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Board 3: East has a huge 5260 hand: what to open in 4th seat? With 18 hcp, the odds of being passed out at the one level are fairly low; if partner can't respond, one of the opponents is likely to bid. Diamonds are the best suit and the hand is certainly strong enough to bid and rebid spades later. Would it be easier to reach slam with a 2C opening? A likely auction might be 2C-2D; 3D-3NT; 4S -- does that suggest 5-6? I'm not sure, so I think I'd try opening 1D. South overcalls 2C, West passes, North raises to 3C -- opposite a passed hand, there's little risk of partner overbidding and the raise helps blockade East. A leap to 4S, however, should clearly suggest the powerful 5-6 shape (at least 5-5 for a jump shift opposite a passing partner, and longer diamonds since East bid the lower ranking suit first.) Holding an Ace and tolerance for both suits, West can pass or take a preference back to diamonds. In general, it's wrong for the shorter trump hand to insist on a non-fit (5-2 or 4-3) when there is a known fit. It's fine to suggest playing in a major, but the decision should be left to the one with the trump length, who will have a better idea how solid the suit is. Here West may suspect spades is a good spot but as partner could've opened spades with good spades and indifferent diaonds, I think it's safest to return to the known fit, 5D. East does not have enough information to bid further.
In the play, East expects to lose a club and a spade or possibly a diamond, hopefully not both. In fact both suits split well and East rolls up +620; as it happens spades would score +680, but slam would be a poor bet.
Board 4: North opens 1C in second seat, and East's suit is too weak for a vulnerable preempt. South responds 1H. North counts 7 likely winners and several plus values; if the clubs run or partner can provide some help in whatever suit they lead 3NT looks like a good bet. Note that this is the normal type of hand for a 3NT rebid -- with 18 or 19 balanced, North would rebid 2NT; with more, North would open 2NT or 2C. So North's 3NT suggests long, strong clubs and at least 7.5 tricks. South can expect to add at least 4 tricks and should invite slam in case North has extras. 4NT here should be invitational, and if not 4C should be a clear slam try (it would be silly to run from a game to a part-score) but in many partnerships South can expect 4NT to be taken as Blackwood. Still, there's probably some play for 12 trick if partner has at least two Aces. As North, I'd pass 4NT (only 6 clubs and 3NT was a bit of a stretch) but would react favorably to 4C with 3 Aces and the Queen of trumps: a possible sequence might be 1C-1H; 3NT-4C; 4D-4H (cue-bids); 4NT-1 ace or 2 key card reply; 6C or 6NT-all pass. If South bids 4NT as Blackwood, North replies 5S (3 Aces) and South should bid 6C -- the trump suit may be needed to set up hearts for 12 tricks.
North can win a spade lead and set the hearts up with a losing finesse. A diamond lead is trickier -- perhaps West doubled 4D for a lead. This dooms 6NT but 6C can be made by ruffing a heart before pulling the last trump. Should declarer try the ruff or finesse? A 3-3 split is about a 36% chance; in half of those cases the finesse also works, so we can say the ruff gains 18% (Qxx offside.) If East has Qxxx, the finesse wins and declarer can ruff a heart, return to dummy with the King of trumps, and pitch two diamonds; I make the odds of East having Qxxx about 16%. Hmm, the ruff also gains when West has Qx, another 8%, so it looks like ruffing is the better play. A singleton Queen or Qx with East will be obvious in any case, so overall the ruff looks like a better than 50% chance.
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