After North rebids 1NT, showing a balanced hand with 12-14 points, South needs to make a forcing bid to ensure game is reached.  3♦ is the standard way to go, but many will have a modern gadget called New Minor Forcing and will be able to rebid 2♦ as a forcing artificial call.  Either way, South should get to 4♠ and will lose one trick in both black suits with the K♦ onside.  South might make six if East doesn't cash a club when in with the trump winner.  Masterminds who bid 3NT will usually make eleven tricks unless the defence starts with clubs.
 

Many different results on this hand by the machines, some opening 2♥ with the South hand making it easier for West to come in.  If West plays in spades, a heart to the ace and a fairly clear diamond switch will net North-South a heart, two diamonds, a diamond ruff, and a trump.  Over 3♥, many Wests may pass knowing that partner cannot have much after passing originally.  4♥ looks like a reasonable spot until the opponents begin with two clubs, a club ruff with the T♥, and a spade trick.  If South realizes that East passed originally and would probably find an opener with AK♣ and the K♥, it becomes clear that West has the K♥, and it drops!  If the defense forgot to cash a spade after the club ruff, the spade loser goes away on clubs, after pulling East's last trump and 4♥ makes!
 

Just barely enough for East to make a Jacoby 2NT forcing raise.  West shows a diamond singleton and East bails in 4♥, since Kxxxx opposite a singleton is not exactly optimal.  Eleven tricks are routine, one trick to lose in each minor.  If you were South and considered bidding 4♠ on this vulnerability, good idea, and in fact it works this time, but only because North turns up with very useful cards.  But if you get the reputation of being a "4♠ over 4♥ addict" people will start bidding iffy heart games with high spades on the side, hoping to double you if you follow your instincts!
 

Textbook Stayman auction.  Hard to see how 4♥ goes down here, two trumps and a diamond should be the only losers.  Did some of the computers run the J♠?  Surely there cannot be a spade ruff for the defenders: if I saw the Q♠ opening lead I would play ace and another heart quicker than Usain Bolt runs an Olympic sprint...
 

A tip for you. When one opponent opens, or overcalls, or makes a takeout double, there is value in that for your side if you declare. You'll have slightly better odds of guessing where highcards are, because one opponent has claimed most of them. When an opponent opens, or overcalls, or makes a takeout double, the number of highcard points you need to make game goes down by one or two. West has an easy 4♥ call after the takeout double. Raising only to 3♥ merits a bad score.
 

An unlucky slam that deserves to be bid, failing only on a bad trump break.  North's rebid of 4♦ is the launcher, jumping past 3NT to prefer a minor is always a slam try.  South cooperates by cuebidding a singleton, responds to Blackwood, and gets to declare a slam that has zero chance.  Three of the computer players didn't lead a spade when in with the K♦, and South had 12 tricks: four trumps, five clubs and three hearts.  Oops!!

If you get to 6NT instead of 6♦ you are gold unless they lead a diamond and switch to a spade: you have three spades, three hearts, a diamond (no need to finesse) and five clubs: just knock out the A♠ and claim!  Then you can tell me how North knew South's singleton heart was the queen.  The computers would like to know as well...
 

A very instructive deal.  North, in the given auction, responds 2♦ and then rebids 3♣ to show a very bad hand.  South continues to 3NT and North corrects to 4♥, promising at least three-card support.  South can envision a possible slam with as little as Qxx♣ and QJ♠, but that is a supermaximum for North's bidding, so passing 4♥ is best.  South plays the percentages in 4♥ and loses a trump and a spade for eleven tricks.

The other option South might try is a rebid of 3NT instead of 2♥.  Problem is, unless you have agreed that 4♣ over 3NT is Stayman in this sequence, North will probably bid spades, expecting a fit, and the pair will play in the seven-card spade "fit" instead of the nine-card heart fit.  Seeing that hearts will make at least eleven tricks, twelve if the suit splits, North will take the heart finesse after playing three rounds of trumps and finding them 3-3.  A very lucky escape for 650!

