The high cards will be with the length

Max Rebattu ( Netherlands )

Born in 1939, MAX REBATTU is a long-time  bridge journalist and teacher in Amstelveen , The  Netherlands . His greatest achievement in the playing  of the game was to be second in the World Pairs in  Biarritz in 1982; unfortunately he and his partner Anton Maas had originally been proclaimed winners  but because of a scoring error  his second place must have been something of a disappointment. He is the bridge columnist of the biggest Dutch newspaper Telegraaf. He first introduced bridge to Teletext in 1980 and continues to organize it.

IT is well known that missing high cards will most probably be found in the hand containing most cards of that suit. If, for example, five cards including the queen are missing, and the suit is divided 3-2, the queen can be expected in the three-card holding. The probability is three out of five or 60%. This is, of course, true not only for the queen, but for any other card.

The converse is, of course, also true. The player possessing the queen has most probably the length in the suit. If five cards are missing including the queen, and the suit is divided  3-2, the chance that the player possessing the queen also has the three-card holding, is again 60%. The same goes for the other four cards in the suit.

By forcing the opponents to discard certain low cards it is possible to obtain information about the most probable distribution of the suit between both opponents. If, for example, KQ2 of a suit are missing and the ace is played, collecting an honour and the deuce, it can be concluded that the one who plays the deuce most probably has the missing honour. The chance of the two being singleton is only one out of three of the 2-1 distributions.

The same principle can be applied to other distributions. If declarer has AKQ3 opposite 54 in a suit, the opponents can be forced to show the two by playing the ace, king and queen. If both opponents follow suit three times, the position of the two indicates the most probable position of the missing card (four out of seven or 57%). What applies to the two does not apply to the six or higher cards in this case. These cards need not be shown, but may be played by choice by the owner of the four-card holding, or may be kept until the last card.

If the two and three are the only missing low cards, it applies to both cards. If they are divided there is no clue, but if both are played from the same hand the probability that this hand contains the length is very high. On the other hand nothing can be said if the two drops by only playing the ace. The opponents may false-card by playing the two from the three-card holding but keep it from four cards.

THE use of this principle is fairly rare, but I have never seen this theory in previous bridge literature. It could be applied when trying to count the opponents' hands, thinking of a throw-in or looking for the right squeeze.

In the next deal the principle can be applied twice. So the chance of success is even higher:

♠ 65

♥ 76

♦ A9876

♣ AKQJ

N-S Game Dealer South

          ♠ AKQ3

♥ AKQ5

♦ K2

♣ 762

Suppose South is playing in 7NT and West leads some middle card in clubs. There are twelve sure tricks and the thirteenth has to come from some squeeze. If the guards in the majors are divided – and that is the most probable case – the contract can be made on a double squeeze, provided declarer guesses the position of the majors right. My tip may be very useful.

North wins the club lead and South now plays his winners in the majors. North discards two diamonds. South looks, eagle-eyed, to see who plays the two of spades and the two, three and four of hearts. Suppose East plays the two of spades and three of hearts and West plays the two and four of hearts. The probability that East has four spades is now 57% and West four hearts about 60%. Now clubs are played. If clubs are 3-3, East is forced to throw a diamond on the fourth club. Now it is vital that South throws the menace that East has kept. In the example given, South has to throw the three of spades. The probability that South has taken the wrong decision is only 43% x 40% = 17%. Now there is a high probability that West is squeezed in hearts and diamonds. By using this tip declarer is able to raise his chances of success remarkably. I expect that in the near future many more hands will be found on which it is possible

 to use my BOLS bridge tip which is:

Expect a missing high card to be held by the opponent possessing the most worthless low cards in that suit.