Source: IBPA Column Service Jan. 2019

Dealer South. E/W Vul

5 3
Q 4
A J 7 6 5
9 6 4 3
10 9 7
8 7 2
Q 9 8 3 2
10 2
8 6
K 10 9 6
K 10 4
K Q J 8
A K Q J 4 2
A J 5 3

A 7 5
West North East South
1
Pass 1NT Pass 3
Pass 3 Pass 4
Pass 4 Pass 4
Pass 4 End

Even though the partnership had made moves toward slam, declarer saw that making game would be no easy task. West led the ten of spades, taken by declarer with the jack, while East followed with the six.

Declarer had eight top winners, with another trick that could be developed in hearts. Declarer asked himself, “What is the best plan to make a tenth trick?”

Also, he wondered, “How can I get to dummy to cash the ace of diamonds?”

Tim Bourke
Tim Bourke

Declarer observed that if West held the king of hearts he could succeed by leading a low heart towards the queen. If West had the king of hearts and played it, then declarer would score three heart tricks with the queen, ace, and jack, as well as the ace of diamonds for the overtrick. If instead, West played low when holding the king, then dummy’s queen of hearts would win the trick.  Declarer would then cash the ace of diamonds, throwing a club, for his eventual tenth trick. He could then try to ruff a heart for trick 11.

However, declarer saw that that plan would fail whenever East held the king of hearts. If declarer did lead a low heart at trick two when this was the case, East would take dummy’s queen with his king and return a second trump. In that case, declarer saw that there would be no way to make dummy’s ace of diamonds, and he would lose two hearts and two clubs. Declarer eventually came to the winning play, which would succeed whenever hearts were 4-3: he led the jack of hearts from hand at trick two!

East took this with the king and returned a trump. Declarer won and drew West’s remaining trump. Then he crossed to dummy with a heart to the queen. All that remained was to cash the ace of diamonds to guarantee his contract. Note that, if East had allowed the heart jack to win, declarer would have cashed the ace of hearts and ruffed a heart in dummy. The ace of diamonds would then have provided a bonus overtrick. Finally, we know that the probability that West has the king of hearts is an even-money bet, 0.5. The chance that hearts are 4-3 is a good deal better than 50% (in fact, it’s about 62%).

Declarer chose the better plan. There were a few circumstances where declarer could make four spades even when hearts were 5:2 and East ducked the king – for example, when West had a doubleton in both majors. In that case, West could have ruffed the third heart but would not have been able to prevent declarer from ruffing his fourth heart in the dummy to reach the ace of diamonds.

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