The real lesson of the hand is about opening notrump bids (including 2♣ followed by 2NT or 3NT as an effective notrump opener) with five-card majors.  If you have 5-2 in the majors, there is a real danger that partner will place you in the wrong major, tranferring you to your two-card suit with decent support for your five-card suit.  That's why South's 2♥ rebid is best.

One of the dangers when learning the game is ignoring hands like this if you played in spades but escaped with a decent score through sheer luck.  On most days, falling into a spade contract would be such a disaster it would generate a close look at the deal.  On a hand like this where spades miraculously break 3-3 and the inferior finesse in hearts gets you an undeserved tie with everyone who played in hearts, it's easy to laugh it off and never take a second look.  But it's those second looks, even when you escape with a good result, that help you improve!
 

West opens, East responds, and South has 18 highcard points.  How many do you think North has?  Counting a minimum of 12 for the opener and 6 for the response, there are only four points left for North, maximum.  A bid over 1♠ is just inviting trouble.  It turns out that N-S can make eight tricks in notrump because North has the maximum, but not many are taking a chance on it.  Safer to defend 2♠ and take the plus.
 

South doesn't really have enough to make a 2/1 response, even in standard where such a response does not force to game as it does in modern systems.  It is an 11-count, but with a singleton queen and no aces, it is about as bad an 11-count as they come.  North's 2♣ rebid does not promise extras but shows a real second suit.  South suggests game with 2NT but North has no extras and 2NT is where it ends. 2NT is no easy contract, declarer can establish seven tricks fairly easily: two spades, a diamond, three hearts, and the king of clubs.  The defenders should be able to set up three club tricks to go with two aces for five.  Who gets the thirteenth trick is anyone's guess!
 

With five hearts, four clubs, and two top diamonds, only one more trick is required to land this slam, but there are traps.  If South leads away from either queen, the jack from dummy sets up a twelfth trick.  On a trump lead, East wins in dummy and plays K♦, A♦, and ruffs a diamond high.  Dummy's last trump reveals the 4-1 break and everything hinges on what route East chooses to get back to his hand.  Ruffing a spade is the winning play; a club gets ruffed by South and the Q♦ follows.

In the example auction, 2♦ is fourth suit forcing, 3♦ shows a three-suiter, 3♥ confirms three-card support for hearts.  East will learn nothing useful from Blackwood so 3♠ is a cue-bid.  West's 5♥ promises a good hand and invites slam based on how good East's trumps are, ace-king fifth is clearly enough.
 

A very borderline opener for South, but the positives are that if West passes South will probably find out immediately whether N-S have a fit in a major.  West makes an offshape takeout double because passing or picking a suit to overcall doesn't seem right.  North jumps to 3♥, a pre-emptive jump which doesn't keep East out.  East's 4♠ ends the auction; everyone before East has overbid and East joins the party.  In the play, the spotlight is on South: N-S have third-round winners in both minors—if South can resist the urge to ruff in. Not so easy when you have no idea what everyone has and partner has made a weak bid!
 

South opens 1♠, not 1NT, in fourth seat to avoid being transferred to hearts with a better spade fit if partner has five hearts and three spades.  It's OK to open balanced hands with 5-card majors 1NT, but it is risky if you have 5-2 in the majors: you may get transferred to an inferior fit and left there.  After the 2♣ response, South knows that the partnership has enough for game, and the scene shifts to the defenders.  Singleton kings are going to take the first two tricks. How should West continue?  A spade continuation sets up two tricks; switching to diamonds or hearts is a disaster, as West will have to decide which suits to keep and break up others, creating extra tricks for declarer.

East can help a lot at trick one by recognizing that West must have some values on this auction and will get in at least once. Playing the enciuraging 6♠ instead of the autopilot 2♠ lets East know it is OK to continue spades.  East is OK with a spade continuation, holding an honour to knock out whatever declarer might have.  East is not thrilled by a switch once West gets in. Beware of the autopilot signal!
 

East might have three or even four hearts for the 18-19 2NT rebid.  But in matchpoints it is probably not worth it to find out.  Once the partnership is beyond 28 combined points and the bidding gives away no obvious suits for the defense to attack, notrump usually makes the same number of tricks as an eight-card fit in the major for a matchpoint bonus.  So 3NT is probably the best bid by West even if they have a convention like New Minor Forcing or Checkback Stayman to find out whether East has three-card heart support.

