Alder's NEA Bridge: The negative can be positive

John Keats claimed that Samuel Taylor Coleridge would "let go by a fine isolated verisimilitude caught from the Penetralium of mystery, from being incapable of remaining content with halfknowledge."

Wow — but you get the gist. Look at today's deal. Against South's four-spade contract, West leads the club king. He continues with the queen, but East overtakes with the ace and shifts to the heart three. Should South play the jack or the king?

South opened four spades because he couldn't envisage a slam opposite a passed partner and wished to keep the opponents quiet.

Declarer had three top losers: two clubs and one heart. If the diamond finesse was losing, he was going down. So he assumed that it was working. Given that (a fine isolated verisimilitude?), South would make his game as long as he didn't lose two heart tricks.

He knew of eight points in the West hand: the club king-queen and the presupposed diamond king. If West had the heart ace as well, probably he would have opened the bidding. So declarer should play for East to have the heart ace. Put up the king. If it loses, South will finish down two (because the diamond finesse will fail). However, if the king wins, he will probably be home. (If East had the heart ace and diamond king, he wouldn't have overtaken at trick two. He would have willed his partner to shift to a diamond.)

By assuming where one key card lies, you may be able to conclude which opponent holds another key card.

Perhaps — perhaps — the Penetralium of mystery isn't so mysterious after all.