Answers: (More advanced stuff in blue)
1.
Hint: How many clubs will you lose? How many diamonds will you lose? etc.
Answer: If hearts are trump, you won't lose any clubs or spades because your dummy will trump. Partner showed at least five hearts with his 2H overcall. The opponents have at most one trump and your ace will drop it. You have no heart losers. Diamonds? If partner has three or less, he can trump your small diamonds. If partner has four or more diamonds, the opponents have at most three and they will fall under your top three diamonds, so you won't lose any diamonds either.
Since you can't lose any tricks if hearts are trump, bid 7H.
Tramticket's point was that the opponents might not let you play 7H, since they can bid 7S. Most weak opponents won't do this, and if you are a novice, a good player might not also, assuming that you are taking a dangerous flyer. However, if you think it's really likely that the opponents will keep bidding up to 6S but not 7S, you may in theory enhance your chances of being allowed to play in hearts. The downside is that any decent player will know that if you, and only you, are bidding more hearts all the way to the seven level, they should realize what you are doing and bid 7S. Bidding slow gives both the opponents to bid more spades, whereas bidding 7H now means that one or the other opponent must take the plunge right now. Full credit to anyone who knew they could make a grand slam in hearts.
It is dangerous to bid 4NT hoping to find two aces to bid 7NT, and then bailing in 7H when missing an ace. Partner may think his one ace was all you were looking for and correct to 7NT.
2.
2NT=20-21
Hint: What will you make if partner has three aces?
Answer: Partner should have at least two hearts, so once again, the opponents have at most one heart and it will drop under the ace. The number of aces partner has will tell you what you can make. Bid 4C, Gerber, asking partner how many aces he has. (4NT is not Blackwood; it is quantitative and can be passed.) When partner tells you how many aces he has, bid the appropriate number of hearts. Don't bid 7NT if partner shows all three aces; if partner has a doubleton
♥QJ, his second honor will block the suit after you drop the opponents' singleton king.
I wouldn't worry about the new ACBL regulation allowing partner to open notrump with a singleton honor. First, if it's the king, you can drop the ♥QJ in one hand. For you to go down, partner will have had to open 2NT on a singleton queen, and hearts will have to be 2-0. Partner will almost always have a better bidding plan than opening 2NT with a singleton heart.
3.
2D = weak 2 (5-10HCP, decent 6 card diamond suit; 2S = forcing; 3H = denying spade support, maximum weak two, heart feature (A,K, or Q))
Hint: How many clubs will you lose? How many diamond will you lose? etc.
Answer: Since partner has no spade support, you'll lose no spades, having the
♠AK yourself.
Partner's heart feature must be the
♥K which means you have no heart losers.
Your singleton club means one club loser since partner can trump any other clubs in your hand.
If partner has the
♦A, they are likely to split 2-1 even when partner doesn't have the queen. Partner is very likely to have that
♦A but it doesn't hurt to check for it using Blackwood. Bid 6D if partner shows an ace.
4.
2C = strong and artificial; 2S = 5 or more spades including 2 of the top 3 honors
4NT=normal Blackwood; 5D=one ace
If your agreement is to play Roman Keycard, partner showed two key cards and no queen of trump
Do you agree with 4NT? What do you bid now?
Hint: How many tricks do you have?
Second hint: Does it matter who plays the hand?
Answer: Don't count points, count tricks! Your partner showed 5 spades with 2 of the top 3 honors; if you don't know which honors those are, I would suggest taking up another game. Partner has
♠AKxxx which will produce 5 tricks (barring a very unlikely 5-0 split with partner not having either the
♠10 or a well-placed
♠9.) You have 6 heart tricks. You have 1 club trick. That's 12 tricks. Your only loser will be the
♦A.
However, if you play in spades, your right hand opponent is on lead and might lead a diamond through your
♦K. Protect the
♦K by playing the hand yourself. Bid 6NT.
You should agree with 4NT since the only thing that matters is whether partner has the
♦A to give you 13 tricks.
Bonus question: Would you bid any differently in rubber bridge?
5.
Hint: What has partner got? How many tricks do you expect to lose in each suit?
Answer: The opponents have shown 8 hearts and you have the other 5. Partner is void in hearts. Assume partner doesn't have spade support so he has at least 11 cards in clubs and diamonds, giving him at least 6 clubs if he bid his longest suit.
I should have 5 spade tricks and 6 club tricks if partner has the
♣A. If partner doesn't also have the
♦A, two hearts can be trumped in dummy to give 13 tricks as long as partner's clubs are good enough to ruff with my queen and still not lose any club tricks.
Give yourself full credit for bidding 6C (or 7C.) While I expect 7C to make, it may not, and you will usually pick up IMPs or most of the matchpoints for bidding and making 6C on this hand. If you want to ask for aces and bid 7C if partner has two, fine, but it would really be a shame if your partner thinks he has extra values and corrects to 7NT, so the bid isn't totally safe.