A 5-or-7 hand, at the one-level

I was kibitzing a hand from the Spingold QFs where Fantoni, in a 3-card ending, wound up having to guess whether the opposing trumps were initially 97/KJ54 or 95/KJ74. This was necessary in order to get out for 800 instead of 1100 in 1S doubled! In particular, declarer’s trumps were initially T863/AQ2. LHO had earlier overruffed declarer’s 8 with the 9, righty had ruffed a plain suit with the 4, dummy had ruffed with the A to avoid an overruff, and RHO had just ruffed ahead of declarer with the J, leaving a remaining trump position of

Q2

x Ky

T63

where {x,y}={5,7}. Now RHO led a suit where declarer and LHO but not dummy were void. To take 2 tricks, declarer must ruff with the 6 if x=5, but with the T if x=7. Yikes! The commentators were all saying this was a pure guess. A waste of time to even think about it, right? What possible inference could there be about the 5 and 7? There is one clue, though…do you see it? Answer below.

The key is to ask yourself whether either defender had a choice of how to defend with either holding. For lefty, there is no inference whatsoever as he had no choice from either 97 or 95. RHO, though, could have ruffed with the 5 or 4 from KJ54, but his choice would be restricted to the 4 from KJ74. That’s right, restricted choice operates on the 5 and 4 spots! Declarer should therefore play righty for KJ74 and ruff with the 6. By the way, it’s a very good habit to play randomly from equivalent spots when you are not signaling…this doesn’t require that you foresee esoteric positions like this, it’s just good general technique that minimizes declarer’s information.

In real life, Fantoni ruffed with the T and was punished with -1100. At the other table, oddly, they got to 2H-X in a slightly stronger 4-3 fit and did two tricks better for -800. You can see the hand record here.

Thanks to vugraph operator Dan Wolkowitz for the joke in the title. He’s the best I’ve seen at operating accurately and making good comments at the same time.