, and declarer will have the rest of the tricks when he gets the lead back. You would really like partner to lead a club to your ace. How do you do that?
Go back to trick one. You know what declarer's problem is if he has one. You know that partner will be wondering what to lead when in with his trump trick. If you let dummy's ♠Q win, you give declarer three spade tricks instead of two, but that is irrelevant because declarer has tons of diamonds to discard spades on anyway. The upside of not covering the ♠Q is that partner will think there is no future in spades. The only possible trick (other than an unlikely diamond ruff) is in clubs, and partner will lead a club to your ace. If you cover the ♠Q with the ♠K, partner will win his trump trick and may hope for you to have the ♠J rather than the ♣A. That would lead to a very bad result.
So, while playing the king is best when the spade suit is taken in isolation, playing low at trick 1 is recommended for this hand.