A Challenging 3NT

Susanna Scouller showed me this interesting 3 NT deal from my club. After West led the nine of spades (East having overcalled in the suit) and declarer played dummy’s jack, plan the play if:
(a) East plays ace, king and a third spade (as he did at the table, West discarding a club on the third), or
(b) East lets dummy’s jack of spades win (stronger defence in truth, preserving the defensive spade communications).

(a). You cash the four top diamonds and are disappointed when East discards (a club then a spade) on the third and fourth rounds. Without a fifth diamond winner, you are a trick short.

The ninth trick could come from clubs but the finesse into the danger hand is a risk you should not take. East’s club-then-spade discard suggests his actual hand, with either two small hearts or ♥ Qx/ ♥ Jx.

Does East’s doubleton heart rate to contain an honour? To simulate the situation, imagine a bag with four white balls (spot cards) and two red ones (honours). You reach in and (without peeking) pick out two balls. The chances of the first ball being white is 4/6 ie 2/3. Having picked one white, the chances of the second ball you pick out also being white is 3/5. Soyour chances of both balls being white is 2/3 x 3/5 = 6/15 = 2/5. Sixty per cent of the time East will have a heart honour.

You cross to the ace-king of hearts and are pleased to see East’s jack fall. You lead the ten to West’s queen and let West cash his fifth diamond but dummy has an extra heart winner (or two). Game made.

(b). In dummy with the jack of spades, you cross to the four top diamonds, observing the 5-2 split as East lets go the club and the spade. You cannot afford to lose a heart trick to West’s queen in this scenario, as West still holds a spade.

There is an ingenious route to the ninth trick. Cross to the ace king of hearts, removing East’s hearts, then exit with dummy’s spade. Let East cash his spades, for at trick 12 he will have to lead from king-small of clubs, giving you a second trick in the suit. Game made.