In the semi-finals of the open trials, you must decide how aggressively to bid a strong hand opposite a weak hand.
N-S vul, South deals. As North, you hold:
1♣: 16+ points. You can't open 2NT, since that would show both minors, less than an opening bid.
Pass: 0-4 points
With partner limited to 4 HCP, you having no major-suit fit, and your spade honors badly placed, game looks unlikely. There is no need to jump to 2NT to show this strength, as you would normally be doing if there had been no interference and partner had responded 1♦ showing 0-7. You should either be passing or bidding 1NT.
In general, it does not pay to let the opponents play at the 1-level unless they are clearly in a bad contract or your side is badly outgunned. Defending 1♠ is the equivalent of contracting for 7 tricks in spades, since that is what you would need to get a plus score. It is better to contract for 7 tricks with no trump suit than to contract for 7 tricks in a suit where the opponents probably have the majority of trumps.
You bid 1NT. The bidding continues:
2♥: Invitational in hearts (transfer to the opponent's major shows an invite in the other major)
Partner's call is invitational. However, that is only in context of his previous bidding. His previous pass shows 0-4 points, and that isn't going to change. Even giving him a maximum of 4 HCP, your side will have only 25 HCP. You don't fit his hearts well, and your spades appear to be badly placed. Where would 9 tricks in notrump or 10 tricks in hearts come from, particularly since partner's hand is probably almost entryless. Game figures to be hopeless. There is no need to correct to 2NT. 2♥ in the known 5-2 fit figures to be best.
You pass, ending the auction.
Partner's "transfer" makes him the declarer. But this is Kit's Korner, so you transfer yourself over to his seat to play the hand.
West leads the ♠10.
What spade do you play from dummy at trick 1?
If the spade lead is a singleton, you do best by ducking. This would force East to overtake in order to continue spades, which would establish spade winners in dummy. Those winners won't do you any good, but East doesn't know that.
If East has AQ98xx of spades, at favorable vulnerability he probably would have bid more than 1♠. Assuming the spades are 5-2 you might as well cover, since this limits the enemy options. Which spade you cover with probably doesn't matter since East appears to be marked with AQ, but on the off-chance that West has led the 10 from Q10 doubleton you might as well cover with the ♠J.
You play the ♠J. East wins the queen, and shifts to the ♦7. How do you plan the play?
You can afford to lose 2 trump tricks, as you have only 3 black suit losers. It is the second ruff you are afraid of. The diamond return is very likely to be a singleton. You must find the best way to stop the crossruff.
The two obvious approaches are to take a heart finesse, or just bang out ace and jack of hearts. Clearly if you take the finesse and it wins you will make the hand, but if the finesse is offside you would have done better to get as many trumps out of the way as possible.
Suppose the trumps are 3-3. If you finesse and lose, the spade return will almost certainly defeat you. What happens if you bang down ace and jack of hearts? If West has the king of hearts, he can give East a diamond ruff, and East can play ace and a spade promoting West's 10 or 9 of hearts (if West has neither you will always make). If East has the king of hearts you can survive if you play for the heart to be 3-3. When East plays ace and a spade, you can ruff with the queen of hearts and draw their trumps. However, if West has the ace of clubs, East can cross to the ace of clubs, get his diamond ruff, and then get the trump promotion. Thus, on the 3-3 splits it looks slightly better to finesse. The finesse is successful when West has the king, but playing ace and jack is probably successful when East has the king.
Suppose the trumps are 4-2. Now it is clear to take the finesse. The reason is that if East has the king of hearts he wouldn't have returned a diamond. If he has, say, K9xx, he would have continued ace and a spade, hoping to promote his partner's 10 and then score two trump tricks on power himself. Similarly, if East started with king-doubleton he would have continued ace and a spade. His hope would be to promote one trump trick now, and another trump trick when he gets in with his king of hearts.
The above analysis indicates that finessing is clear. Assuming correct defense, the finesse can only gain when trumps are 4-2 while it is better than break-even when trumps are 3-3.
You choose win the diamond in dummy and play ace and jack of hearts. East follows with the ♥3 and the ♥5. West follows with the ♥4, and wins the ♥K. West now leads the ♠8 to East's ♠9, and East returns a small spade. What do you do?
The 10 and 9 of hearts are still out. If the hearts were initially 3-3, you must ruff high and draw their trumps together. If you fail to do so, they will score their trumps separately. On the other hand, if the hearts are initially 4-2 you will always go down if you ruff high, while you have a chance to make by discarding -- to defeat you West will have to hold both trumps and East the ace of clubs.
If the opponents have defended correctly, the hearts should not be 3-3. If they are, West could have given his partner a diamond ruff and then scored his remaining trump via the trump promotion on the third round of spades. You should discard, hoping that the hearts are 4-2.
You discard. West ruffs, and gives East a diamond ruff. East cashes his ♣A for down 1. The full hand is:
Taking the heart finesse would have been successful. As it turns out West misdefended when in with the ♥K, giving declarer a chance to make. Had West properly given his partner a diamond ruff, declarer would have had no chance.
Do you agree with South's bidding?
While the pass over 1♠ is supposed to show 0-4 points, it is quite reasonable to downgrade the queens and jack a point. If South doubles showing 5-8 points, the auction is likely to get out of hand.
Having started showing 0-4, South is clearly worth the invitational transfer. He has a complete maximum in context of his previous auction, and that might be what North needs to bid a game. It was unfortunate that the sequence wrong-sided the contract. To make matters worse, 3NT will be making on the normal spade lead since South has the unexpected diamond entries to the hearts.
The reason we use 2NT opening to show minors is that we prefer to open strong balanced hands 1♣. The ranges don't present a problem. 1♣-1♦;2NT = 20-21 points, just like a standard 2NT opening. A 2♥ rebid by opener is similar to Kokish -- either a strong balanced hand or one of several other game-forcing hand types. After responder's forced 2♠ call, opener's 2NT rebid shows 22-24 points, just like a standard 2♣-2♦;2NT sequence. Where we show the big gain is when responder has a positive response. We will have established a game force at a very low level and the strong hand will be in control, which helps our slam bidding greatly. By contrast, after a standard 2NT opener, the weak hand is in control with the bidding at a higher level, so slam auctions will not be as accurate.
Plus... it's free!