| ♠ | A J 7 2 |
| ♥ | A 5 4 3 |
| ♦ | A Q J 10 6 |
| ♣ | |
| ♠ | K 10 9 6 |
| ♥ | K 9 2 |
| ♦ | K 2 |
| ♣ | 9 6 4 3 |
East overcalls 2♣ on your way to 6♦. The problem specifies that West leads a 3rd highest ♣2, so you can take as given that clubs are 3=6. It also points out that finding the trump queen or ruffing 2 clubs is sufficient, but warns of a trap.
I've put the book's solution and my own below the fold.
Say you play a trump to the ten. If it loses, it's relatively straightforward to ruff another club and draw trumps.
If it holds, then what? The book points out that against a tricky defender, you might play a spade to the Ace and see East show out. It asserts that Qxxx/x is a 38% chance and xx/Qxx is only 29%, so against someone who is up to ducking the queen you should finesse the jack. A pretty cute play, finessing one way and then the other.
I agree that those are the relevant holdings. I get that their odds are 56:45 (12c6 * 4 : 12c4 * 6), which is very close to their numbers (not quite within rounding but I'm going to ignore that). But, it seems that after the ♠A and East shows out, you still have play: ruff a 2nd club and try shaking your other 2 on diamonds. The chance of West having 2 or fewer diamonds (which is required for this backup plan to fail) is under 30% (of the 38%), so the winning case for ♠J is more like 11%, a clear loser.
More generally: this sort of defensive play, ducking when declarer takes a loosing finesse, comes up from time to time. There was a nice hand in an early daily bulletin from San Diego with a similar theme. What should I look for so as to better recognize such situations on defense in the future?
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