East should have no trouble making six if South chooses a black suit lead.  On a diamond lead, East wins and finesses to North's K♥.  Another diamond comes back and East wins, cashes two clubs and four more hearts, bringing everyone down to four cards.  East might be able to read the position by noting which defender is sweating the most over the discards, but South is down to ♣Q and ♠Q73: if East puts South in with a club, South has to lead spades and East makes eleven tricks.  If East places South with the Q♠, South can take the last four and make twelve.
 

West has a slightly offshape but nonetheless obvious takeout double of 1♣, and East responds with a jump to 2♥, showing eight highcard points or more.  South sees a stopper and eight nearly ironclad tricks, so tries 2NT.  West competes to 3♥, knowing that they probably make game if East has any extras at all.  But North, wih just one highcard point, has decided to compete further, and South bids 5♣.  West doubles and it depends on the lead.  KJ72 is an ugly suit to lead from, but without a heart lead, South makes 5♣ by setting up spades.  Even if West craftily ducks the second spade, allowing South's jack to win, South has a counter: club to jack, third spade ruffed in hand, pull the last trump, and a trump to the eight is an entry to the rest of the spades!  The only way to beat it is to lead hearts, setting up a heart trick to go with a spade and a diamond for the defense—before the heart trick disappears on spades.  Lesson: when the bidding strongly suggests a suit to lead and partner rates to have help in the suit, don't let an awkward holding dissuade you from leading that suit!
 

Does West have enough to open?  11 points and two doubletons, two and a half quick tricks, indicate enough strength.  If East responds a major, some might not want to rebid 1NT with a small doubleton in an unbid suit, and rebidding five-card suits is not a good habit to get into.  One solution would be to open 1♦, planning to rebid 2♣ if partner bids a major.  With West having chosen to open the bidding, East doesn't want to sell out to 2♥, and the only bid available is 2♠.  If you thought that showed six spades and competed on to 3♠ as West, you have my sympathy, for I too was led down that garden path into the manure pit when spades broke 5-1...  3♥ is not easy to beat, defenders need to set up two diamond tricks before North gets diamond pitches on good spades.
 

JACK's version of Standard American Yellow Card is a bit weird in spots, and this is one of them: partner transfers and you do not want to be dropped in 2♠ if partner has a fair hand of about 5 points or so.  JACK-style SAYC appears to have several different ways to make a super accept: 3♠ with a minimum and four-card support, 2NT with a maximum, four-card support but 4-3-3-3, and 3♣ with a maximum, four-card support and some shape.  3♣ it is then.  Partner bids 3♥ as a "retransfer," I comply (no need to jump to game since partner might have zero points), and partner raises to game.  When I see two aces in dummy I wonder if we haven't missed a slam, but when the K♠ is offside a diamond comes back and in fact I have two diamonds to eventually lose.

There is a well-known bridge saying called "Zia's Rule" which is usually remembered as "if they don't cover, they don't have it!"  When declarer leads the Q♠ and North ducks, you might decide the only chance is to drop the offside singleton king, especially while looking at the hand record.  An online search for "Zia's rule bridge" (add the third word or you will read a lot about Pakistani politics...) will get you the original article by expert Zia Mahmood, which contains provisos that make it inapplicable here.  (If you led the Q♠ from dummy and the next player didn't cover, that would be different!!)
 

Sometimes the most fascinating hands are those where nobody can bid.  East has a clear 1♣ opener and this silences almost every South in the world except those radicals who think a 1♠ overcall is the way out of this mess. West has a standard 1♥ response (it has become normal to bypass diamonds, even longer diamonds, to respond a four-card major) and this silences North!  East bids 1♠ in case that is where the E-W fit is (a 1NT rebid would give up on the chance of finding a spade fit), and again South is stymied.  Having scraped up just enough to respond at the one level, only a forcing bid will spur West to make a second call, so it is up to North to decide whether to let 1♠ be played or take some dubious action.

North's best bet is a balancing 1NT call, which probably buys the contract.  Four club tricks and three more aces will be enough to make +90 for a decent score.  Oddly enough, E-W might make 1NT if N-S don't attack clubs!

