Most experts advocate opening one notrump even when the opener holds a weak doubleton in one suit — provided the rest of the hand meets all the usual distributional and point-count requirements. The chief advantage of this is that it simplifies the bidding on many hands while resulting in very little harm over the long haul.

One natural adversary of notrump bids is the Rule of Eleven, which can dramatically pinpoint a weak spot in declarer’s hand. Today’s hand demonstrates how the rule is applied.

West led the seven of hearts, won by East with the jack. East returned a club to South’s ace, and a diamond finesse lost to East’s king. Declarer won the club return and cashed three diamonds and four spades to make exactly nine tricks.

However, three notrump would have failed had East played the four on the opening heart lead, allowing West’s seven to hold the trick! A heart continuation by West would have given the defenders the first four tricks, and East’s king of diamonds eventually would have done South in.

How could East have known that West’s seven would win the first trick? The answer lies in the Rule of Eleven, which can applied whenever a player leads the fourth-best card of a suit.

Since there was no reason to doubt that West’s lead was fourth-best, East should have subtracted seven — the card led — from 11. The resulting number — in this case four — would have told East how many cards higher than the seven were in the other three hands.

Since East could see all four of them in his own hand and dummy, he could conclude that South had no card higher than the seven, enabling him to play the four at trick one.

Tomorrow: Maximizing your chances.