Good players differ from average players mostly in this: that the good player tries to play all fifty-two cards, and the average player plays only the twenty-six which he can see. A player may have first-class technique, but if he plays blind, in the sense that in the play he does not try to reconstruct the unseen hands, he cannot be better than fair; while a player who does this, even if he knows little of elimination and nothing of squeeze play, is a player in a thousand.
To count the opponents’ hands requires no special talent. From a defender’s side, for example, the distribution of the suit led is often established at the first trick and almost always when the suit is played a second time; then a round or two of trumps by declarer and nine times out of ten it is possible to say how many trumps he started with. So in most cases the distribution of two suits is known after three or four leads ; and as a rule the picture can be completed a trick or two later. There is nothing very difficult or abstruse about this kind of analysis; but it does require a conscious effort, and very few players consistently make the effort.
It is not so easy for declarer to gauge the distribution of the defending hands; he has much less to go on, especially in respect of inferences from the bidding. In the early stages of most hands declarer has to rely on his knowledge of simple probabilities, and on the theory of symmetry; as the play develops, the picture of the enemy distribution becomes more clear. There is nothing very remarkable about the hand which follows; but it will serve as a starting point for discussion.
East-West were vulnerable and North dealt. The bidding was:
The A was led, followed by another Spade which declarer trumped. The problem was to place the missing Queens correctly. Declarer decided that as the opponents had bid to Four Spades vulnerable, the trumps were more likely to be 3 – 1 than 2 – 2. So when East followed to a second trump, South successfully finessed the Knave.
This hurdle over, it remained only to find the Q. As West had a singleton Heart, it was likely that he had the long Clubs. To complete his count of the hand South played Diamonds before tackling the Clubs. After three rounds of Diamonds it was established that East held six cards in the red suits as East had made the overcall of one Spade, it was likely that he had six Spades, so declarer finessed Clubs against West with every confidence.
Only the two Aces were lost, so South landed his contract of Five Hearts. Most players would have done as much, but although the play was not difficult, it does raise some important points. First of all, the finesse in trumps before much was known about the East and Eest hands: there was an inference to be drawn from the bidding that the trumps were, more likely to be 3 – 1 than 2 – 2, but suppose there had been no opposition bidding: then would it have been right to finesse trumps or to play for the drop ?
The answer depends on two things: simple probabilities and the theory’ of symmetry.
A COUNT TO AVOID A FINESSE
Although in general it is more difficult for declarer to count the hands than it is for a defender, declarer has this advantage, that he can plan the play so as to obtain a complete picture of the hand. He does this in the following hand.
South plays in Four Hearts after West has made an overcall of One Spade. West leads the K and continues with three rounds of the suit in order to kill dummy’s 9. South plays Hearts and West wins the second round and exits with a Heart. Declarer has now the problem of avoiding a loser in Clubs. There is a chance that the Diamonds will break, and also the chance of a Club finesse. Before testing the Diamonds it is correct technique for South to play off the last trump discarding a Club from dummy. Three rounds of Diamonds follow, but East is found to have the suit guarded. Then K is led and another Club; East plays the 10, but as he is known to have a Diamond for his last card the finesse is refused and the doubleton Queen is brought down-not by looking at West’s hand but by counting East’s.
TESTING THE LIE
A hand like the last one is a perfect test of the difference between the player who goes ahead without thinking of what the other players hold, and the good player who explores every means to discover how the cards lie. The next hand is a slightly more advanced example of the same principle.
South plays in Five Diamonds after West has made an overcall of One Heart. West leads K on which East plays the 2. West then switches to Diamonds and declarer takes two rounds, finishing in dummy. There is a reason for this. South can see that he may lose a trick in Spades as well as in Clubs. He wants to get a count on the Spade suit, and an important preliminary is to find out how the Clubs lie, if necessary by playing four rounds. When he leads Clubs South wants the trick to be won by West, for it would interfere with his plans if he had to trump a lead of Hearts from East.
So to the fourth trick a small Club is led from dummy and the Knave is won by West’s King. West returns a Club, won in dummy. Declarer ruffs a Club, draws the last trump and leads a low Spade, finessing the 10. Then he leads the fourth Club from dummy and discovers for certain that ‘Vest started with four cards in this suit. West is known to have had two Diamonds and in all probability, since he bid them, five Hearts. So it is clear that West’s K is now single; accordingly South plays a small Spade to the Ace and not one of his honours. Had West turned up with only three Clubs declarer would have placed him with three Spades and 5 – 3 – 3 – 2 distribution, for remember that East played the Two of Hearts on the first trick, from which it was reasonable to infer that East had three Hearts and not a doubleton.