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Counting the Distribution
The bidding, the play of the cards, and the defensive signaling, provide valuable distributional clues for Declarer and the defenders, essential information for finding the right line of play or defense.
Related Play Problems Play Problem 23
Related Extracts from Past Wednesday Games
The barrage of Diamond bids does not keep E-W out of 4♠, a contract in which Declarer needs to have on his guessing shoes. Let’s say that South cashes the A♦, and shifts to the T♣. North jumps up with the A♣ and vainly attempts to give Partner a Club ruff. It looks as if one opponent started with 9 minor cards and the other with 8, and it’s not clear which way round that is, so there seems to be no good reason not to play for the drop of the Q♠. Trumps are drawn and Clubs are cashed, then comes the Q♥, which North declines to cover. Now, do we play for North to have started with Kx in Hearts (in which case we play low to the A♥), or do we play North to have started with Kxx of Hearts (in which case we lead the J♥, squashing South’s Ten)? This one is not really a guess at all … North is known to have started with 2 Spades and 4 Clubs, and presumably 5 Diamonds based on South’s bidding, that leaves an original Heart holding of Kx. So, the King falls under the Ace and it’s 11 tricks.
Of course, if North had known that Declarer was going to be so unsporting as to count out the hand, then she would have done better to cover the Q♥ with the King. Now, Declarer has a guess as to whether or not to finesse against the Ten.
After this auction it seems normal enough for West to lead a Diamond. Declarer can count 7 top tricks, and the Spades and Clubs are the most promising source of extra tricks. It would be dangerous to take an immediate Club finesse … if it loses, West might continue Clubs, and the defense could set up a couple of Club tricks before a second Spade trick is established. Our suggestion would be the following line: Win the Diamond lead on the board Finesse the Spade Eight, losing to the King Win the Diamond continuation (best for the defense) in hand Cash 2 more Diamonds (East must part with 2 Clubs) Finesse the Spade Seven (if it loses, then the Ten will be a board entry) Lead Q♣ losing to West’s King Club return, won by Declarer’s Ace Cash J♣, pitching the T♠ from the board! (unblocking play)
At this point East can be counted for having started with precisely 4-2-2-5 distribution. How so? - Spades: Surely she started with Q9xx - Diamonds: Known to have started with two - Clubs: Known to have started with 5 (he pitched twice, followed suit thrice, and West also followed to three rounds) - Hearts: Ergo, he started with 2 Hearts. We have now arrived at a beautiful 4-card ending. As she contemplates her play for Trick Ten, South knows it’s a racing certainty that the remaining cards are as follows:
North ♠ -- ♥ J652 West East ♠ -- ♠ Q9 4 Hearts 2 Hearts South ♠ AJ ♥ A8
What could be simpler than to play A♥ and out a Heart at this point in the proceedings? If East wins the second Heart, he’ll be end-played in Spades for 10 tricks. If West wins the second Heart, we won’t score our A♠ but we’ll get the J♥ as compensation and it will be the same 9 tricks we would have got if we had lazily cashed our Aces and given up. Pretty clever stuff. But suppose that East drops a high honor under the A♥, let’s say the King. Suddenly we have a choice: - Did East start with ♥KQ, in which case we’ll exit a Heart and collect on the Spade end-play? - Or, did East make a brilliant play from Kx, in which case we should cash the A♠ and lead towards Dummy’s ♥Jx?
Well, our philosophy would be not to assume that East is a genius. No disrespect to East, it’s just going with the odds. And, if it turns out that he made a great play, then more power to him! Congratulate him and ask him what he’s doing next Wednesday!
We’d expect a Spade part-score at most tables, which makes 9 tricks with this line of play: North starts with the A♣ Heart shift, won in Dummy Diamond won by South’s Ace Heart won by Declarer’s King Club to North’s King J♥ is cashed Heart ruffed by Declarer A♠ is cashed K♦ is cashed Here is the end-position: North ♠ ♥ ♦ 8 ♣ 953 Declarer Dummy ♠ Q9 ♠ K87 ♥ ♥ ♦ KJ ♦ ♣ ♣ Q South ♠ T63 ♥ ♦ Q ♣ It may appear that South still has a trump trick coming in the end-game, but that is not the case. Declarer has a perfect count on the hand at this point, and finds it easy to cash the K♦, ruff a Diamond high, and finesse the 9♠. A nice ending, and one that would not have been possible if Declarer had not set up a Diamond trick early in the play, before touching trumps.
11 tricks are possible in 3NT, and may well be made on this line of play: T♠ to Declarer’s Ace Club finesse losing to West’s Jack Q♠ won by Declarer Q♣ won by East’s Ace Heart exit is won by Dummy’s Jack Clubs are cashed (Declarer pitches a Spade, the Q♦ and a low Diamond) Hearts are cashed
At this point in the play Declarer can count 10 tricks. She can also count the distribution. The Hearts and Clubs will be known, and there is a strong presumption that East started with 2-3-6-2. If that doesn’t make the Diamond finesse worth risking then we don’t know what does! If the finesse works it’s 11 tricks, and if West had been dealt the singleton K♦ it will be just 9 tricks.
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