Suit Combinations - Exploiting Defensive Errors

Exploiting Defensive Errors

The optimum treatment of a particular suit combination guarantees a certain minimum likelihood of success against any possible defense. However, such a treatment, whilst guarding against opponents who would exploit any error in declarer play, does not itself exploit defensive errors. In some practical cases when defensive errors are likely, it might be advisable to deviate from the optimum play of the suit so as to benefit from the assumed defensive errors.

In this example, from 5th edition of the Official Encyclopedia of Bridge, declarer needs two tricks from a suit in which he has three small spotcards and dummy has K Q 10:

The game-theoretical optimum approach is to lead towards the king in dummy, and subsequently - whether the king won or not - to lead to the queen.

An expert defender sitting East with the ace, but no jack, is likely to duck on the first round to protect partner's jack. Thus, if this expert defender plays the ace on the first trick, he is most likely to have either the ace singleton, or the ace and jack because with any other combination he would have ducked. In the latter case, declarer's only chance to get two tricks from this suit is to play East for ace-jack doubleton. As the chance for ace-jack doubleton (0.73%) is larger than the chance for ace singleton (0.48%), if the king loses to the ace in trick one, declarer's optimum play is to play for the drop of the jack in trick two and put up the queen.

In practice however, if in the first round the king loses to East's ace, declarer must decide whether East would hold up the ace in the first round when not holding the jack. If East is judged as likely to play the ace in the first round regardless of the holding of the jack, declarer should finesse the ten in the second round. Note that an expert sitting East who deliberately makes the exploitative defense of catching the king with the ace whilst holding one or more small cards in the suit (but not the jack), is counting on the fact that declarer would judge him not to make that suboptimal play.