# Playing the Odds

Dlr:
North
Vul
E-W
North
♠ K 9
A K Q 10 3
9 7 3
♣ 10 8 2
South
♠ A J 8 7 6 3
5
A K 4
♣ A 5 3
 West North East South 1♥ Pass 1♠ Pass 1NT Pass 2♦(1) Pass 2♥ Pass 2♠ Pass 3♠ Pass 4NT(2) Pass 5♥ Pass 6♠ All Pass

1. Artificial game force
2. Roman Key Card Blackwood
3. Two key cards, no ♠Q

Your bid of 2 was a game-forcing inquiry. Your partnerâ€™s bid of 2 promised a good five-card suit. That news prompted you to push on to the spade slam. West leads the ♣K. How will you arrive at 12 tricks with the North-South cards?

## Solution

After studying dummy after the opening lead was made, declarer saw that playing for trumps to be 3-2 and for East to hold the queen was little better than a one-in-three chance. Instead, he decided to play on hearts, hoping that the suit was 4-3. Accordingly, declarer cashed the three top hearts and discarded his two low clubs. Next, instead of playing a trump, he led a fourth heart. When East followed, South ruffed with the ♠J. If East had held the ♠Q and the suit had been 3-2, this would have insured the contract. After West overruffed with the ♠Q, he tried to cash the ♣Q, but declarer ruffed it low in hand then took the ace and king of trumps. As West had started with 3-3 in the majors, declarer claimed 12 tricks: five trumps, four hearts and the three minor-suit tops. Once the hearts had proved to be 4-3, with the jack still outstanding, using this approach rated to succeed about 60% of the time.
You should note that if the J had fallen doubleton, declarer would have continued with a third heart winner, hoping that the player who ruffed this had started with exactly three trumps.

The full deal:

Dlr:
North
Vul
E-W
North
♠ K 9
A K Q 10 3
9 7 3
♣ 10 8 2
West
♠ Q 10 4
9 8 7
Q J 6
♣ K Q J 4
East
♠ 5 2
J 6 4 2
10 8 5 2
♣ 9 7 6
South
♠ A J 8 7 6 3
5
A K 4
♣ A 5 3

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