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
Against 4♠ North leads a Diamond and Declarer will win this in Dummy, fearing that North has a singleton. Now trumps are drawn in three rounds, and the ultimate success or failure of the contract will depend upon the Heart suit. Trumps are drawn and, before playing on Hearts, Declarer will go fishing for clues. Heíll lose to the ♦K, ruff the Diamond return, and lead a Club towards Dummy. North wins that with the Six, so know Declarer knows that South probably started life with 3=3=4=3 shape, in which case it doesnít matter how he plays the Hearts, thereís only one loser in the suit. However, South could have started with 3=2=4=4, in which case Declarer is probably down (unless Southís doubleton was ♥QJ). So, it all turns out to be much counting for little reward, 10 tricks are always there for the taking, regardless of whether or not Declarer is exercising his gray cells.
The play in Hearts is most interesting!
Club Two to the Ten and Declarerís Queen
Spade Ten to Westís Jack
A♥ is cashed
K♦ is cashed
A♣ is cashed
Club to the King, Declarer pitching a Spade
Heart to the King
With 4 cards left, and Declarer needing all the tricks, here is the end-position:
♠ Q ♠ A5
♥ ♥ T
♦ A2 ♦ 8
♣ T ♣
Looking at all 4 hands itís clear enough that Declarer makes the rest by leading the K♠, squashing Westís Queen. But will that be obvious to Declarer? Hereís what can be deduced:
- The A♠ is with East. West has already shown up with J♠, A♥, AK♦, AJ♣, thatís 17 HCPís. Surely West cannot also have the A♠, that would be too much.
- What is the enemy distribution? Thatís a bit harder to fathom than the missing high cards. Letís give West 5 Clubs (perhaps East would have supported with 4, perhaps his opening lead was 3rd best). Did West start out life as 4=1=3=5 or 3=1=4=5? It wonít be obvious!
Anyway, full marks if you realized that the A♠ had to be with East, and bad luck if you misguessed the distribution.
E-W stop short of game, but how many tricks will East make? South will probably lead a Spade (nothing else appeals), and North takes her Ace. Letís say that North continues Spades, ruffed on the board. Now a Heart to the King and the Ace. Another Spade is ruffed and now itís decision time! Will Declarer correctly guess the Heart situation and make 10 tricks? Before making his decision, East will weight up the evidence:
- North showed up with ♠AQ and yet did not open 2♠. It looks safe to assume that the North has 5 Spades and South has 4.
- When North won the opening Spade lead, she did not fire back a Diamond in search of a ruff. Surely, North has two Diamonds and South has 5.
- Having passed originally, South overcalled a vulnerable 2♦. Would she bid that with ♠ Jxxx, ♥ AJ, ♦ AJxxx, ♣ xx? Probably not.
Yes, Southís length in Spades and Diamonds makes it likely that she has fewer Hearts than North. And her 2♦ bid suggests some distribution.
Against 4♥, North leads the ♠T, won by Declarerís Ace. Declarer will draw trumps, ruff a couple Spades and a couple of Clubs, hoping for a King to fall. Finally, Diamonds must be tackled. Declarer leads to his King, taken by the Ace. Back comes a Spade, ruffed by Declarer, and now West leads a Diamond towards the board. North has been doing some counting, of course. She knows that Westís initial distribution was 1=5=3=4, so with nerves of steel she plays low on the second round of Diamonds. Declarer finesses the Nine and is held to 10 tricks! Note that Declarer would have done better to ruff one less Club and one less Spade. Now, when South wins her doubleton ♦T, she is end-played! Whichever black suit South leads will hand Declarer his 11th trick.
Against 3♥, North leads the ♠Q, and then the ♠J, both of which hold. Next comes a Club shift. How would you play the Heart suit? The theoretically correct play is the ♥A followed by a Heart to the Queen. Does the bidding suggest a different line? South opened the bidding and North responded, so it looks as if the ♦A is in one hand and the ♥K in the other. So one suggestion is to win the Club shift in hand and play the ♦K. North wins this and, as it happens, can give South a Diamond ruff. Declarer wins the Club return in Dummy, and will play South for 3=3=1=6 distribution. That being the case, his only chance is to lead the ♥Q from the board, hoping to pin Northís singleton Jack. Bingo!
Playing on Diamonds first was a good example of a Discovery Play. By finding out who had the ♦A, Declarer was in a better position to play the Hearts correctly. True, the Diamond ruff was a setback, but 9 tricks were still possible. Now look what happens if Declarer wins the Club shift and plays ♥A and a Heart to Southís King. That is followed by a Diamond to Northís Ace and a Diamond ruff for down one!
With or without the Diamond bid, North is likely to declare a Heart contract, probably in game at most tables. 4♥ is a poor contract but it makes with this delightful line of play:
Diamond lead is won by the Ace
♠A is unblocked!
♠K is cashed (pitching a Diamond)
Cash the ♥A
By now, all the Spades and Hearts have gone and this is the end-position:
♦ KQ8 ♦
♣ Q9 ♣ KT862
Declarer has a perfect count on the hand, and knows that West started with 4=2=5=2 distribution. The best hope for Declarer is that Westís doubleton Club includes the ♣K or ♣Q, so she cashes the ♣A and exits with a low Club. Now, if East grabs his ♣K he will crash Westís Queen and set up Declarerís Jack. So, East ducks the Club and when West wins the Queen he is end-played in Diamonds!
In the above line of play, note the importance of ruffing those Spades early in the play. If Declarer had failed to do so, then the Spade suit would have provided the defense with safe exit cards.
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. Letís 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 itís 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 Southís Ten)? This one is not really a guess at all Ö North is known to have started with 2 Spades and 4 Clubs, and presumably 5 Diamonds based on Southís bidding, that leaves an original Heart holding of Kx. So, the King falls under the Ace and itís 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 Ö 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 Westís King
Club return, won by Declarerís 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 itís a racing certainty that the remaining cards are as follows:
♠ -- ♠ Q9
4 Hearts 2 Hearts
What could be simpler than to play A♥ and out a Heart at this point in the proceedings? If East wins the second Heart, heíll be end-played in Spades for 10 tricks. If West wins the second Heart, we wonít score our A♠ but weíll 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♥, letís say the King. Suddenly we have a choice:
- Did East start with ♥KQ, in which case weíll 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 Dummyís ♥Jx?
Well, our philosophy would be not to assume that East is a genius. No disrespect to East, itís 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 heís doing next Wednesday!
Weíd 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 Southís Ace
Heart won by Declarerís King
Club to Northís King
J♥ is cashed
Heart ruffed by Declarer
A♠ is cashed
K♦ is cashed
Here is the end-position:
♠ Q9 ♠ K87
♦ KJ ♦
♣ ♣ 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 Declarerís Ace
Club finesse losing to Westís Jack
Q♠ won by Declarer
Q♣ won by Eastís Ace
Heart exit is won by Dummyís 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 doesnít make the Diamond finesse worth risking then we donít know what does! If the finesse works itís 11 tricks, and if West had been dealt the singleton K♦ it will be just 9 tricks.
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