One assumption or two assumptions

G.H. Lewes, a 19th-century English philosopher and critic, wrote, “We must never assume that which is incapable of proof.”

Usually in bridge, the best play can be proven. Occasionally, though, we have to guess what to do. At other times, making one assumption leads to another. Because we assume A to be true, then B must be also.

How does that apply in today’s deal? South is in four hearts. West cashes the spade ace: three, nine, jack. He continues with the spade king: six, two, four. Then West plays a third spade: 10, queen, ruff. What should declarer do next?

Most pairs would stop in a heart partscore. But we need North-South in four hearts to have a story to tell.

South has lost two tricks and must concede a trick to the heart ace. So, he cannot afford to lose either a club or a second trump. That leads to the first assumption: West holds the club king.

So, what about the trump suit? If the missing hearts are 2-2, there is no problem. If they are 3-1, though, declarer needs the ace to be a singleton. But which defender is more likely to have that ace?

So far, West is known to have 10 high-card points: the spade ace-king and club king (necessary from assumption one). This makes it more likely that East has the heart ace. It isn’t certain, but with 14 points, West would probably have bid.

South should play a diamond to dummy’s jack and return a low heart. Here, East has to win with his ace, and shortly South is scoring up his lucky game.