My computer opponent with the North cards chose 2♦ (!) on the stellar suit 7542. This was happily passed out and early on North led a diamond to dummy's ace and continued with the other diamond.  With KJT9, I dropped the jack on the ace and played the ten on the second one, hoping declarer would place me with T9 doubleton and duck the queen.  My ten won, and as I was congratulating myself for this deception, it turned out a few tricks later that partner had the queen!

Matchpoints is a funny game.  With only 270 between the top (+150 in 1NT) and bottom (-120 defending 1NT!) scores, this board would swing a few IMPs in a team match and probably not affect the result much.  In matchpoints, someone will get a top on this board by some small amount and improve their score by almost 3%—or vice versa!
 

JACK's bidding can be a bit conservative: even if South passed (I wouldn't), very few Wests would pass in third seat.  One theme I hear often is that hands like the West hand are too strong for a weak two and too weak for an opening bid. I don't think there is such a hand, you pick 1♥ or 2♥ and go with it.  Once North overcalls spades, South will eschew defending and since only nine tricks are available to either side, 4♥ is a good sacrifice against the making 3♠, but 4♠ fails because most of the finesses available—K♦, Q♦, A♣—lose.  Unlucky!
 

North's 2♦ call is "fourth-suit forcing," an artificial call—North promises nothing in diamonds but wants to hear more about South's hand.  Most play FSF as a game-forcing call.  The first priority is to show a stopper by bidding notrump or raising the suit if South actually can envision a possible fit.  North rebids his hearts (3♥ is forcing, since 3♦ forced to game), but South is not interested and 3NT ends the auction.

West will probably lead a diamond and South will win the eight.  Everything depends on which suit South attacks first.  A small club to the queen puts East in to lead a diamond through South, and West gets the K♦ and the A♠.  Attacking spades first leads to eleven tricks and possibly even twelve if West is lazy and tosses a heart when South plays a spade to dummy.  Did you see your 8♥ as a possible stopper?
 

A diamond lead is needed to prevent West from making at least 12 tricks.  But when South passes the diamond transfer, North may decide to lead something else.  Now West simply leads a spade to the nine, then a spade to the jack, for a twelfth trick.

You are no doubt well-aware that 3NT after a transfer promises exactly five of the suit you have transferred partner into, and gives partner the choice of 3NT or 4 of the major.  After a 1NT opener and a transfer, 2NT is similar, but partner can choose to pass 2NT or bid 3 of the major with a minimum, and bid 3NT or 4 of the major with a maximum.  Tip: when the notrump bidder thinks before deciding on 3NT or 4 of the suit, it usually means the notrump bidder has three small in the transfer suit and is considering notrump despite the eight card fit.
 

It's not common to bid a game when the opponents open 1NT, but here is the hand for it.  West has enough to make a raise worth it and East has a solid 4♠ call after being raised, with shape and decent strength.  Knowing that most of the missing high cards will be with the 1NT opener means you hardly need a combined 26 points to make this game.  For example, if South, with no opposition bidding, leads the 2♣ against 4♠, you might finesse, thinking that if it wins, you get a heart pitch and can afford two diamond losers.  But on this auction there is a zero percent chance that South has the KQ♦ and the K♣.  It's best to win the A♣ and finesse in diamonds immediately.  Win the return, pull trumps ending in dummy, and take a second diamond finesse.  If South has both diamond honors, ask North where his 15-17 is.
 

A wild one to end the set.  My auction was not standard: with the West hand I could not bear to lose a possible spade fit by jumping to 3♥, so I made a weird takeout double, then when partner bid 1NT over North's 2♦ call (1NT goes down four off the top!) I bid 2♥, which should show a huge hand with lots of hearts.  Not recommended!  Partner put me in 4♥ and I went one down doubled like most of the computers.

6♦ can be made by simply leading spades three times towards the North hand, covering whatever West plays (exception: if West ducks and the seven wins the first trick, you must duck in both hands on the second spade trick).  You lose only one spade this way and the rest is gin! Would I find this play at the table?  I doubt it.