Source: IBPA Column Service FEB 2021

Marcelo Castello Branco
Marcelo Castello Branco

**Source: wikipedia: Marcelo Castello Branco (born 1945) is a Brazilian bridge player from Rio de Janeiro.  Among other successes, he was the winner of World Team Olympiad in Monte Carlo 1976, Bermuda Bowl in Perth 1989, and World Open pairs Championship in New Orleans 1978 and Geneva 1990. He is one of 10 players to achieve the Triple Crown of Bridge and the only player to have won the World Pairs twice – in Geneva with his most frequent partner Gabriel Chagas and in New Orleans with Gabino Cintra.

Good declarers are constantly drawing inferences from the cards played by the defenders. Honour leads usually reveal a touching honour; a high spot indicates that the opening leader is short or lacks high honours in the suit; declarer play is always based on deductions of this sort.

There are situations which are not as blatant. For example, if you eliminate the side suits in a trump contract and give up the lead so as to force the opponents to break a suit in which you have ace-low in your hand and queen-ten in the dummy, if the opponents could choose which hand would win the throw-in trick and LHO won the trick (i.e., he will start the trick and dummy, with queen-ten, will be the next to play), you may be sure that LHO does not have the king.

If he had the king, he would have let his partner win the trick so as to play the problem suit correctly for the defence. There are many discussions, in articles and books, about this theme. But it is not so common to find discussions about what may be called negative inferences, that is, inferences based on what the opponents did not do.

J 6 2
J 7 3
7 5 4
Q 7 4 2
A 7
A K Q 5
A K J 10 6 2
9

You are playing in three notrump after a strong 2 opening, a 2 response and a 3 bid by the strong hand. Three notrump by the weak hand finished the auction.

North led the five of clubs. South won with the king, and played back the jack, then the ten, and finally the four… and you are still alive since clubs were four-four originally. You discarded one spade and two diamonds from dummy. North, upon winning the last club trick, led a spade to dummy’s now-singleton ace.

You must guess diamonds to make your contract. You cash the ace of diamonds (no luck there, all you see are low cards), and play three rounds of hearts, ending in hand with your jack. Everybody follows suit. Now you play a diamond from your hand, and North plays the nine.

What should you do?

If you play the king (“Eight ever, nine never”), you are in effect playing the opening leader to have started with the three hearts he has shown, two diamonds (only), exactly four clubs, and therefore four spades, i.e., a 4=3=2=4 hand.

And if you finesse in diamonds, you are playing for him to have one extra diamond, that can come only at the expense of the spade suit (since the count in the other suits is known by now). That is, you will be playing him for a 3=3=3=4 hand.

In the first case, LHO would have had four spades and four clubs, and he led clubs from a suit such as ace-eight-six-five.

Is that likely?

Is it not more probable that he would have led spades (from whichever holding he has in the suit)? Reasoning like that, I finessed in diamonds, and was rewarded when East showed out. If you are a math genius, willing to do these kinds of calculations in your head while playing the deal (which is not my case, truth be told), you will see that the 4=3=2=4 hand is almost twice as likely as the 3=3=3=4 hand, which is an argument against the diamond finesse.

You have to weigh this kind of consideration along with the psychological aspects of the choice of opening lead. As you know by now, in my opinion, the psychological clue is dominant in our example hand, but there are situations in which the math is compelling; each player must make his own decisions at the table.

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