Even though the you and your partner made moves toward slam, when you see dummy after West leads the ♠10, you can see that getting to 10 tricks is not going to be easy. How do you plan to bring in this contract?
After West’s opening lead, declarer won with the ♠J as East followed with the 6. 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 *D*A?” Declarer observed that he could succeed if West held the ♥ K by leading a low heart from hand towards dummy’s queen.
If West had the ♥ K and played it, declarer would score three heart tricks with the queen, ace, and jack, as well as the ♦ A for the overtrick. If instead, West played low when holding the king, dummy’s ♥Q would win the trick. Declarer could then cash the ♦ A, 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 ♥K. 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 ♦A, 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 e led the ♥ 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 ♦A to guarantee his contract.
Note that if East had allowed the heart jack to win, declarer would have cashed the ♥A and ruffed a heart in dummy. The ♦A would then have provided a bonus overtrick.
Finally, we know that the probability that West has the ♥K 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 4♠ even when hearts were 5:2 and East ducked the king – for example, when West doubletons 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 ♦A. The full deal: