A Bridge Phantasmagoria




One should be aware of the odds for the split of the adverse cards when holding a suit of eight or more combined cards. When holding eight, the missing five cards will divide 3-2 68% of the time, 4-1 28% and 5-0 4%. Four missing cards will split 3-1 50% of the time, 2-2 40% and 4-0 10% and three missing cards will divide 78% for 2-1 and 22% for 3-0.

The hoary old shibboleth “Eight ever- Nine never” purports to teach us how to play a suit of 8 or 9 cards in the combined hands, when the only missing honour is the queen. With 8 cards we should finesse as the queen figures to be in the hand with the longer holding, but with 9 cards we are told to play for the drop. I used to believe that as 3-1 was the more probable, then a finesse was preferable until the odds were presented to me in a different way. Any particular card will have one card with it 40% of the time and two cards with it 38% of the time, so after all the play for the drop has a slight edge with a 9 card holding.

On this point the late and great Ely Culbertson had an interesting theory which he called “The Law of Symmetry.” Despite the mathematical odds, he claimed that in his experience the hand shape is often duplicated in the suit so that when the suit shape was 5-4-3-1 he would finesse for the queen.

The trouble is that all this advice is fair enough for a suit taken in isolation, but may not be good enough for a hand as a whole. When with the 8 cards holding a losing finesse might expose us to a dangerous lead, it could be prudent to play off the ace and king and once in a while virtue will be rewarded with the fall of the queen. This method maintains control. On the other hand, a finesse is often taken with the 9 card holding to shut out a dangerous opponent.

Now what about ten cards? In view of the odds 78% for 2-1 and 22% for 3-0 would one have to be stark raving mad to opt for the finesse for the queen? Not necessarily so, as the following hand will illustrate.


S 532
H A10
D KQ1096
C 862


S -
H QJ985
D 7542
C Q1075


S Q86
H K732
C J94


S AKJ10974
H 64
D 3













4S (end)


When dummy was revealed, the lead of the queen of hearts posed an immediate threat to the entry for a diamond trick. In the vain hope that West might switch or pull a wrong card, South ducked, but West continued the suit with obscene haste.

Saying goodbye to eleven tricks, South came to hand with the ace of spades with the comforting thought that it was nearly 4-1 on, to bring down the queen in two rounds.

When West discarded a heart, South began to sweat. Desperately he played off the ace and king and another club on the off chance that an opponent would return a club or a heart and give him a ruff and discard.

East, however, had a perfect count. Clearly his partner had four clubs to the queen and so declarer was left with six trumps and a singleton diamond. He had no difficulty in playing the ace and another diamond, enjoying the thought that South would be forced to ruff the good diamond. East still had to make a trump and so South was one done.

On this hand, we encounter a strange phenomenon. The play for the drop offers a 78% probability of success but the 22% for the finesse becomes 100% for the hand.

Even were the finesse to lose to the bare queen, we have an alternative entry to the required diamond trick in the shape of The Five of Spades.


by Carl Dickel