Hopeless contract?

[rod]

You won't win by habitually bidding unmakable contracts, but when it happens you have to try your best. Here's one I played against the computer today.

♠ AK97
♥ J94
♦ QJ6
♣ J108

♠ Q108652
♥ Q865
♦ 43
♣ A

Partner deals and opens 1♣. This is a poor choice with nine losers and no shape. East overcalled 1♦ and we quickly ended in 4♠ with West leading the ♥2. East cashed King and Ace and played a small diamond. West took ♦A and exited with a third heart, all following.

It seems impossible to avoid losing another diamond, but there is a tiny glimmer of hope. It takes a bit of imagination, knowing the opponents cannot see your cards. I crossed to the ♠A and tried the ♣J from dummy. East covered with the Q and I played another spade to the King and the ♣8 from dummy.

It's hard to blame East for playing the King. He might have figured out the distribution with partner showing count in clubs, but most players would not. The opposing cards were:

♠ J4
♥ 1072
♦ A98
♣ 97642

♠ 3
♥ AK3
♦ K10752
♣ KQ53

[rod]

East's figuring out the distribution goes something like this:

1. Assume partner started with J4 of trumps, because if it's QJ4 then the contract is already down.
2. Partner had 3 or 4 hearts and didn't raise diamonds so presumably 3 or fewer diamonds.
3. Therefore partner had at least 4 clubs.
4. Since partner first played the 2 of clubs he had 5, and declarer must have started with a singleton.