Visualizing the Ending

After the Vanderbilt comes the Masters. Golf and bridge have much in common. Pro golfers are taught when addressing the ball to imagine it hitting the green and rolling up to the cup. Even a fleeting memory of ball striking water, rock, wood, or spectator invites disaster. The same method applies to playing a bridge hand. One must form a plan and envision success, not fear failure. No golfer, even Phil Michelson, plans to hit the ball into the trees so as to get a lucky bounce on the green, so why should bridge players close their eyes, swing wildly, and hope for the best? What’s the hurry?

Krythoff Martens in his book, Calf, notes that most defenders play automatically according to a fixed set of rules rather than think independently and take the action appropriate to the circumstances at hand.  Sometimes a defender can avoid a bad result by foreseeing the end position at an early stage, sometimes at trick 2. This is the hard part for those who tend to see only the cards before them. They have no plan.

It is easier for a declarer to anticipate the end game.  Generally he has greater control of the sequence of plays and may benefit from early disclosures from the bidding and opening lead. The declarer’s point-of-view is well represented by the deals discussed by Chien-Hwa Wang in his book Practical Bridge Endings (1997), a collection of hands that occurred at the table in which success was achieved through either a squeeze or a throw-in. In forming a plan a player must envision the location of the significant cards. One may say that he ‘reads the cards’ or that he ‘places the cards’. The difference is just a matter of degree. Reading the cards implies there is strong evidence that indicates what is most likely. Placing the cards means one assumes the cards are in the positions that allow for success, regardless of how improbable that may be. As Terrence Reese put it, it is a not only a question of where the cards lie, but also where I want them to be. It is ascetically pleasing if what you want is also what is most probable given what is known. This makes it most likely your plan will succeed.

If the defenders are silent throughout the auction, it is normal to assume the cards are distributed evenly between them. With nothing much to go on, declarer should assume tentatively that the card distribution are the single most likely distribution given what is known at the time. It is better than playing blindly and hoping for later inspiration. Here is an example from Wang’s book.

The ♣Q is led, overtaken by the ♣A and the ♣3 is returned to declarer’s ♣K. It appears the defenders’ clubs are split 5-2. What is the most likely distribution of their suits? Declarer notes the division of sides for the defenders is 7=5=7=7. He plays off 3 rounds of hearts and finds West was dealt a doubleton. The single most likely split is West: 3=2=3=5, and East: 4=3=4=2. Place East with 4 spades and 4 diamonds and West with 3 of each. Furthermore, it is most likely that the king and queen in each suit are split between the two defenders. No guarantees, but it provides the basis for a plan.

Declarer can concentrate his attention on West. With 5 clubs held, when declarer runs off 5 hearts, West is likely to come down to 3 cards in spades and diamonds, and these should be, according to our preliminary assessment, Hx and H, one way or the other. So declarer watches West’s discards on the run of the hearts, and if he sees 2 cards from either diamonds or spades, he plays that suit towards dummy expecting to see the king or queen pop up. He can then safely establish his ninth winner in that suit.

The assumption of a particular distribution simplifies the problem. As it happens the most likely distribution of the cards is what occurred in practice on this occasion. Very often this is the case when authors write up successful endplays. It is not luck but good management if one succeeds when the cards are in the most likely mode.

A final note on this deal: in practice West did not bare an honour, rather he discarded a club to remain 2-2 in spades and diamonds. The club discard was a strong indication of which way the wind was blowing. As Wang points out, the easiest counter is to finesse safely in spades losing to East who has no clubs left.

Here is another deal from Professor Wang in which it appears that West has given away too much information in his bidding and play. West opened 1♦ and South played in 4♠ on the ♦K lead. West took his 2 top diamonds and exited safely with a third which was ruffed by South. Once again the defenders hold 7 cards in 3 suits.

One sees that West has done most of the work for declarer, even to the point of setting up the ♦9 as a threat card against the ♦T. He played like a calf. There were 9 tricks available off the top so just one more was needed. As West would have opened 1NT with 14 HCP, declarer could place him with either the ♣Q or the ♥Q, but not both. Declarer placed the ♣Q in the West, rather than the ♥Q, presumably because the ♣Q would result in one less loser in an obviously substandard opening bid. He eliminated West’s side suits by running off 5 spades, cashed his top hearts, ruffed the ♦9 and endplayed West with a club. Once the ♣KQ were placed with West, the play became more-or-less automatic.

Early Recognition
In this example the opening leader made it easy for declarer to find the winning play. Generally, declarers will get less help from the defenders, so should be aware of the possibilities of an endplay at an early stage. The Law of Total Tricks predicts 15 tricks with an 8-6-6-6 division of sides. To overcome this barrier, declarers have to make up some tricks in their 6-card fits, and thrown-in play is a way of achieving a promotion without relying directly on a finesse. In order to succeed in a throw-in one must hold a suit which the defender has to break and give declarer the advantage of scoring a trick not available without help. In his article on throw-in plays in the Official Encyclopedia of Bridge, the late Monroe Ingberman listed several suit combinations that provide this advantage. One combination we have seen above: ATx opposite Jxx, where an extra trick is assured. Upon seeing this combination shared with the dummy declarer should be prepared to take advantage of its existence.

We note that most the combinations listed by Ingberman involve 3-3 splits, making 7 cards held in the defenders’ hands of particular interest. Seven of the 10 combinations listed contain a jack, a lowly honour that can be promoted with help from the defence. Qxx opposite Jxx is often encountered when playing 1NT contracts, and most declarers recognize the advantage of not breaking the suit. Potentially Kxx opposite Jxx is just as useful, although there is the temptation of leading towards the king hoping the ace is onside. In addition declarers should be alert to the extra chance obtained with Axx opposite J9x. Recognition is the key to throw-ins.

Replay the Deal
On the above deal, suppose West, prompted by his weakness in the majors, had decided to pass in first seat, giving up on playing in 1NT and South again reached 4♠. West stays consistently passive by leading the ♠3, usually a rotten choice. The opening lead gives rise to suspicion, otherwise the information provided is scant. The most likely distribution of the 7-card side suits has West holding two 4-card suits to East’s one. It is also most likely that the two missing courtly honours in each suit are split between the defenders, just as in the previous example. The situation is not hopeful, but it is not hopeless, either.

Declarer can see the useful combination in clubs, so that suit can become the target for a throw-in play which can function even if the club honours are split, however, the communications between the defenders must be severed or they can escape the trap. With this in mind declarer plays 2 more rounds of trumps, keeping 3 hearts as dummy decoys. It is to be expected that East will keep parity with the dummy by discarding from the minors. West may find 3 discards, one from each side suit. The paring down of the minors is a hopeful sign, while the ♥5 from West provides the clue that West has come under pressure in the minors. Declarer plays off ♥KA to strip West of hearts and runs the ♦9 to West who is endplayed into breaking the club suit. The effect is similar to that achieved when West was active, but the timing is different and the solution much less obvious. Other possibilities exist, and reading the discards is of paramount importance.

On this construction it appears that it would be better to play a passive game leaving declarer to find his way in the dark. That was the old way of playing in Teams where great reliance was placed on balancing. Also, it is possible that if West passes NS will not reach game and a calf-like declarer will be content with his 9 easy tricks off the top. Not bridge at its most exciting. Most modern experts opt for the impatient approach. Partial scores are important and the evidence shows that there is more to gain by aggression rather than by passivity. So, don’t start underbidding, but, as declarer, be resolved to make use of what the opponents have told you. As Sherlock Holmes might say, ‘Watson, I never guess. The most miraculous solution may be no more than a reasonable deduction based on the known facts.’